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Foreword

The International System of Units, universally abbreviated SI (from the

French Le Système

International d’Unités

), is the modern metric system of measurement. Long the dominant system used

in science, the SI is rapidly becoming the dominant measurement system used in international
commerce. In recognition of this fact and the increasing global nature of the marketplace, the
Omnibus Trade and Competitiveness Act of 1988, which changed the name of the National Bureau of
Standards (NBS) to the National Institute of Standards and Technology (NIST) and gave to NIST the
added task of helping U.S. industry increase its competitiveness, designates “the metric system of
measurement as the preferred system of weights and measures for United States trade and commerce.”

The definitive international reference on the SI is a booklet published by the International Bureau of
Weights and Measures (BIPM,

Bureau International des Poids et Mesures

) and often referred to as

the BIPM SI Brochure. Entitled

Le Système International d' Unités (SI)

, the booklet is in French

followed by a text in English. This 2008 edition of NIST Special Publication (SP) 330 is the United
States version of the English text of the eighth edition of the Brochure (the most current) published in
2006. The 2008 edition of NIST SP 330 replaces its immediate predecessor, the 2001 edition, which
was based on the seventh edition of the BIPM SI Brochure published in 1998, but including

Supplement 2000: addenda and corrigenda to the 7th edition (1998)

, published by the BIPM in June

2000.

Like its 2001 predecessor, the 2008 edition of NIST SP 330 conforms with the English text in the
BIPM SI Brochure but contains a few minor differences to reflect the most recent interpretation of the
SI for the United States by the Secretary of Commerce, as published in the

Federal Register

of July

28, 1998, 63 FR 40334-40340. (The Metric Conversion Act of 1975 gives the Secretary of Commerce
the responsibility of interpreting or modifying the SI for use in the United States. A slightly updated
version of the 1998 interpretation is expected to be published in the

Federal Register

in 2008.) These

differences include the following: (i) The spelling of English words is in accordance with the

United

States Government Printing Office Style Manual

, which follows

Webster's Third New International

Dictionary

rather than the

Oxford Dictionary

. Thus the spellings “meter,” “liter,” and “deka” are used

rather than “metre,” “litre,” and “deca” as in the original BIPM English text; (ii) the name of the unit
with symbol t and defined according to 1 t = 10

kg is called “metric ton” rather than "tonne"; (iii) the

four units curie, roentgen, rad, and rem are given in Table 10, p. 38; (iv) a number of "Editors’ notes"
are added in order to indicate such differences where significant (except spelling differences) and to
clarify the text; and (v) a few very minor editorial changes are made in order to “Americanize” some
phrases.

Because of the importance of the SI to science, technology, and commerce, and because (i) NIST
coordinates the Federal Government policy on the conversion to the SI by Federal agencies and on the
use of the SI by U.S. industry, (ii) NIST provides official U.S. representation in the various
international bodies established by the Meter Convention (see p. 1), and (iii) the Secretary of
Commerce has delegated his authority to interpret or modify the SI for use in the United States to the

The BIPM
and the Meter Convention

The International Bureau of Weights and Measures (BIPM) was set up by the Meter
Convention (

Convention du Mètre

) signed in Paris on 20 May 1875 by seventeen

States during the final session of the diplomatic Conference of the Meter. This
Convention was amended in 1921.

The BIPM has its headquarters near Paris, in the grounds (43 520 m

) of the

Pavillon de Breteuil (Parc de Saint-Cloud) placed at its disposal by the French
Government; its upkeep is financed jointly by the Member States of the Meter
Convention.

The task of the BIPM is to ensure worldwide unification of measurements; its
function is thus to:

•

establish fundamental standards and scales for the measurement of the principal
physical quantities and maintain the international prototypes;

•

carry out comparisons of national and international standards;

•

ensure the coordination of corresponding measurement techniques;

•

carry out and coordinate measurements of the fundamental physical constants
relevant to these activities.

The BIPM operates under the exclusive supervision of the International Committee
for Weights and Measures (CIPM) which itself comes under the authority of the
General Conference on Weights and Measures (CGPM) and reports to it on the work
accomplished by the BIPM.

Delegates from all Member States of the Meter Convention attend the General
Conference which, at present, meets every four years. The function of these
meetings is to:

•

discuss and initiate the arrangements required to ensure the propagation and
improvement of the International System of Units (SI), which is the modern
form of the metric system;

•

confirm the results of new fundamental metrological determinations and various
scientific resolutions of international scope;

•

take all major decisions concerning the finance, organization and development
of the BIPM.

The CIPM has eighteen members each from a different State: at present, it meets
every year. The officers of this committee present an annual report on the
administrative and financial position of the BIPM to the Governments of the
Member States of the Meter Convention. The principal task of the CIPM is to ensure

As of 31 December 2005,
fifty-one States were
members of this
Convention: Argentina,
Australia, Austria, Belgium,
Brazil, Bulgaria, Cameroon,
Canada, Chile, China,
Czech Republic, Denmark,
Dominican Republic,
Egypt, Finland, France,
Germany, Greece, Hungary,
India, Indonesia, Iran
(Islamic Rep. of), Ireland,
Israel, Italy, Japan, Korea
(Dem. People's Rep. of),
Korea (Rep. of), Malaysia,
Mexico, The Netherlands,
New Zealand, Norway,
Pakistan, Poland, Portugal,
Romania, Russian
Federation, Serbia and
Montenegro, Singapore,
Slovakia, South Africa,
Spain, Sweden,
Switzerland, Thailand,
Turkey, United Kingdom,
United States, Uruguay, and
Venezuela.

Twenty States and
Economies were Associates
of the General Conference:
Belarus, CARICOM,
Chinese Taipei, Costa Rica,
Croatia, Cuba, Ecuador,
Estonia, Hong Kong
(China), Jamaica,
Kazakhstan, Kenya, Latvia,
Lithuania, Malta, Panama,
Philippines, Slovenia,
Ukraine, and Viet Nam.

worldwide uniformity in units of measurement. It does this by direct action or by
submitting proposals to the CGPM.

The activities of the BIPM, which in the beginning were limited to measurements of
length and mass, and to metrological studies in relation to these quantities, have
been extended to standards of measurement of electricity (1927), photometry and
radiometry (1937), ionizing radiation (1960), time scales (1988) and to chemistry
(2000). To this end the original laboratories, built from 1876

to 1878, were enlarged

in 1929; new buildings were constructed in 1963 to 1964 for the ionizing radiation
laboratories, in 1984 for the laser work and in 1988 for a library and offices. In 2001
a new building for the workshop, offices and meeting rooms was opened.

Some forty-five physicists and technicians work in the BIPM laboratories. They
mainly conduct metrological research, international comparisons of realizations of
units and calibrations of standards. An annual report, the

Director’s Report on the

Activity and Management of the International Bureau of Weights and Measures

gives details of the work in progress.

Following the extension of the work entrusted to the BIPM in 1927, the CIPM has
set up bodies, known as Consultative Committees, whose function is to provide it
with information on matters that it refers to them for study and advice. These
Consultative Committees, which may form temporary or permanent working groups
to study special topics, are responsible for coordinating the international work
carried out in their respective fields and for proposing recommendations to the
CIPM concerning units.

The Consultative Committees have common regulations (

BIPM Proc.-Verb. Com.

Int. Poids et Mesures

, 1963,

, 97). They meet at irregular intervals. The president

of each Consultative Committee is designated by the CIPM and is normally a
member of the CIPM. The members of the Consultative Committees are metrology
laboratories and specialized institutes, agreed by the CIPM, which send delegates of
their choice. In addition, there are individual members appointed by the CIPM, and
a representative of the BIPM (Criteria for membership of Consultative Committees,

BIPM Proc.-Verb. Com. Int. Poids et Mesures

, 1996,

, 124). At present, there are

ten such committees:

1. The Consultative Committee for Electricity and Magnetism (CCEM), new

name given in 1997 to the Consultative Committee for Electricity (CCE) set up
in 1927;

2. The Consultative Committee for Photometry and Radiometry (CCPR), new

name given in 1971 to the Consultative Committee for Photometry (CCP) set
up in 1933 (between 1930 and 1933 the CCE dealt with matters concerning
photometry);

3. The Consultative Committee for Thermometry (CCT), set up in 1937;

4. The Consultative Committee for Length (CCL), new name given in 1997 to the

Consultative Committee for the Definition of the Meter (CCDM), set up in
1952;

5. The Consultative Committee for Time and Frequency (CCTF), new name given

in 1997 to the Consultative Committee for the Definition of the Second (CCDS)
set up in 1956;

6. The Consultative Committee for Ionizing Radiation (CCRI), new name given in

1997 to the Consultative Committee for Standards of Ionizing Radiation
(CCEMRI) set up in 1958 (in 1969 this committee established four sections:
Section I (x and

rays, electrons), Section II (Measurement of radionuclides),

Section III (Neutron measurements), Section IV (

-energy standards); in 1975

this last section was dissolved and Section II was made responsible for its field
of activity;

7. The Consultative Committee for Units (CCU), set up in 1964 (this committee

replaced the Commission for the System of Units set up by the CIPM in 1954);

8. The Consultative Committee for Mass and Related Quantities (CCM), set up in

1980;

9. The Consultative Committee for Amount of Substance: Metrology in chemistry

(CCQM), set up in 1993;

10. The Consultative Committee for Acoustics, Ultrasound and Vibration

(CCAUV), set up un 1999.

The proceedings of the General Conference and the CIPM are published by the
BIPM in the following series:

•

Report of the meeting of the General Conference on Weights and Measures

;

•

Report of the meeting of the International Committee for Weights and Measures

The CIPM decided in 2003 that the reports of meetings of the Consultative
Committees should no longer be printed, but would be placed on the BIPM website,
in their original language.

The BIPM also publishes monographs on special metrological subjects and, under
the title The International System of Units (SI), a brochure, periodically updated, in
which are collected all the decisions and recommendations concerning units.

The collection of the

Travaux et Mémoires du Bureau International des Poids et

Mesures

(22 volumes published between 1881 and 1966) and the

Recueil de

Travaux du Bureau International des Poids et Mesures

(11 volumes published

between 1966 and 1988) ceased by a decision of the CIPM.

The scientific work of the BIPM is published in the open scientific literature and an
annual list of publications appears in the

Director’s Report on the Activity and

Management of the International Bureau of Weights and Measures

Since 1965

Metrologia

, an international journal published under the auspices of the

CIPM, has printed articles dealing with scientific metrology, improvements in
methods of measurement, work on standards and units, as well as reports concerning
the activities, decisions and recommendations of the various bodies created under
the Meter Convention.

Preface
to the 8th edition

We have pleasure in introducing the 8th edition of this publication, commonly called
the SI Brochure, which defines and presents the

Système International d’Unités

, the

SI (known in English as the International System of Units). This Brochure is
published as a hard copy, and is also available in electronic form at
http://www.bipm.org/en/si/si_brochure/.
Since 1970, the

Bureau International des Poids et Mesures

, the BIPM (known in

English as the International Bureau of Weights and Measures), has published seven
previous editions of this document. Its main purpose is to define and promote the SI,
which has been used around the world as the preferred language of science and
technology since its adoption in 1948 through a Resolution of the 9th

Conférence

Générale des Poids et Mesures

, the CGPM (known in English as the General

Conference on Weights and Measures).

†

The SI is, of course, a living system which evolves, and which reflects current best
measurement practice. This 8th edition therefore contains a number of changes since
the previous edition. As before, it lists the definitions of all the base units, and all the
Resolutions and Recommendations of the CGPM and the

Comité International des

Poids et Mesures

, the CIPM (known in English as the International Committee for

Weights and Measures), relating to the International System of Units. Formal
reference to CGPM and CIPM decisions are to be found in the successive volumes
of the

Comptes Rendus

of the CGPM (CR) and the

Procès-Verbaux

of the CIPM

(PV); many of these are also listed in

Metrologia

. To simplify practical use of the

system, the text provides explanations of these decisions, and the first chapter
provides a general introduction to establishing a system of units and to the SI in
particular. The definitions and the practical realizations of all the units are also
considered in the context of general relativity. A brief discussion of units associated
with biological quantities has been introduced for the first time.
Appendix 1 reproduces, in chronological order, all the decisions (Resolutions,
Recommendations, Declarations) promulgated since 1889 by the CGPM and the
CIPM on units of measurement and the International System of Units.
Appendix

2 exists only in the electronic version, which is available at

http://www.bipm.org/en/si/si_brochure/appendix2/. It outlines the practical
realization of some important units, consistent with the definitions given in the
principal text, which metrological laboratories can make to realize physical units and
to calibrate material standards and measuring instruments of the highest quality. This

†

Editors’ note: The 9th CGPM in 1948 initiated the study that led to the formal establishment of

the SI by the 11th CGPM in 1960.

•

Preface

appendix will be updated regularly to reflect improvements in the experimental
techniques for realizing the units.
Appendix 3 presents units used to measure actinic effects in biological materials.
The

Comité Consultatif des Unités

of the CIPM, the CCU (known in English as the

Consultative Committee for Units), was responsible for drafting this document, and
both the CCU and the CIPM approved the final text. This 8th edition is a revision of
the 7th edition (1998); it takes into consideration decisions made by the CGPM and
the CIPM since the 7th edition was published.
For more than thirty-five years this document has been used as a work of reference
in many countries, organizations, and scientific unions. To make its contents
accessible to a greater number of readers, the CIPM decided, in 1985, to include an
English version of the text in the 5th edition; this double presentation is continued in
all later editions. For the first English version the BIPM endeavoured to produce a
faithful translation of the French original by close collaboration with the National
Physical Laboratory (Teddington, United Kingdom) and the National Institute of
Standards and Technology (Gaithersburg, United States), at that time the National
Bureau of Standards. For the present edition the French and English versions were
prepared by the CCU in close collaboration with the BIPM.
The 22nd CGPM decided, in 2003, following a decision of the CIPM in 1997, that
“the symbol for the decimal marker shall be either the point on the line or the comma
on the line”. Following this decision, and following custom in the two languages, in
this edition the point on the line is used as a decimal marker in the English text, and
a comma on the line is used in the French text. This has no implication for the
translation of the decimal marker into other languages. A point to note is that small
spelling variations occur in the language of the English speaking countries (for
instance, “metre” and “meter”, “litre” and “liter”)

†

. In this respect, the English text

presented here follows the International Standard ISO 31,

Quantities and Units

Readers should note that the official record is always that of the French text. This
must be used when an authoritative reference is required or when there is doubt
about the interpretation of the text.

March

2006

E. Göbel

I. M. Mills

A. J. Wallard

President, CIPM

President, CCU

Director,

BIPM

†

Editors’ note: See the Foreword regarding the spelling of English words in this United States

version of the BIPM SI Brochure.

The terms

quantity

and

unit

are defined in the

International Vocabulary of
Basic and General Terms in
Metrology

, the VIM.

The quantity speed,

may

be expressed in terms of the
quantities distance,

, and

time,

, by the equation

= d

In most systems of
quantities and units,
distance

and time

are

regarded as base quantities,
for which the meter, m, and
the second, s, may be
chosen as base units. Speed

is then taken as a derived

quantity, with the derived
unit meter per second, m/s.

For example, in
electrochemistry, the
electric mobility of an ion,

, is defined as the ratio of

its velocity

to the electric

field strength,

The derived unit of electric
mobility is then given as
(m/s)/(V/m) = m

−

in units which may be easily
related to the chosen base
units (V is the symbol for
the SI derived unit volt).

1 Introduction

1.1

Quantities and units

The value of a quantity is generally expressed as the product of a number and a unit.
The unit is simply a particular example of the quantity concerned which is used as a
reference, and the number is the ratio of the value of the quantity to the unit. For a
particular quantity, many different units may be used. For example, the speed

of a

particle may be expressed in the form

= 25 m/s = 90 km/h, where meter per

second and kilometer per hour are alternative units for expressing the same value of
the quantity speed. However, because of the importance of a set of well defined and
easily accessible units universally agreed for the multitude of measurements that
support today’s complex society, units should be chosen so that they are readily
available to all, are constant throughout time and space, and are easy to realize with
high accuracy.
In order to establish a system of units, such as the International System of Units, the
SI, it is necessary first to establish a system of quantities, including a set of
equations defining the relations between those quantities. This is necessary because
the equations between the quantities determine the equations relating the units, as
described below. It is also convenient to choose definitions for a small number of
units that we call

base units

, and then to define units for all other quantities as

products of powers of the base units that we call

derived units

. In a similar way the

corresponding quantities are described as

base quantities

and

derived quantities

, and

the equations giving the derived quantities in terms of the base quantities are used to
determine the expression for the derived units in terms of the base units, as
discussed further in Section 1.4 below. Thus in a logical development of this subject,
the choice of quantities and the equations relating the quantities comes first, and the
choice of units comes second.
From a scientific point of view, the division of quantities into base quantities and
derived quantities is a matter of convention, and is not essential to the physics of the
subject. However for the corresponding units, it is important that the definition of
each base unit is made with particular care, to satisfy the requirements outlined in
the first paragraph above, since they provide the foundation for the entire system of
units. The definitions of the derived units in terms of the base units then follow from
the equations defining the derived quantities in terms of the base quantities. Thus
the establishment of a system of units, which is the subject of this brochure, is
intimately connected with the algebraic equations relating the corresponding
quantities.
The number of derived quantities of interest in science and technology can, of
course, be extended without limit. As new fields of science develop, new quantities

•

Introduction

are devised by researchers to represent the interests of the field, and with these new
quantities come new equations relating them to those quantities that were previously
familiar, and hence ultimately to the base quantities. In this way the derived units to
be used with the new quantities may always be defined as products of powers of the
previously chosen base units.

1.2

The International System of Units (SI) and the corresponding
system of quantities

This Brochure is concerned with presenting the information necessary to define and
use the International System of Units, universally known as the SI (from the French

Système International d’Unités

). The SI was established by and is defined by the

General Conference on Weights and Measures, the CGPM, as described in the
Historical note in Section 1.8 below*.
The system of quantities, including the equations relating the quantities, to be used
with the SI, is in fact just the quantities and equations of physics that are familiar to
all scientists, technologists, and engineers. They are listed in many textbooks and in
many references, but any such list can only be a selection of the possible quantities
and equations, which is without limit. Many of the quantities, their recommended
names and symbols, and the equations relating them, are listed in the International
Standards ISO 31 and IEC 60027 produced by Technical Committee 12 of the
International Organization for Standardization, ISO/TC 12, and by Technical
Committee 25 of the International Electrotechnical Commission, IEC/TC 25. The
ISO 31 and IEC 60027 Standards are at present being revised by the two
standardization organizations in collaboration. The revised harmonized standard will
be known as ISO/IEC 80000,

Quantities and Units

, in which it is proposed that the

quantities and equations used with the SI will be known as the International System
of Quantities.
The base quantities used in the SI are length, mass, time, electric current,
thermodynamic temperature, amount of substance, and luminous intensity. The base
quantities are by convention assumed to be independent. The corresponding base
units of the SI were chosen by the CGPM to be the meter, the kilogram, the second,
the ampere, the kelvin, the mole, and the candela. The definitions of these base units
are presented in Section 2.1.1 in the following chapter. The derived units of the SI
are then formed as products of powers of the base units, according to the algebraic
relations that define the corresponding derived quantities in terms of the base
quantities, see Section 1.4 below.
On rare occasions a choice may arise between different forms of the relations
between the quantities. An important example occurs in defining the
electromagnetic quantities. In this case the rationalized four-quantity
electromagnetic equations used with the SI are based on length, mass, time, and
electric current. In these equations, the electric constant

(the permittivity of

vacuum) and the magnetic constant

(the permeability of vacuum) have

* Acronyms used in this Brochure are listed with their meaning on p. 87.

The name

Système

International d’Unités

and the abbreviation SI,
were established by the
11th CGPM in 1960.

Examples of the equations
relating quantities used in
the SI are the Newtonian
inertial equation relating
force,

, to mass,

, and

acceleration,

for a particle:

, and

the equation giving the
kinetic energy,

, of a

particle moving with
velocity,

/2.

Introduction

•

dimensions and values such that

= 1/

, where

is the speed of light in

vacuum. The Coulomb law of electrostatic force between two particles with charges

and

separated by a distance

is written

1 2

q q

and the corresponding equation for the magnetic force between two thin wire
elements carrying electric currents,

d and d

, is written

( d

)

where d

is the double differential of the force

. These equations, on which the SI

is based, are different from those used in the CGS-ESU (electrostatic), CGS-EMU
(electromagnetic), and CGS-Gaussian systems, where

and

are dimensionless

quantities, chosen to be equal to one, and where the rationalizing factors of 4

are

omitted.

1.3

Dimensions of quantities

By convention physical quantities are organized in a system of dimensions. Each of
the seven base quantities used in the SI is regarded as having its own dimension,
which is symbolically represented by a single sans serif roman capital letter. The
symbols used for the base quantities, and the symbols used to denote their
dimension, are given as follows.

Base quantities and dimensions used in the SI

Base quantity

Symbol for quantity

Symbol for dimension

length

, etc.

mass

time, duration

electric current

thermodynamic temperature

amount of substance

luminous intensity

All other quantities are derived quantities, which may be written in terms of the base
quantities by the equations of physics. The dimensions of the derived quantities are
written as products of powers of the dimensions of the base quantities using the
equations that relate the derived quantities to the base quantities. In general the
dimension of any quantity

is written in the form of a dimensional product,

dim

where the exponents

, and

, which are generally small integers which

can be positive, negative or zero, are called the dimensional exponents. The
dimension of a derived quantity provides the same information about the relation of

** Symbols in bold print are used to denote vectors.

Quantity symbols are
always written in an italic
font, and symbols for
dimensions in sans-serif
roman capitals.
For some quantities a
variety of alternative
symbols may be used, as
indicated for length and
electric current.
Note that symbols for
quantities are only

recommendations

, in

contrast to symbols for
units that appear elsewhere
in this brochure whose style
and form is

mandatory

(see

Chapter 5).
Dimensional symbols and
exponents are manipulated
using the ordinary rules of
algebra. For example, the
dimension of area is written
as

; the dimension of

velocity as

−

; the

dimension of force as

LMT

−

; and the dimension

of energy is written as

−

Editors’ Note

: A non-SI

system of units is the CGS
(centimeter-gram-second)
System. There are several
versions of CGS units used
for electricity and
magnetism: electrostatic
units (ESU),
electromagnetic units
(EMU), and Gaussian
units. See discussion
associated with Table 9.

•

Introduction

that quantity to the base quantities as is provided by the SI unit of the derived
quantity as a product of powers of the SI base units.
There are some derived quantities

for which the defining equation is such that all

of the dimensional exponents in the expression for the dimension of

are zero. This

is true, in particular, for any quantity that is defined as the ratio of two quantities of
the same kind. Such quantities are described as being

dimensionless

, or alternatively

as being

of dimension one

. The coherent derived unit for such dimensionless

quantities is always the number one, 1, since it is the ratio of two identical units for
two quantities of the same kind.
There are also some quantities that cannot be described in terms of the seven base
quantities of the SI at all, but have the nature of a count. Examples are number of
molecules, degeneracy in quantum mechanics (the number of independent states of
the same energy), and the partition function in statistical thermodynamics (the
number of thermally accessible states). Such counting quantities are also usually
regarded as dimensionless quantities, or quantities of dimension one, with the unit
one, 1.

1.4

Coherent units, derived units with special names,
and the SI prefixes

Derived units are defined as products of powers of the base units. When the product
of powers includes no numerical factor other than one, the derived units are called

coherent derived

units. The base and coherent derived units of the SI form a

coherent set, designated the set of

coherent SI units

. The word coherent is used here

in the following sense: when coherent units are used, equations between the
numerical values of quantities take exactly the same form as the equations between
the quantities themselves. Thus if only units from a coherent set are used,
conversion factors between units are never required.
The expression for the coherent unit of a derived quantity may be obtained from the
dimensional product of that quantity by replacing the symbol for each dimension by
the symbol of the corresponding base unit.
Some of the coherent derived units in the SI are given special names, to simplify
their expression (see 2.2.2, p. 25). It is important to emphasize that each physical
quantity has only one coherent SI unit, even if this unit can be expressed in different
forms by using some of the special names and symbols. The inverse, however, is not
true: in some cases the same SI unit can be used to express the values of several
different quantities (see p. 26).
The CGPM has, in addition, adopted a series of prefixes for use in forming the
decimal multiples and submultiples of the coherent SI units (see 3.1, p. 29, where
the prefix names and symbols are listed). These are convenient for expressing the
values of quantities that are much larger than or much smaller than the coherent unit.
Following the CIPM Recommendation 1 (1969) (see p. 64) these are given the name

SI prefixes

. (These prefixes are also sometimes used with other non-SI units, as

described in Chapter 4 below.) However when prefixes are used with coherent SI
units, the resulting units are no longer coherent, because a prefix on a coherent unit,

As an example of a special
name, the particular
combination of base units
m

kg s

−

for energy is given

the special name joule,
symbol J, where by
definition J = m

kg s

−

For example, refractive
index is defined as the ratio
of the speed of light in
vacuum to that in the
medium, and is thus a ratio
of two quantities of the
same kind. It is therefore a
dimensionless quantity.
Other examples of
dimensionless quantities are
plane angle, mass fraction,
relative permittivity,
relative permeability, and
finesse of a Fabry-Perot
cavity.

The length of a chemical
bond is more conveniently
given in nanometers, nm,
than in meters, m; and the
distance from London to
Paris is more conveniently
given in kilometers, km,
than in meters, m.

Introduction

•

either base or derived, effectively introduces a numerical factor in the expression for
the unit in terms of the base units.

†

As an exception, the name of the kilogram, which is the base unit of mass, includes
the prefix kilo, for historical reasons. It is nonetheless taken to be a base unit of the
SI. The multiples and submultiples of the kilogram are formed by attaching prefix
names to the unit name “gram”, and prefix symbols to the unit symbol “g” (see 3.2,
p. 30). Thus 10

−

kg is written as a milligram, mg, not as a microkilogram,

kg.

The complete set of SI units, including both the coherent set and the multiples and
submultiples of these units formed by combining them with the SI prefixes, are
designated as the

complete set of

SI units

, or simply the

SI units

, or the

units of the

. Note, however, that the decimal multiples and submultiples of the SI units do not

form a coherent set.

1.5

SI units in the framework of general relativity

The definitions of the base units of the SI were adopted in a context that takes no
account of relativistic effects. When such account is taken, it is clear that the
definitions apply only in a small spatial domain sharing the motion of the standards
that realize them. These units are known as

proper units

; they are realized from local

experiments in which the relativistic effects that need to be taken into account are
those of special relativity. The constants of physics are local quantities with their
values expressed in proper units.
Physical realizations of the definition of a unit are usually compared locally. For
frequency standards, however, it is possible to make such comparisons at a distance
by means of electromagnetic signals. To interpret the results the theory of general
relativity is required since it predicts, among other things, a relative frequency shift
between standards of about 1 part in 10

per meter of altitude difference at the

surface of the Earth. Effects of this magnitude cannot be neglected when comparing
the best frequency standards.

1.6

Units for quantities that describe biological effects

Units for quantities that describe biological effects are often difficult to relate to
units of the SI because they typically involve weighting factors that may not be
precisely known or defined, and which may be both energy and frequency
dependent. These units, which are not SI units, are described briefly in this section.
Optical radiation may cause chemical changes in living or non-living materials: this
property is called

actinism

and radiation capable of causing such changes is referred

to as

actinic radiation

. In some cases, the results of measurements of photochemical

and photobiological quantities of this kind can be expressed in terms of SI units.
This is discussed briefly in Appendix 3.
Sound causes small pressure fluctuations in the air, superimposed on the normal
atmospheric pressure, that are sensed by the human ear. The sensitivity of the ear
depends on the frequency of the sound, but is not a simple function of either the

†

Editors’ note: This last sentence has been slightly modified for clarity.

The question of proper units
is addressed in Resolution
A4 adopted by the
XXIst General Assembly
of the International
Astronomical Union (IAU)
in 1991 and by the report of
the CCDS Working Group
on the Application of
General Relativity to
Metrology (

Metrologia

1997,

, 261-290).

The meter per second,
symbol m/s, is the coherent
SI unit of speed. The
kilometer per second, km/s,
the centimeter per second,
cm/s, and the millimeter per
second, mm/s, are also SI
units, but they are not
coherent SI units.

•

Introduction

pressure changes or the frequency. Therefore frequency-weighted quantities are
used in acoustics to approximate the way in which sound is perceived. Such
frequency-weighted quantities are employed, for example, in work to protect against
hearing damage. The effects of ultrasonic acoustic waves pose similar concerns in
medical diagnosis and therapy.
Ionizing radiation deposits energy in irradiated matter. The ratio of deposited energy
to mass is termed

absorbed dose

. High doses of ionizing radiation kill cells, and this

is used in radiation therapy. Appropriate biological weighting functions are used to
compare therapeutic effects of different radiation treatments. Low sub-lethal doses
can cause damage to living organisms, for instance by inducing cancer. Appropriate
risk-weighted functions are used at low doses as the basis of radiation protection
regulations.
There is a class of units for quantifying the biological activity of certain substances
used in medical diagnosis and therapy that cannot yet be defined in terms of the
units of the SI. This is because the mechanism of the specific biological effect that
gives these substances their medical use is not yet sufficiently well understood for it
to be quantifiable in terms of physico-chemical parameters. In view of their
importance for human health and safety, the World Health Organization (WHO) has
taken responsibility for defining WHO International Units (IU) for the biological
activity of such substances.

1.7

Legislation on units

By legislation, individual countries have established rules concerning the use of
units on a national basis, either for general use or for specific areas such as
commerce, health, public safety, and education. In almost all countries this
legislation is based on the International System of Units.
The

Organisation Internationale de Métrologie Légale

(OIML), founded in 1955, is

charged with the international harmonization of this legislation.

1.8 Historical

note

The previous paragraphs of this chapter give a brief overview of the way in which a
system of units, and the International System of Units in particular, is established.
This note gives a brief account of the historical development of the International
System.
The 9th CGPM (1948, Resolution 6; CR, 64) instructed the CIPM:

•

to study the establishment of a complete set of rules for units of measurement;

•

to find out for this purpose, by official enquiry, the opinion prevailing in
scientific, technical and educational circles in all countries;

•

to make recommendations on the establishment of a

practical system of units of

measurement

suitable for adoption by all signatories to the Meter Convention.

Introduction

•

The same CGPM also laid down, in Resolution 7 (CR, 70), general principles for the
writing of unit symbols, and listed some coherent derived units which were assigned
special names.
The 10th CGPM (1954, Resolution 6; CR, 80) and the 14th CGPM (1971,
Resolution 3, CR, 78, and

Metrologia

, 1972,

, 36) adopted as base units of this

practical system of units the units of the following seven quantities: length, mass,
time, electric current, thermodynamic temperature, amount of substance, and
luminous intensity.
The 11th CGPM (1960, Resolution 12; CR, 87) adopted the name

Système

International d’Unités

, with the international abbreviation SI, for this practical

system of units and laid down rules for prefixes, derived units, and the former
supplementary units, and other matters; it thus established a comprehensive
specification for units of measurement. Subsequent meetings of the CGPM and
CIPM have added to, and modified as necessary, the original structure of the SI to
take account of advances in science and of the needs of users.
The historical sequence that led to these important CGPM decisions may be
summarized as follows.

•

The creation of the decimal metric system at the time of the French Revolution
and the subsequent deposition of two platinum standards representing the meter
and the kilogram, on 22 June 1799, in the

Archives de la République

in Paris

can be seen as the first step in the development of the present International
System of Units.

•

In 1832, Gauss strongly promoted the application of this metric system, together
with the second defined in astronomy, as a coherent system of units for the
physical sciences. Gauss was the first to make

absolute

measurements of the

Earth’s magnetic field in terms of a decimal system based on the

three

mechanical units

millimeter, gram, and second for, respectively, the quantities

length, mass, and time. In later years, Gauss and Weber extended these
measurements to include other electrical phenomena.

•

These applications in the field of electricity and magnetism were further
developed in the 1860s under the active leadership of Maxwell and Thomson
through the British Association for the Advancement of Science (BAAS). They
formulated the requirement for a

coherent system of units

with

base

units and

derived

units. In 1874 the BAAS introduced the

CGS system

, a three-

dimensional coherent unit system based on the three mechanical units
centimeter, gram, and second, using prefixes ranging from micro to mega to
express decimal submultiples and multiples. The subsequent development of
physics as an experimental science was largely based on this system.

•

The sizes of the coherent CGS units in the fields of electricity and magnetism
proved to be inconvenient so, in the 1880s, the BAAS and the International
Electrical Congress, predecessor of the International Electrotechnical
Commission (IEC), approved a mutually coherent set of

practical units

. Among

them were the ohm for electrical resistance, the volt for electromotive force, and
the ampere for electric current.

2 SI

units

2.1

SI base units

Formal definitions of all SI base units are adopted by the CGPM. The first two
definitions were adopted in 1889, and the most recent in 1983. These definitions are
modified from time to time as science advances.

2.1.1 Definitions

Current definitions of the base units, as taken from the

Comptes Rendus

(CR) of the

corresponding CGPM, are shown below indented and in a heavy sans-serif font.
Related decisions which clarify these definitions but are not formally part of them,
as taken from the

Comptes Rendus

of the corresponding CGPM or the

Procès-

Verbaux

(PV) of the CIPM, are also shown indented but in a sans-serif font of

normal weight. The linking text provides historical notes and explanations, but is
not part of the definitions themselves.
It is important to distinguish between the definition of a unit and its realization. The
definition of each base unit of the SI is carefully drawn up so that it is unique and
provides a sound theoretical basis upon which the most accurate and reproducible
measurements can be made. The realization of the definition of a unit is the
procedure by which the definition may be used to establish the value and associated
uncertainty of a quantity of the same kind as the unit. A description of how the
definitions of some important units are realized in practice is given on the BIPM
website,

http://www.bipm.org/en/si/si_brochure/appendix2

A coherent SI derived unit is defined uniquely only in terms of SI base units. For
example, the coherent SI derived unit of resistance, the ohm, symbol

Ω

, is uniquely

defined by the relation

Ω

= m

kg s

–3

–2

which follows from the definition of the

quantity electrical resistance. However any method consistent with the laws of
physics could be used to realize any SI unit. For example, the unit ohm can be
realized

with high accuracy using the quantum Hall effect and the value of the von

Klitzing constant recommended by the CIPM (see pp. 73 and 76, respectively,
Appendix 1).
Finally, it should be recognized that although the seven base quantities – length,
mass, time, electric current, thermodynamic temperature, amount of substance, and
luminous intensity – are by convention regarded as independent, their respective
base units – the meter, kilogram, second, ampere, kelvin, mole, and candela – are in
a number of instances interdependent. Thus the definition of the meter incorporates
the second; the definition of the ampere incorporates the meter, kilogram, and

•

SI Units

second; the definition of the mole incorporates the kilogram; and the definition of
the candela incorporates the meter, kilogram, and second.

2.1.1.1 Unit of length (meter)

The 1889 definition of the meter, based on the international prototype of platinum-
iridium, was replaced by the 11th CGPM (1960) using a definition based on the
wavelength of krypton 86 radiation. This change was adopted in order to improve
the accuracy with which the definition of the meter could be realized, the realization
being achieved using an interferometer with a travelling microscope to measure the
optical path difference as the fringes were counted. In turn, this was replaced in
1983 by the 17th CGPM (1983, Resolution 1, CR, 97, and

Metrologia

, 1984,

, 25)

that specified the current definition, as follows:

The meter is the length of the path travelled by light in vacuum during a
time interval of 1/299 792 458 of a second.

It follows that the speed of light in vacuum is exactly 299 792 458 meters per
second,

= 299 792 458 m/s.

The original international prototype of the meter, which was sanctioned by the
1st CGPM in 1889 (CR, 34-38), is still kept at the BIPM under conditions specified
in 1889.

2.1.1.2 Unit of mass (kilogram)

The international prototype of the kilogram, an artifact made of platinum-iridium, is
kept at the BIPM under the conditions specified by the 1st CGPM in 1889 (CR, 34-
38) when it sanctioned the prototype and declared:

This prototype shall henceforth be considered to be the unit of mass.

The 3rd CGPM (1901, CR, 70), in a declaration intended to end the ambiguity in
popular usage concerning the use of the word “weight,” confirmed that:

The kilogram is the unit of mass; it is equal to the mass of the
international prototype of the kilogram.

The complete declaration appears on p. 52.
It follows that the mass of the international prototype of the kilogram is always
1 kilogram exactly,

(

) = 1 kg. However, due to the inevitable accumulation of

contaminants on surfaces, the international prototype is subject to reversible surface
contamination that approaches 1

g per year in mass. For this reason, the CIPM

declared that, pending further research, the reference mass of the international
prototype is that immediately after cleaning and washing by a specified method (PV,
1989,

, 104-105 and PV, 1990,

, 95-97). The reference mass thus defined is

used to calibrate national standards of platinum-iridium alloy (

Metrologia

, 1994,

317-336).

The symbol

(or

sometimes simply

) is the

conventional symbol for the
speed of light in vacuum

The symbol

(

) is used to

denote the mass of the
international prototype of
the kilogram,

SI Units

• 19

2.1.1.3 Unit of time (second)

The unit of time, the second, was at one time considered to be the fraction 1/86 400
of the mean solar day. The exact definition of “mean solar day” was left to the
astronomers. However measurements showed that irregularities in the rotation of the
Earth made this an unsatisfactory definition. In order to define the unit of time more
precisely, the 11th CGPM (1960, Resolution 9; CR, 86) adopted a definition given
by the International Astronomical Union based on the tropical year 1900.
Experimental work, however, had already shown that an atomic standard of time,
based on a transition between two energy levels of an atom or a molecule, could be
realized and reproduced much more accurately. Considering that a very precise
definition of the unit of time is indispensable for science and technology, the 13th
CGPM (1967/68, Resolution 1; CR, 103 and

Metrologia

, 1968,

, 43) replaced the

definition of the second by the following:

The second is the duration of 9 192 631 770 periods of the radiation
corresponding to the transition between the two hyperfine levels of the
ground state of the cesium 133 atom.

It follows that the hyperfine splitting in the ground state of the cesium 133 atom is
exactly 9 192 631 770 hertz,

(

133

Cs)

hfs

= 9 192 631 770 Hz.

At its 1997 meeting the CIPM affirmed that:

This definition refers to a cesium atom at rest at a temperature of 0 K.

This note was intended to make it clear that the definition of the SI second is based
on a cesium atom unperturbed by black body radiation, that is, in an environment
whose thermodynamic temperature is 0 K. The frequencies of all primary frequency
standards should therefore be corrected for the shift due to ambient radiation, as
stated at the meeting of the Consultative Committee for Time and Frequency in
1999.

2.1.1.4 Unit of electric current (ampere)

Electric units, called “international units,” for current and resistance, were
introduced by the International Electrical Congress held in Chicago in 1893, and
definitions of the “international ampere” and “international ohm” were confirmed by
the International Conference in London in 1908.
Although it was already obvious on the occasion of the 8th CGPM (1933) that there
was a unanimous desire to replace those “international units” by so-called “absolute
units,” the official decision to abolish them was only taken by the 9th CGPM
(1948), which adopted the ampere for the unit of electric current, following a
definition proposed by the CIPM (1946, Resolution 2; PV,

, 129-137):

The ampere is that constant current which, if maintained in two straight
parallel conductors of infinite length, of negligible circular cross-
section, and placed 1 meter apart in vacuum, would produce between
these conductors a force equal to 2 × 10

−

newton per meter of length.

The symbol

(

133

Cs)

hfs

used to denote the
frequency of the hyperfine
transition in the ground
state of the cesium atom.

•

SI Units

It follows that the magnetic constant

, also known as the permeability of vacuum,

is exactly 4

−

henries per meter,

= 4

−

H/m.

The expression “MKS unit of force” which occurs in the original text of 1946 has
been replaced here by “newton,” a name adopted for this unit by the 9th CGPM
(1948, Resolution 7; CR, 70).

2.1.1.5 Unit of thermodynamic temperature (kelvin)

The definition of the unit of thermodynamic temperature was given in substance by
the 10th CGPM (1954, Resolution 3; CR, 79) which selected the triple point of
water as the fundamental fixed point and assigned to it the temperature 273.16 K, so
defining the unit. The 13th CGPM (1967/68, Resolution 3; CR, 104 and

Metrologia

1968,

, 43) adopted the name kelvin, symbol K, instead of “degree Kelvin,” symbol

K, and defined the unit of thermodynamic temperature as follows (1967/68,

Resolution 4; CR, 104 and

Metrologia

, 1968,

, 43):

The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16
of the thermodynamic temperature of the triple point of water.

It follows that the thermodynamic temperature of the triple point of water is exactly
273.16 kelvins,

TPW

= 273.16 K.

At its 2005 meeting the CIPM affirmed that:

This definition refers to water having the isotopic composition defined exactly
by the following amount of substance ratios: 0.000

155

76 mole of

H per mole

H, 0.000

379

9 mole of

O per mole of

O, and 0.002 005 2 mole of

per mole of

Because of the manner in which temperature scales used to be defined, it remains
common practice to express a thermodynamic temperature, symbol

, in terms of its

difference from the reference temperature

= 273.15 K, the ice point. This

difference is called the Celsius temperature, symbol

, which is defined by the

quantity equation:

−

The unit of Celsius temperature is the degree Celsius, symbol

C, which is by

definition equal in magnitude to the kelvin. A difference or interval of temperature
may be expressed in kelvins or in degrees Celsius (13th CGPM, 1967/68, Reso-
lution 3, mentioned above), the numerical value of the temperature difference being
the same. However, the numerical value of a Celsius temperature expressed in
degrees Celsius is related to the numerical value of the thermodynamic temperature
expressed in kelvins by the relation

C =

−

273.15.

The kelvin and the degree Celsius are also units of the International Temperature
Scale of 1990 (ITS-90) adopted by the CIPM in 1989 in its Recommendation 5 (CI-
1989; PV,

, 115 and

Metrologia

, 1990,

, 13).

The symbol

TPW

is used to

denote the thermodynamic
temperature of the triple
point of water.

SI Units

• 21

2.1.1.6 Unit of amount of substance (mole)

Following the discovery of the fundamental laws of chemistry, units called, for
example, “gram-atom” and “gram-molecule,” were used to specify amounts of
chemical elements or compounds. These units had a direct connection with “atomic
weights” and “molecular weights,” which are in fact relative masses. “Atomic
weights” were originally referred to the atomic weight of oxygen, by general
agreement taken as 16. But whereas physicists separated the isotopes in a mass
spectrometer and attributed the value 16 to one of the isotopes of oxygen, chemists
attributed the same value to the (slightly variable) mixture of isotopes 16, 17 and 18,
which was for them the naturally occurring element oxygen. Finally an agreement
between the International Union of Pure and Applied Physics (IUPAP) and the
International Union of Pure and Applied Chemistry (IUPAC) brought this duality to
an end in 1959/60. Physicists and chemists have ever since agreed to assign the
value 12, exactly, to the so-called atomic weight of the isotope of carbon with mass
number 12 (carbon 12,

C), correctly called the relative atomic mass

(

C). The

unified scale thus obtained gives the relative atomic and molecular masses, also
known as the atomic and molecular weights, respectively.
The quantity used by chemists to specify the amount of chemical elements or
compounds is now called “amount of substance.” Amount of substance is defined to
be proportional to the number of specified elementary entities in a sample, the
proportionality constant being a universal constant which is the same for all
samples. The unit of amount of substance is called the

mole

, symbol mol, and the

mole is defined by specifying the mass of carbon 12 that constitutes one mole of
carbon 12 atoms. By international agreement this was fixed at 0.012 kg, i.e. 12 g.
Following proposals by the IUPAP, the IUPAC, and the ISO, the CIPM gave a
definition of the mole in 1967 and confirmed it in 1969. This was adopted by the
14th CGPM (1971, Resolution 3; CR, 78 and

Metrologia

, 1972,

, 36):

1. The mole is the amount of substance of a system which contains as many

elementary entities as there are atoms in 0.012 kilogram of carbon 12; its
symbol is “mol.”

2. When the mole is used, the elementary entities must be specified and may

be atoms, molecules, ions, electrons, other particles, or specified groups of
such particles.

It follows that the molar mass of carbon 12 is exactly 12 grams per mole,

(

C) = 12 g/mol.

In 1980 the CIPM approved the report of the CCU (1980) which specified that

In this definition, it is understood that unbound atoms of carbon 12, at rest and
in their ground state, are referred to.

The definition of the mole also determines the value of the universal constant that
relates the number of entities to amount of substance for any sample. This constant
is called the Avogadro constant, symbol

. If

(

) denotes the number of

entities

in a specified sample, and if

(

) denotes the amount of substance of

entities

in the same sample, the relation is

(

) =

(

The recommended symbol
for relative atomic mass
(atomic weight) is

(

where the atomic entity

should be specified, and for
relative molecular mass of a
molecule (molecular
weight) it is

(

), where

the molecular entity

should be specified.

The molar mass of an atom
or molecule

is denoted

(

) or

, and is the mass

per mole of

When the definition of the
mole is quoted, it is
conventional also to include
this remark.

•

SI Units

Note that since

(

) is dimensionless, and

(

) has the SI unit mole, the Avogadro

constant has the coherent SI unit reciprocal mole.
In the name “amount of substance,” the words “of substance” could for simplicity be
replaced by words to specify the substance concerned in any particular application,
so that one may, for example, talk of “amount of hydrogen chloride, HCl,” or
“amount of benzene, C

.” It is important to always give a precise specification of

the entity involved (as emphasized in the second sentence of the definition of the
mole); this should preferably be done by giving the empirical chemical formula of
the material involved. Although the word “amount” has a more general dictionary
definition, this abbreviation of the full name “amount of substance” may be used for
brevity. This also applies to derived quantities such as “amount of substance
concentration,” which may simply be called “amount concentration.” However, in
the field of clinical chemistry the name “amount of substance concentration” is
generally abbreviated to “substance concentration.”

2.1.1.7 Unit of luminous intensity (candela)

The units of luminous intensity based on flame or incandescent filament standards in
use in various countries before 1948 were replaced initially by the “new candle”
based on the luminance of a Planck radiator (a black body) at the temperature of
freezing platinum. This modification had been prepared by the International
Commission on Illumination (CIE) and by the CIPM before 1937, and the decision
was promulgated by the CIPM in 1946. It was then ratified in 1948 by the 9th
CGPM which adopted a new international name for this unit, the

candela

, symbol

cd; in 1967 the 13th CGPM (Resolution 5, CR, 104 and

Metrologia

, 1968,

, 43-44)

gave an amended version of this definition.
In 1979, because of the difficulties in realizing a Planck radiator at high
temperatures, and the new possibilities offered by radiometry, i.e. the measurement
of optical radiation power, the 16th CGPM (1979, Resolution 3; CR, 100 and

Metrologia

, 1980,

, 56) adopted a new definition of the candela:

The candela is the luminous intensity, in a given direction, of a source
that emits monochromatic radiation of frequency 540 × 10

hertz and

that has a radiant intensity in that direction of 1/683 watt per steradian.

It follows that the spectral luminous efficacy for monochromatic radiation of
frequency of 540

hertz is exactly 683 lumens per watt,

(

555

) = 683 lm/W

= 683 cd sr/W (the wavelength

of radiation of this frequency is about 555 nm).

2.1.2

Symbols for the seven base units

The base units of the International System are listed in Table 1, which relates the
base quantity to the unit name and unit symbol for each of the seven base units
(10th CGPM (1954, Resolution 6; CR, 80); 11th CGPM (1960, Resolution 12; CR,
87); 13th CGPM (1967/68, Resolution 3; CR, 104 and

Metrologia

, 1968,

, 43);

14th CGPM (1971, Resolution 3; CR, 78 and

Metrologia

, 1972,

, 36)).

SI Units

• 23

Table 1. SI base units

Base quantity

SI base unit

________________________________ ____________________________

Name

Symbol Name

Symbol

length

l, x, r

etc.

meter

mass

kilogram

time, duration

second

electric current

I, i

ampere

thermodynamic temperature

kelvin

amount of substance

mole

mol

luminous intensity

candela

2.2

SI derived units

Derived units are products of powers of base units. Coherent derived units are
products of powers of base units that include no numerical factor other than 1. The
base and coherent derived units of the SI form a coherent set, designated the set of

coherent SI units

(see 1.4, p. 12).

2.2.1

Derived units expressed in terms of base units

The number of quantities in science is without limit, and it is not possible to provide
a complete list of derived quantities and derived units. However, Table 2 lists some
examples of derived quantities, and the corresponding coherent derived units
expressed directly in terms of base units.

The symbols for quantities
are generally single letters
of the Latin or Greek
alphabets, printed in an
italic font, and are

recommendations

The symbols for units are

mandatory

, see chapter 5.

•

SI Units

Table 2. Examples of coherent derived units in the SI expressed in terms of base
units

Derived quantity

SI coherent derived unit

__________________________________ ______________________________________

Name

Symbol

Name

Symbol

area

square

meter

volume

cubic

meter

speed, velocity

meter per second

m/s

acceleration

meter per second squared

m/s

wavenumber

~ reciprocal

meter

−

density, mass density

kilogram per cubic meter

kg/m

surface density

kilogram per square meter

kg/m

specific volume

cubic meter per kilogram

/kg

current density

ampere per square meter

A/m

magnetic field strength

ampere per meter

A/m

amount concentration

(

)

mole per cubic meter

mol/m

concentration
mass concentration

kilogram per cubic meter

kg/m

luminance

candela per square meter

cd/m

refractive index

(

)

one

relative permeability

(

)

one

(

) In the field of clinical chemistry this quantity is also called “substance concentration.”

(

) These are dimensionless quantities, or quantities of dimension one, and the symbol “1” for the

unit (the number “one”) is generally omitted in specifying the values of dimensionless
quantities.

2.2.2

Units with special names and symbols; units that incorporate special
names and symbols

For convenience, certain coherent derived units have been given special names and
symbols. There are 22 such units, as listed in Table 3. These special names and
symbols may themselves be used in combination with the names and symbols for
base units and for other derived units to express the units of other derived quantities.
Some examples are given in Table 4. The special names and symbols are simply a
compact form for the expression of combinations of base units that are used
frequently, but in many cases they also serve to remind the reader of the quantity
involved. The SI prefixes may be used with any of the special names and symbols,
but when this is done the resulting unit will no longer be coherent.
Among these names and symbols the last four entries in Table 3 are of particular
note since they were adopted by the 15th CGPM (1975, Resolutions 8 and 9; CR,
105 and

Metrologia

, 1975,

, 180), the 16th CGPM (1979, Resolution 5; CR, 100

and

Metrologia

, 1980,

, 56) and the 21st CGPM (1999, Resolution 12; CR, 334-

335 and

Metrologia

, 2000,

, 95) specifically with a view to safeguarding human

health.

SI Units

• 25

In both Tables 3 and 4 the final column shows how the SI units concerned may be
expressed in terms of SI base units. In this column factors such as m

, kg

, etc.,

which are all equal to 1, are not shown explicitly.

Table 3. Coherent derived units in the SI with special names and symbols

SI coherent derived unit

(

)

——————————————————————————

Expressed

in terms of

Derived quantity

Name

Symbol

other SI units SI base units

plane angle

radian

(

)

rad

(

)

m/m

solid angle

steradian

(

)

(

)

(

)

frequency hertz

(

)

−

force

newton

m kg s

−

pressure, stress

pascal

N/m

−

kg s

−

energy, work,

joule

N m

kg s

−

amount of heat

power, radiant flux

watt

J/s

kg s

−

electric charge,

coulomb

s A

amount of electricity

electric potential difference

(

)

, volt

W/A

kg s

−

electromotive

force

capacitance farad

C/V

−

electric resistance

ohm

Ω

V/A m

kg s

−

electric conductance

siemens

A/V

−

magnetic flux

weber

V s

kg s

−

magnetic flux density

tesla

Wb/m

−

inductance henry

Wb/A

kg s

−

Celsius temperature

degree Celsius

(

)

luminous flux

lumen

cd sr

(

)

illuminance lux

lm/m

−

activity referred to

becquerel

(

)

−

radionuclide

(

)

absorbed dose,

gray

J/kg

−

specific energy (imparted),

kerma
dose equivalent,

sievert

(

)

J/kg

−

ambient dose equivalent,

directional dose equivalent,

personal dose equivalent

catalytic activity

katal

kat

−

mol

(

) The SI prefixes may be used with any of the special names and symbols, but when this is

done the resulting unit will no longer be coherent.

(

) The radian and steradian are special names for the number one that may be used to convey

information about the quantity concerned. In practice the symbols rad and sr are used where
appropriate, but the symbol for the derived unit one is generally omitted in specifying the
values of dimensionless quantities.

(

) In photometry the name steradian and the symbol sr are usually retained in expressions for

units.

(

) The hertz is used only for periodic phenomena, and the becquerel is used only for stochastic

processes in activity referred to a radionuclide.

•

SI Units

(

)

Editors’ note:

Electric potential difference is also called “voltage” in the United States and in

many other countries, as well as “electric tension” or simply “tension” in some countries.

(

) The degree Celsius is the special name for the kelvin used to express Celsius temperatures.

The degree Celsius and the kelvin are equal in size, so that the numerical value of a
temperature difference or temperature interval is the same when expressed in either degrees
Celsius or in kelvins.

(

)

Activity referred to a radionuclide is sometimes incorrectly called radioactivity.

(h)

See CIPM Recommendation 2 (CI-2002), p. 78, on the use of the sievert (PV, 2002, 70, 205).

Table 4. Examples of SI coherent derived units whose names and symbols include
SI coherent derived units with special names and symbols

SI coherent derived unit

————————————————————————————

Expressed in terms of

Derived quantity

Name

Symbol

SI base units

dynamic viscosity

pascal second

Pa s

−

kg s

−

moment of force

newton meter

N m

kg s

−

surface tension

newton per meter

N/m

kg s

−

angular velocity

radian per second

rad/s

m m

−

= s

−

angular acceleration

radian per second squared

rad/s

m m

−

= s

−

heat flux density,

watt per square meter

W/m

kg s

−

irradiance
heat capacity, entropy

joule per kelvin

J/K

kg s

−

specific heat capacity,

joule per kilogram kelvin

J/(kg K)

−

specific

entropy

specific energy

joule per kilogram

J/kg

−

thermal conductivity

watt per meter kelvin

W/(m K) m kg s

−

energy density

joule per cubic meter

J/m

−1

kg s

−

electric field strength

volt per meter

V/m

m kg s

−

electric charge density

coulomb per cubic meter

C/m

−

s A

surface charge density

coulomb per square meter

C/m

−

s A

electric flux density,

coulomb per square meter

C/m

−

s A

electric

displacement

permittivity

farad per meter

F/m

−

permeability

henry per meter

H/m

m kg s

−

molar energy

joule per mole

J/mol

kg s

−

mol

−

molar entropy,

joule per mole kelvin

J/(mol K) m

kg s

−

mol

−

molar heat capacity

exposure (x and

rays)

coulomb per kilogram

C/kg

−

s A

absorbed dose rate

gray per second

Gy/s

−

radiant intensity

watt per steradian

W/sr

−

kg s

−

= m

kg s

−

radiance

watt per square meter steradian W/(m

sr) m

−

kg s

−

= kg s

−

catalytic activity

katal per cubic meter

kat/m

−

mol

concentration

The values of several different quantities may be expressed using the same name
and symbol for the SI unit. Thus for the quantity heat capacity as well as the
quantity entropy, the SI unit is the joule per kelvin. Similarly for the base quantity
electric current as well as the derived quantity magnetomotive force, the SI unit is
the ampere. It is therefore important not to use the unit alone to specify the quantity.

SI Units

• 27

This applies not only to scientific and technical texts, but also, for example, to
measuring instruments (i.e. an instrument read-out should indicate both the unit and
the quantity measured).
A derived unit can often be expressed in different ways by combining base units
with derived units having special names. Joule, for example, may formally be
written newton meter, or kilogram meter squared per second squared. This,
however, is an algebraic freedom to be governed by common sense physical
considerations; in a given situation some forms may be more helpful than others.
In practice, with certain quantities, preference is given to the use of certain special
unit names, or combinations of unit names, to facilitate the distinction between
different quantities having the same dimension. When using this freedom, one may
recall the process by which the quantity is defined. For example, the quantity torque
may be thought of as the cross product of force and distance, suggesting the unit
newton meter, or it may be thought of as energy per angle, suggesting the unit joule
per radian. The SI unit of frequency is given as the hertz, implying the unit cycles
per second; the SI unit of angular velocity is given as the radian per second; and the
SI unit of activity is designated the becquerel, implying the unit counts per second.
Although it would be formally correct to write all three of these units as the
reciprocal second, the use of the different names emphasises the different nature of
the quantities concerned. Using the unit radian per second for angular velocity, and
hertz for frequency, also emphasizes that the numerical value of the angular velocity
in radian per second is 2

times the numerical value of the corresponding frequency

in hertz.
In the field of ionizing radiation, the SI unit of activity is designated the becquerel
rather than the reciprocal second, and the SI units of absorbed dose and dose
equivalent are designated the gray and the sievert, respectively, rather than the joule
per kilogram. The special names becquerel, gray, and sievert were specifically
introduced because of the dangers to human health that might arise from mistakes
involving the units reciprocal second and joule per kilogram, in case the latter units
were incorrectly taken to identify the different quantities involved.

2.2.3

Units for dimensionless quantities, also called quantities of dimension
one

Certain quantities are defined as the ratio of two quantities of the same kind, and are
thus dimensionless, or have a dimension that may be expressed by the number one.
The coherent SI unit of all such dimensionless quantities, or quantities of dimension
one, is the number one, since the unit must be the ratio of two identical SI units. The
values of all such quantities are simply expressed as numbers, and the unit one is not
explicitly shown. Examples of such quantities are refractive index, relative
permeability, and friction factor. There are also some quantities that are defined as a
more complex product of simpler quantities in such a way that the product is
dimensionless. Examples include the “characteristic numbers” like the Reynolds
number

, where

is mass density,

is dynamic viscosity,

is speed, and

The CIPM, recognizing the
particular importance of the
health-related units, adopted
a detailed text on the sievert
for the 5th edition of this
Brochure: Recommendation
1 (CI-1984), adopted by the
CIPM (PV, 1984,

, 31

and

Metrologia

, 1985,

90), and Recommenda-
tion 2 (CI-2002), adopted
by the CIPM (PV,

, 205),

see pp. 71 and 78,
respectively.

Decimal multiples and submultiples of SI units

3.1 SI

prefixes

The 11th CGPM (1960, Resolution 12; CR, 87) adopted a series of prefix names and
prefix symbols to form the names and symbols of the decimal multiples and
submultiples of SI units, ranging from 10

to 10

−

. Prefixes for 10

−

and 10

−

were added by the 12th CGPM (1964, Resolution 8; CR, 94), for 10

and 10

the 15th CGPM (1975, Resolution 10; CR, 106 and

Metrologia

, 1975,

, 180-181),

and for 10

, 10

−

and 10

−

by the 19th CGPM (1991, Resolution 4; CR, 185

and

Metrologia

, 1992,

, 3). Table 5 lists all approved prefix names and symbols.

Table 5. SI prefixes

Factor Name Symbol

deka da

−

deci d

hecto h

−

centi c

kilo k

−

milli m

mega M

−

micro

giga G

−

nano n

tera T

−

pico p

peta P

−

femto f

exa E

−

atto a

zetta Z

−

zepto z

yotta Y

−

yocto y

Prefix symbols are printed in roman (upright) type, as are unit symbols, regardless
of the type used in the surrounding text, and are attached to unit symbols without a
space between the prefix symbol and the unit symbol. With the exception of da
(deka), h (hecto), and k (kilo), all multiple prefix symbols are capital (upper case)
letters, and all submultiple prefix symbols are lower case letters. All prefix names
are printed in lower case letters, except at the beginning of a sentence.
The grouping formed by a prefix symbol attached to a unit symbol constitutes a new
inseparable unit symbol (forming a multiple or submultiple of the unit concerned)
that can be raised to a positive or negative power and that can be combined with
other unit symbols to form compound unit symbols.

These SI prefixes refer
strictly to powers of 10.
They should not be used to
indicate powers of 2 (for
example, one kilobit
represents 1000 bits and not
1024 bits). The IEC has
adopted prefixes for binary
powers in the international
standard IEC 60027-2:
2005, third edition,

Letter symbols to be
used in electrical
technology – Part

Telecommunications and
electronics.

The names and

symbols for the prefixes
corresponding to 2

, 2

, and 2

are,

respectively: kibi, Ki; mebi,
Mi; gibi, Gi; tebi, Ti; pebi,
Pi; and exbi, Ei. Thus, for
example, one kibibyte
would be written:
1 KiB = 2

B = 1024 B,

where B denotes a byte.
Although these prefixes are
not part of the SI, they
should be used in the field
of information technology
to avoid the incorrect usage
of the SI prefixes.

Examples of the use of
prefixes:
pm (picometer)
mmol (millimole)
G

Ω

(gigaohm)

THz (terahertz)

•

Decimal multiples and submultiples

Examples

: 2.3

= 2.3 (cm)

= 2.3 (10

–2

= 2.3 × 10

–6

–1

= 1 (cm)

–1

= 1 (10

–2

–1

= 10

–1

= 100 m

−

1 V/cm = (1 V)/(10

–2

m) = 10

V/m = 100 V/m

5000

−

= 5000 (

−

= 5000 (10

−

= 5 × 10

−

Similarly prefix names are also inseparable from the unit names to which they are
attached. Thus, for example, millimeter, micropascal, and meganewton are single
words.
Compound prefix symbols, that is, prefix symbols formed by the juxtaposition of
two or more prefix symbols, are not permitted. This rule also applies to compound
prefix names.
Prefix symbols can neither stand alone nor be attached to the number 1, the symbol
for the unit one. Similarly, prefix names cannot be attached to the name of the unit
one, that is, to the word “one.”
Prefix names and symbols are used with a number of non-SI units (see Chapter 5),
but they are never used with the units of time: minute, min; hour, h; day, d. However
astronomers use milliarcsecond, which they denote by the symbol mas, and
microarcsecond, which they denote by the symbol

as, and they use both as units for

measuring very small angles.

†

3.2 The

kilogram

Among the base units of the International System, the kilogram is the only one
whose name and symbol, for historical reasons, include a prefix. Names and
symbols for decimal multiples and submultiples of the unit of mass are formed by
attaching prefix names to the unit name “gram,” and prefix symbols to the unit
symbol “g” (CIPM 1967, Recommendation 2; PV,

, 29 and

Metrologia

1968,

45).

†

Editors’ note: This last sentence has been slightly modified for clarity.

nm (nanometer),

but not

(millimicrometer)

The number of lead atoms
in the sample is

(Pb) = 5 × 10

but not

(Pb) = 5 M,

where M is intended
to be the prefix mega
standing on its own.

−

kg = 1 mg,

but not

(microkilogram)

•

Units outside the SI

related to fundamental constants, and their values have to be determined
experimentally. Tables 8 and 9 contain units that have exactly defined values in
terms of SI units, and are used in particular circumstances to satisfy the needs of
commercial, legal, or specialized scientific interests. It is likely that these units will
continue to be used for many years. Many of these units are also important for the
interpretation of older scientific texts. Each of the Tables 6, 7, 8 and 9 is discussed
in turn below.
Table 6

includes the traditional units of time and angle. It also contains the hectare,

the liter, and the metric ton (or tonne), which are all in common everyday use
throughout the world, and which differ from the corresponding coherent SI unit by
an integer power of ten. The SI prefixes are used with several of these units, but not
with the units of time.

Table 6. Non-SI units accepted for use with the International System of Units

Quantity

Name of unit

Symbol for unit

Value in SI units

time

minute

min

1 min = 60 s

hour

(

)

1 h = 60 min = 3600 s

day

1 d = 24 h = 86 400 s

plane angle

degree

(

)

= (

/180) rad

minute

′

= (1/60)

= (

/ 10 800) rad

second

(

)

″

= (1/60)

′

= (

/ 648 000) rad

area

hectare

(

)

1 ha = 1 hm

= 10

volume

liter

(

)

1 L = 1 dm

= 10

−

mass

metric

ton

(

)

1 t = 10

(

) The symbol for this unit is included in Resolution 7 of the 9th CGPM (1948; CR, 70).

(

) ISO 31 recommends that the degree be divided decimally rather than using the minute and the

second. For navigation and surveying, however, the minute has the advantage that one minute
of latitude on the surface of the Earth corresponds (approximately) to one nautical mile.

(

) The gon (or grad, where grad is an alternative name for the gon) is an alternative unit of plane

angle to the degree, defined as (

/200) rad. Thus there are 100 gon in a right angle. The

potential value of the gon in navigation is that because the distance from the pole to the
equator of the Earth is approximately 10 000 km, 1 km on the surface of the Earth subtends
an angle of one centigon at the center of the Earth. However the gon is rarely used.

(

) For applications in astronomy, small angles are measured in arcseconds (i.e. seconds of plane

angle), denoted by the symbol as or by the symbol

″

, milliarcseconds, microarcseconds, and

picoarcseconds, denoted by the symbols mas,

as, and pas, respectively, where arcsecond is

an alternative name for second of plane angle.

(

) The unit hectare, and its symbol ha, were adopted by the CIPM in 1879 (PV, 1879, 41). The

hectare is used to express land area.

(

) The liter, and the symbol lower-case l, were adopted by the CIPM in 1879 (PV, 1879, 41).

The alternative symbol, capital L, was adopted by the 16th CGPM (1979, Resolution 6; CR,
101 and

Metrologia,

1980,

, 56-57) in order to avoid the risk of confusion between the

letter l (el) and the numeral 1 (one).

Editors’ note:

Since the preferred unit symbol for the

liter in the United States is L, only L is given in the table; see the

Federal Register

notice of

July 28, 1998, “Metric System of Measurement: Interpretation of the International System of
Units for the United States” (FR 40334-4030).

(

)

Editors’ note:

Metric ton is the name to be used for this unit in the United States; see the

aforementioned

Federal Register

notice. The original English text in the BIPM SI Brochure

uses the CGPM adopted name “tonne” and footnote (

) reads as follows: The tonne, and its

symbol t, were adopted by the CIPM in 1879 (PV, 1879, 41). In English speaking countries
this unit is usually called “metric ton.”

Units outside the SI

•

Table 7 contains units whose values in SI units have to be determined
experimentally, and thus have an associated uncertainty. Except for the astronomical
unit, all other units in Table 7 are related to fundamental physical constants. The
first four units, the non-SI units electronvolt, symbol eV, dalton or unified atomic
mass unit, symbol Da or u, respectively, and the astronomical unit, symbol ua, have
been accepted for use with the SI by the CIPM. The units in Table 7 play important
roles in a number of specialized fields in which the results of measurements or
calculations are most conveniently and usefully expressed in these units. For the
electronvolt and the dalton the values depend on the elementary charge

and the

Avogadro constant

, respectively.

There are many other units of this kind, because there are many fields in which it is
most convenient to express the results of experimental observations or of theoretical
calculations in terms of fundamental constants of nature. The two most important of
such unit systems based on fundamental constants are the natural unit (n.u.) system
used in high energy or particle physics, and the atomic unit (a.u.) system used in
atomic physics and quantum chemistry. In the n.u. system, the base quantities for
mechanics are speed, action, and mass, for which the base units are the speed of
light in vacuum

, the Planck constant

divided by 2

, called the reduced Planck

constant with symbol

, and the mass of the electron

, respectively. In general

these units are not given any special names or symbols but are simply called the n.u.
of speed, symbol

, the n.u. of action, symbol

, and the n.u. of mass, symbol

. In

this system, time is a derived quantity and the n.u. of time is a derived unit equal to
the combination of base units

. Similarly, in the a.u. system, any four of the

five quantities charge, mass, action, length, and energy are taken as base quantities.
The corresponding base units are the elementary charge

, electron mass

, action

, Bohr radius (or bohr)

, and Hartree energy (or hartree)

, respectively. In this

system, time is again a derived quantity and the a.u. of time a derived unit, equal to
the combination of units

. Note that

/(4

∞

), where

is the fine-structure

constant and

∞

is the Rydberg constant; and

/(4

) = 2

∞

where

is the electric constant and has an exact value in the SI.

For information, these ten natural and atomic units and their values in SI units are
also listed in Table 7. Because the quantity systems on which these units are based
differ so fundamentally from that on which the SI is based, they are not generally
used with the SI, and the CIPM has not formally accepted them for use with the
International System. To ensure understanding, the final result of a measurement or
calculation expressed in natural or atomic units should also always be expressed in
the corresponding SI unit. Natural units (n.u.) and atomic units (a.u.) are used only
in their own special fields of particle physics, and atomic physics and quantum
chemistry, respectively. Standard uncertainties in the least significant digits are
shown in parenthesis after each numerical value.

•

Units outside the SI

Table 7. Non-SI units whose values in SI units must be obtained experimentally

†

Quantity Name of unit

Symbol for unit

Value in SI units

(

)

Units accepted for use with the SI

energy electronvolt

(

)

1 eV = 1.602 176 53(14)

−

mass dalton,

(

)

1 Da = 1.660 538 86(28)

−

unified atomic mass unit

1 u = 1 Da

length astronomical

unit

(

)

1 ua = 1.495 978 706 91(6)

Natural units (n.u.)

speed

n.u. of speed

299 792 458 m/s (exact)

(speed of light in vacuum)

action

n.u. of action

1.054 571 68(18)

−

J s

(reduced Planck constant)

mass

n.u. of mass

9.109

3826(16)

−

(electron

mass)

time

n.u. of time

(

)

1.288 088 6677(86)

−

Atomic units (a.u.)

charge

a.u. of charge

1.602 176 53(14)

−

(elementary

charge)

mass

a.u. of mass

9.109

3826(16)

−

(electron

mass)

action

a.u. of action

1.054 571 68(18)

−

J s

(reduced Planck constant)

length

a.u. of length, bohr

0.529 177 2108(18)

−

(Bohr

radius)

energy

a.u. of energy, hartree

4.359 744 17(75)

−

(Hartree

energy)

time

a.u. of time

2.418 884 326 505(16)

−

(

) The values in SI units of all units in this table, except the astronomical unit, are taken from

the 2002 CODATA set of recommended values of the fundamental physical constants, P.J.
Mohr and B.N. Taylor,

Rev

Mod. Phys

., 2005,

, 1-107. The standard uncertainty in the last

two digits is given in parenthesis (see 5.3.5, p. 43).

(

) The electronvolt is the kinetic energy acquired by an electron in passing through a potential

difference of one volt in vacuum. The electronvolt is often combined with the SI prefixes.

(

) The dalton (Da) and the unified atomic mass unit (u) are alternative names (and symbols) for

the same unit, equal to 1/12 times the mass of a free carbon 12 atom, at rest and in its ground
state. The dalton is often combined with SI prefixes, for example to express the masses of
large molecules in kilodaltons, kDa, or megadaltons, MDa, or to express the values of small
mass differences of atoms or molecules in nanodaltons, nDa, or even picodaltons, pDa.

(

) The astronomical unit is approximately equal to the mean Earth-Sun distance. It is the radius

of an unperturbed circular Newtonian orbit about the Sun of a particle having infinitesimal
mass, moving with a mean motion of 0.017 202 098 95 radians per day (known as the
Gaussian constant). The value given for the astronomical unit is quoted from the IERS
Conventions 2003 (D.D. McCarthy and G. Petit eds.,

IERS Technical Note

32, Frankfurt am

Main: Verlag des Bundesamts für Kartographie und Geodäsie, 2004, 12). The value of the
astronomical unit in meters comes from the JPL ephemerides DE403 (Standish E.M., Report
of the IAU WGAS Sub-Group on Numerical Standards,

Highlights of Astronomy

Appenzeller ed., Dordrecht: Kluwer Academic Publishers, 1995, 180-184).

†

Editors’ note: Only the units in Table 6, the first four units in Table 7, and the neper, bel, and

decibel in Table 8 have been formally accepted for use with the SI by the CIPM.

Units outside the SI

•

Tables 8 and 9 contain non-SI units that are used by special interest groups for a
variety of different reasons. Although the use of SI units is to be preferred for
reasons already emphasized, authors who see a particular advantage in using these
non-SI units should have the freedom to use the units that they consider to be best
suited to their purpose. Since, however, SI units are the international meeting
ground in terms of which all other units are defined, those who use units from
Tables 8 and 9 should always give the definition of the units they use in terms of SI
units.
Table 8 also gives the units of logarithmic ratio quantities, the neper, bel, and
decibel. These are dimensionless units that are somewhat different in their nature
from other dimensionless units, and some scientists consider that they should not
even be called units. They are used to convey information on the nature of the
logarithmic ratio quantity concerned. The neper, Np, is used to express the values of
quantities whose numerical values are based on the use of the Napierian (or natural)
logarithm, ln = log

. The bel and the decibel, B and dB, where 1 dB = (1/10) B, are

used to express the values of logarithmic ratio quantities whose numerical values are
based on the decadic logarithm, lg = log

. The way in which these units are

interpreted is described in footnotes (

) and (

) of Table 8. The numerical values of

these units are rarely required. The units neper, bel, and decibel have been accepted
by the CIPM for use with the International System, but are not considered as SI
units.
The SI prefixes are used with two of the units in Table 8, namely, with the bar (e.g.
millibar, mbar), and with the bel, specifically for the decibel, dB. The decibel is
listed explicitly in the table because the bel is rarely used without the prefix.

Table 8. Other non-SI units

Quantity

Name of unit

Symbol for unit

Value in SI units

pressure bar

(

)

bar

1 bar = 0.1 MPa = 100 kPa = 10

millimeter of mercury

(

)

mmHg

≈

133.322 Pa

length ångström

(

)

1 Å = 0.1 nm = 100 pm = 10

−

distance nautical

mile

(

)

1 M = 1852 m

area barn

(

)

1 b = 100 fm

= (10

−

cm)

= 10

−

speed knot

(

)

1 kn = (1852/3600) m/s

logarithmic neper

(

)

[see footnote (

) regarding the

ratio quantities

bel

(

)

numerical value of the neper, the

decibel

(

)

bel, and the decibel]

(

) The bar and its symbol are included in Resolution 7 of the 9th CGPM (1948; CR, 70). Since

1982 one bar has been used as the standard pressure for tabulating all thermodynamic data.
Prior to 1982 the standard pressure used to be the standard atmosphere, equal to 1.013

bar,

or 101

325

Pa.

(

) The millimeter of mercury is a legal unit for the measurement of blood pressure in some

countries.

(

) The ångström is widely used by x-ray crystallographers and structural chemists because all

chemical bonds lie in the range 1 to 3 ångströms. However, it has no official sanction from
the CIPM or the CGPM.

•

Units outside the SI

(

) The nautical mile is a special unit employed for marine and aerial navigation to express

distance. The conventional value given here was adopted by the First International Extra-
ordinary Hydrographic Conference, Monaco 1929, under the name “International nautical
mile.” As yet there is no internationally agreed symbol, but the symbols M, NM, Nm, and
nmi are all used; in the table the symbol M is used. The unit was originally chosen, and
continues to be used, because one nautical mile on the surface of the Earth subtends
approximately one minute of angle at the center of the Earth, which is convenient when
latitude and longitude are measured in degrees and minutes of angle.

(

) The barn is a unit of area employed to express cross sections in nuclear physics.

(

) The knot is defined as one nautical mile per hour. There is no internationally agreed symbol,

but the symbol kn is commonly used.

(

The statement

Np (where

is a number) is interpreted to mean that ln(

) =

. Thus

when

= 1 Np,

= e. The symbol

is used here to denote the amplitude of a sinusoidal

signal, and

is then called the Napierian logarithmic amplitude ratio, or the Napierian

amplitude level difference.

(

) The statement

(

/10)

B (where

is a number) is interpreted to mean that

lg(

)

/10. Thus when

1 B,

10, and when

= 1 dB,

= 10

1/10

. If

denotes a mean square signal or power-like quantity,

is called a power level referred to

(

) In using these units it is important that the nature of the quantity be specified, and that any

reference value used be specified. These units are not SI units, but they have been accepted
by the CIPM for use with the SI.

(

) The numerical values of the neper, bel, and decibel (and hence the relation of the bel and the

decibel to the neper) are rarely required. They depend on the way in which the logarithmic
quantities are defined.

Table 9 differs from Table 8 only in that the units in Table 9 are related to the older
CGS (centimeter-gram-second) system of units, including the CGS electrical units.
In the field of mechanics, the CGS system of units was built upon three quantities
and their corresponding base units: the centimeter, the gram, and the second. The
CGS electrical units were still derived from only these same three base units, using
defining equations different from those used for the SI. Because this can be done in
different ways, it led to the establishment of several different systems, namely the
CGS-ESU (electrostatic), the CGS-EMU (electromagnetic), and the CGS-Gaussian
unit systems. It has always been recognized that the CGS-Gaussian system, in
particular, has advantages in certain areas of physics, particularly in classical and
relativistic electrodynamics (9th CGPM, 1948, Resolution 6). Table 9 gives the
relations between these CGS units and the SI, and lists those CGS units that were
assigned special names. As for the units in Table 8, the SI prefixes are used with
several of these units (e.g.

millidyne, mdyn; milligauss, mG, etc.).

Units outside the SI

•

Table 9. Non-SI units associated with the CGS and the CGS-Gaussian system of
units

Quantity

Name of unit

Symbol for unit

Value in SI units

energy erg

(

)

erg

1 erg = 10

−

force dyne

(

)

dyn

1 dyn = 10

−

dynamic viscosity

poise

(

)

1 P = 1 dyn s cm

−

= 0.1 Pa s

kinematic viscosity

stokes

1 St = 1 cm

−

= 10

−

luminance stilb

(

)

1 sb = 1 cd cm

−

= 10

cd m

−

illuminance

phot

1 ph = 1 cd sr cm

−

= 10

acceleration gal

(

)

Gal

1 Gal = 1 cm s

−

= 10

−

m s

−

magnetic flux

maxwell

(

)

1 Mx = 1 G cm

= 10

−

magnetic flux density

gauss

(

)

1 G = 1 Mx cm

−

= 10

−

magnetic field

œrsted

(

)

(10

) A m

−

(

) This unit and its symbol were included in Resolution 7 of the 9th CGPM (1948; CR, 70).

(

) The gal is a special unit of acceleration employed in geodesy and geophysics to express

acceleration due to gravity.

(

) These units are part of the so-called “electromagnetic” three-dimensional CGS system based

on unrationalized quantity equations, and must be compared with care to the corresponding
unit of the International System which is based on rationalized equations involving four
dimensions and four quantities for electromagnetic theory. The magnetic flux,

, and the

magnetic flux density,

, are defined by similar equations in the CGS system and the SI, so

that the corresponding units can be related as in the table. However, the unrationalized
magnetic field,

(unrationalized) = 4

(rationalized). The equivalence symbol

is used

to indicate that when

(unrationalized) = 1 Oe,

(rationalized) = (10

) A m

−

4.2

Other non-SI units not recommended for use

There are many more non-SI units, which are too numerous to list here, which are
either of historical interest, or are still used but only in specialized fields (for
example, the barrel of oil) or in particular countries (the inch, foot, and yard). The
CIPM can see no case for continuing to use these units in modern scientific and
technical work. However, it is clearly a matter of importance to be able to recall the
relation of these units to the corresponding SI units, and this will continue to be true
for many years. The CIPM has therefore decided to compile a list of the conversion
factors to the SI for such units and to make this available on the BIPM website at
http://www.bipm.org/en/si/si_brochure/chapter4/conversion_factors.html

4.3

The curie, roentgen, rad, and rem

This section and Table 10 below have been added to the United States version of the
BIPM SI Brochure because, although the curie, roentgen rad, and rem are not
accepted by the CIPM for use with the SI, they are widely used in the United States,
especially in regulatory documents dealing with health and safety. The interpretation
of the SI for the United States given in the

Federal Register

notice referenced in

footnote (

) of Table 6, p. 32, does in fact accept their use with the SI. Nevertheless,

that notice strongly discourages the continued use of the curie, roentgen, rad and

Writing unit symbols and names, and expressing the
values of quantities

General principles for the writing of unit symbols and numbers were first given by
the 9th CGPM (1948, Resolution 7). These were subsequently elaborated by ISO,
IEC, and other international bodies. As a consequence, there now exists a general
consensus on how unit symbols and names, including prefix symbols and names, as
well as quantity symbols should be written and used, and how the values of
quantities should be expressed. Compliance with these rules and style conventions,
the most important of which are presented in this chapter, supports the readability of
scientific and technical papers.

5.1 Unit

symbols

Unit symbols are printed in roman (upright) type regardless of the type used in the
surrounding text. They are printed in lower-case letters unless they are derived from
a proper name, in which case the first letter is a capital letter.
An exception, adopted by the 16th CGPM (1979, Resolution 6), is that either capital
L or lower-case l is allowed for the liter, in order to avoid possible confusion
between the numeral 1 (one) and the lower-case letter l (el). [

Editors’ note:

the

symbol L is preferred in the United states; see footnote (

) of Table 6, p. 32.]

A multiple or sub-multiple prefix, if used, is part of the unit and precedes the unit
symbol without a separator. A prefix is never used in isolation, and compound
prefixes are never used.
Unit symbols are mathematical entities and not abbreviations. Therefore, they are
not followed by a period except at the end of a sentence, and one must neither use
the plural nor mix unit symbols and unit names within one expression, since names
are not mathematical entities.
In forming products and quotients of unit symbols the normal rules of algebraic
multiplication or division apply. Multiplication must be indicated by a space or a
half-high (centered) dot (

⋅

), since otherwise some prefixes could be misinterpreted as

a unit symbol. Division is indicated by a horizontal line, by a solidus (oblique
stroke, /) or by negative exponents. When several unit symbols are combined, care
should be taken to avoid ambiguities, for example by using brackets or negative
exponents. A solidus must not be used more than once in a given expression without
brackets to remove ambiguities.
It is not permissible to use abbreviations for unit symbols or unit names, such as sec
(for either s or second), sq. mm (for either mm

or square millimeter), cc (for either

or cubic centimeter), or mps (for either m/s or meter per second). The use of the

m, meter
s, second
Pa, pascal

Ω

, ohm

L, liter

nm,

not

It is 75 cm long,

not

75 cm. long

= 75 cm,

not

75 cms

coulomb per kilogram,

not

coulomb per kg

N m or N

for a newton meter

m/s or

or m s

–1

for meter per second

ms, millisecond
m s, meter times second

m kg/(s

A),

or m kg s

–3

–1

but not

m kg/s

/A,

nor

m kg/s

•

Writing unit symbols and names

correct symbols for SI units, and for units in general, as listed in earlier chapters of
this Brochure, is mandatory. In this way ambiguities and misunderstandings in the
values of quantities are avoided.

5.2 Unit

names

Unit names are normally printed in roman (upright) type, and they are treated like
ordinary nouns. In English, the names of units start with a lower-case letter (even
when the symbol for the unit begins with a capital letter), except at the beginning of
a sentence or in capitalized material such as a title. In keeping with this rule, the
correct spelling of the name of the unit with the symbol °C is “degree Celsius” (the
unit degree begins with a lower-case d and the modifier Celsius begins with an
upper-case C because it is a proper name).
Although the values of quantities are normally expressed using symbols for numbers
and symbols for units, if for some reason the unit name is more appropriate than the
unit symbol, the unit name should be spelled out in full.
When the name of a unit is combined with the name of a multiple or sub-multiple
prefix, no space or hyphen is used between the prefix name and the unit name. The
combination of prefix name plus unit name is a single word. See also Chapter 3,
Section 3.1.
In both English and in French, however, when the name of a derived unit is formed
from the names of individual units by multiplication, then either a space or a hyphen
is used to separate the names of the individual units.
In both English and in French modifiers such as “squared” or “cubed” are used in
the names of units raised to powers, and they are placed after the unit name.
However, in the case of area or volume, as an alternative the modifiers “square” or
“cubic” may be used, and these modifiers are placed before the unit name, but this
applies only in English.

5.3

Rules and style conventions for expressing values of
quantities

5.3.1

Value and numerical value of a quantity, and the use of quantity
calculus

The value of a quantity is expressed as the product of a number and a unit, and the
number multiplying the unit is the numerical value of the quantity expressed in that
unit. The numerical value of a quantity depends on the choice of unit. Thus the
value of a particular quantity is independent of the choice of unit, although the
numerical value will be different for different units.
Symbols for quantities are generally single letters set in an italic font, although they
may be qualified by further information in subscripts or superscripts or in brackets.
Thus

is the recommended symbol for heat capacity,

for molar heat capacity,

for molar heat capacity at constant pressure, and

for molar heat capacity

at constant volume.

milligram,

but not

milli-gram

kilopascal,

but not

kilo-pascal

pascal second, or
pascal-second

meter per second squared,
square centimeter,
cubic millimeter,
ampere per square meter,
kilogram per cubic meter.

unit name symbol

joule

hertz

meter    m
second    s
ampere    A
watt   W

2.6 m/s,
or 2.6 meters per second

The same value of a speed

= d

of a particle

might be given by either
of the expressions

= 25 m/s = 90 km/h,

where 25 is the numerical
value of the speed in the
unit meters per second, and
90 is the numerical value of
the speed in the unit
kilometers per hour.

Writing unit symbols and names

•

Recommended names and symbols for quantities are listed in many standard
references, such as the ISO Standard 31

Quantities and Units

, the IUPAP

SUNAMCO Red Book

Symbols, Units and Nomenclature in Physics

, and the

IUPAC Green Book

Quantities, Units and Symbols in Physical Chemistry

However, symbols for quantities are recommendations (in contrast to symbols for
units, for which the use of the correct form is mandatory). In particular
circumstances authors may wish to use a symbol of their own choice for a quantity,
for example in order to avoid a conflict arising from the use of the same symbol for
two different quantities. In such cases, the meaning of the symbol must be clearly
stated. However, neither the name of a quantity, nor the symbol used to denote it,
should imply any particular choice of unit.
Symbols for units are treated as mathematical entities. In expressing the value of a
quantity as the product of a numerical value and a unit, both the numerical value and
the unit may be treated by the ordinary rules of algebra. This procedure is described
as the use of quantity calculus, or the algebra of quantities. For example, the
equation

= 293 K may equally be written

/K = 293. It is often convenient to write

the quotient of a quantity and a unit in this way for the heading of a column in a
table, so that the entries in the table are all simply numbers. For example, a table of
vapour pressure against temperature, and the natural logarithm of vapour pressure
against reciprocal temperature, may be formatted as shown below.

/MPa ln(

/MPa)

216.55

4.6179

0.5180

−

0.6578

273.15

3.6610

3.4853

1.2486

304.19

3.2874

7.3815

1.9990

The axes of a graph may also be labelled in this way, so that the tick marks are
labelled only with numbers, as in the graph below.

-0.8

0.0

0.8

1.6

2.4

3.2

3.6

4.0

4.4

4.8

1000 K/

(

)

•

Writing unit symbols and names

Algebraically equivalent forms may be used in place of 1000 K/

, such as 10

kK/

, or 10

(

/K)

−

5.3.2 Quantity

symbols and unit symbols

Just as the quantity symbol should not imply any particular choice of unit, the unit
symbol should not be used to provide specific information about the quantity, and
should never be the sole source of information on the quantity. Units are never
qualified by further information about the nature of the quantity; any extra
information on the nature of the quantity should be attached to the quantity symbol
and not to the unit symbol.

5.3.3

Formatting the value of a quantity

The numerical value always precedes the unit, and a space is always used to separate
the unit from the number. Thus the value of the quantity is the product of the
number and the unit, the space being regarded as a multiplication sign (just as a
space between units implies multiplication). The only exceptions to this rule are for
the unit symbols for degree, minute, and second for plane angle, °,

′

, and

″

respectively, for which no space is left between the numerical value and the unit
symbol.
This rule means that the symbol °C for the degree Celsius is preceded by a space
when one expresses values of Celsius temperature

Even when the value of a quantity is used as an adjective, a space is left between the
numerical value and the unit symbol. Only when the name of the unit is spelled out
would the ordinary rules of grammar apply, so that in English a hyphen would be
used to separate the number from the unit.
In any one expression, only one unit is used. An exception to this rule is in
expressing the values of time and of plane angles using non-SI units. However, for
plane angles it is generally preferable to divide the degree decimally. Thus one
would write 22.20° rather than 22° 12

′

, except in fields such as navigation,

cartography, astronomy, and in the measurement of very small angles.

5.3.4

Formatting numbers, and the decimal marker

The symbol used to separate the integral part of a number from its decimal part is
called the decimal marker. Following the 22nd CGPM (2003, Resolution 10), the
decimal marker “shall be either the point on the line or the comma on the line.” The
decimal marker chosen should be that which is customary in the context concerned.
If the number is between +1 and

−

1, then the decimal marker is always preceded by

a zero.
Following the 9th CGPM (1948, Resolution 7) and the 22nd CGPM (2003,
Resolution 10), for numbers with many digits the digits may be divided into groups
of three by a thin space, in order to facilitate reading. Neither dots nor commas are
inserted in the spaces between groups of three. However, when there are only four
digits before or after the decimal marker, it is customary not to use a space to isolate

= 10.234 m,

but not

= 10 m 23.4 cm

−

0.234,

but not

−

.234

= 30.2

but not

= 30.2

nor

= 30.2

a 10 k

Ω

resistor

a 35-millimeter film

= 12.3 g, where

is used

as a symbol for the quantity
mass, but

= 30° 22

′

″

where

is used as a symbol

for the quantity plane angle.

43 279.168 29,

but not

43,279.168,29

either

3279.1683

3 279.168 3

For example:
The maximum electric
potential difference is

max

= 1000 V

but not

= 1000 V

max

The mass fraction of copper
in the sample of silicon is

(Cu) = 1.3 × 10

−

but not

1.3 × 10

−

w/w.

Writing unit symbols and names

•

a single digit. The practice of grouping digits in this way is a matter of choice; it is
not always followed in certain specialized applications such as engineering
drawings, financial statements, and scripts to be read by a computer.
For numbers in a table, the format used should not vary within one column.

5.3.5

Expressing the measurement uncertainty in the value of a quantity

The uncertainty that is associated with the estimated value of a quantity should be
evaluated and expressed in accordance with the

Guide to the Expression of Uncer-

tainty in Measurement

[ISO, 1995]. The standard uncertainty (i.e. estimated

standard deviation, coverage factor

= 1) associated with a quantity

is denoted by

(

). A convenient way to represent the uncertainty is given in the following

example:

1.674 927 28(29)

–27

kg.

where

is the symbol for the quantity (in this case the mass of a neutron), and the

number in parenthesis is the numerical value of the combined standard uncertainty
of the estimated value of

referred to the last two digits of the quoted value; in this

case

(

) = 0.000 000 29 × 10

−

kg. If any coverage factor,

, different from one,

is used, this factor must be stated.

5.3.6

Multiplying or dividing quantity symbols, the values of quantities, or
numbers

When multiplying or dividing quantity symbols any of the following methods may

be used:

a b

⋅

a
b

a b

−

When multiplying the value of quantities either a multiplication sign,

, or brackets

should be used, not a half-high (centered) dot. When multiplying numbers only the
multiplication sign,

, should be used.

When dividing the values of quantities using a solidus, brackets are used to remove
ambiguities.

5.3.7

Stating values of dimensionless quantities, or quantities of dimension
one

As discussed in Section 2.2.3, the coherent SI unit for dimensionless quantities, also
termed quantities of dimension one, is the number one, symbol 1. Values of such
quantities are expressed simply as numbers. The unit symbol 1 or unit name “one”
are not explicitly shown, nor are special symbols or names given to the unit one,
apart from a few exceptions as follows. For the quantity plane angle, the unit one is
given the special name radian, symbol rad, and for the quantity solid angle, the unit
one is given the special name steradian, symbol sr. For the logarithmic ratio
quantities, the special names neper, symbol Np, bel, symbol B, and decibel, symbol
dB, are used (see 4.1 and Table 8, p. 35).
Because SI prefix symbols can neither be attached to the symbol 1 nor to the name
“one,” powers of 10 are used to express the values of particularly large or small
dimensionless quantities.

Examples:

for force equals

mass times acceleration

(53 m/s)

10.2 s

or (53 m/s)(10.2 s)

25

60.5

but not

60.5

(20 m)/(5 s) = 4 m/s

(

a/b

)

not

a/b/c

= 1.51,

but not

= 1.51 × 1,

where

is the quantity

symbol for refractive index.

•

Writing unit symbols and names

In mathematical expressions, the internationally recognized symbol % (percent) may
be used with the SI to represent the number 0.01. Thus, it can be used to express the
values of dimensionless quantities. When it is used, a space separates the number
and the symbol %. In expressing the values of dimensionless quantities in this way,
the symbol % should be used rather than the name “percent.”
In written text, however, the symbol % generally takes the meaning of “parts per
hundred.”
Phrases such as “percentage by mass,” “percentage by volume,” or “percentage by
amount of substance” should not be used; the extra information on the quantity
should instead be conveyed in the name and symbol for the quantity.
In expressing the values of dimensionless fractions (e.g. mass fraction, volume
fraction, relative uncertainties), the use of a ratio of two units of the same kind is
sometimes useful.
The term “ppm,” meaning 10

−

relative value, or 1 in 10

, or parts per million, is

also used. This is analogous to the meaning of percent as parts per hundred. The
terms “parts per billion,” and “parts per trillion,” and their respective abbreviations
“ppb,” and “ppt,” are also used, but their meanings are language dependent. For this
reason the terms ppb and ppt are best avoided. (In English-speaking countries, a
billion is now generally taken to be 10

and a trillion to be 10

; however, a billion

may still sometimes be interpreted as 10

and a trillion as 10

. The abbreviation

ppt is also sometimes read as parts per thousand, adding further confusion.)
When any of the terms %, ppm, etc., are used it is important to state the
dimensionless quantity whose value is being specified.

†

Editors

note: The NIST policy on the proper way to employ the International System of Units to

express the values of quantities does not allow the use of parts per million, parts per billion or
parts per trillion and the like, nor the abbreviations ppm, ppb or ppt and the like. Further, it only
allows the use of the word “percent” and the symbol % to mean the number 0.01 in the expression
of the value of a quantity. See NIST SP 811, available as noted in the Foreword.

= 0.0025 = 0.25 %,

where

is the quantity

symbol for amount fraction
(mole fraction) of entity B.

The mirror reflects 95 % of
the incident photons.

= 3.6 %,

but not

= 3.6 % (

where

denotes volume

fraction.

= 2.5 × 10

−

= 2.5 mmol/mol

(

) = 0.3 µV/V,

where

(

) is the relative

uncertainty of the measured
voltage

Appendix 1

•

1st CGPM, 1889

■

Sanction of the international prototypes of the meter and the kilogram

(CR, 34-38)*

The Conférence Générale des Poids et Mesures,

considering

•

the “Compte rendu of the President of the Comité International des Poids et Mesures

(CIPM)” and the “Report of the CIPM,” which show that, by the collaboration of the
French section of the International Meter Commission and of the CIPM, the
fundamental measurements of the international and national prototypes of the meter
and of the kilogram have been made with all the accuracy and reliability which the
present state of science permits;

•

that the international and national prototypes of the meter and the kilogram are made

of an alloy of platinum with 10 per cent iridium, to within 0.0001;

•

the equality in length of the international Meter and the equality in mass of the

international Kilogram with the length of the Meter and the mass of the Kilogram kept
in the Archives of France;

•

that the differences between the national Meters and the international Meter lie within

0.01 millimeter and that these differences are based on a hydrogen thermometer scale
which can always be reproduced thanks to the stability of hydrogen, provided identical
conditions are secured;

•

that the differences between the national Kilograms and the international Kilogram lie

within 1 milligram;

•

that the international Meter and Kilogram and the national Meters and Kilograms fulfil

the requirements of the Meter Convention,

sanctions

A. As regards international prototypes:

1. The Prototype of the meter chosen by the CIPM. This prototype, at the temperature of

melting ice, shall henceforth represent the metric unit of length.

2. The Prototype of the kilogram adopted by the CIPM. This prototype shall henceforth

be considered as the unit of mass.

3. The hydrogen thermometer centigrade scale in terms of which the equations of the

prototype Meters have been established.

B. As regards national prototypes: .....

…

3rd CGPM, 1901

■

Declaration concerning the definition of the liter

(CR, 38-39)

…

he Conference declares

1. The unit of volume, for high accuracy determinations, is the volume occupied by a

mass of 1 kilogram of pure water, at its maximum density and at standard atmospheric
pressure: this volume is called “liter.”

2. …

* The definition of the
meter was abrogated in
1960 by the 11th CGPM
(Resolution 6,
see p. 57).

* This definition was
abrogated in 1964 by the
12th CGPM (Resolution 6,
see p. 61).

•

Appendix 1

■

Declaration on the unit of mass and on the definition of weight;

conventional value of

(CR, 70)

Taking into account

the decision of the Comité International des Poids et Mesures of

15 October 1887, according to which the kilogram has been defined as unit of mass;

Taking into account

the decision contained in the sanction of the prototypes of the

Metric System, unanimously accepted by the Conférence Générale des Poids et Mesures
on 26 September 1889;

Considering

the necessity to put an end to the ambiguity which in current practice still

exists on the meaning of the word

weight

, used sometimes for

mass

, sometimes for

mechanical force

;

The Conference declares

1. The kilogram is the unit of mass; it is equal to the mass of the international prototype

of the kilogram;

2. The word “weight” denotes a quantity of the same nature as a “force”: the weight of a

body is the product of its mass and the acceleration due to gravity; in particular, the
standard weight of a body is the product of its mass and the standard acceleration due
to gravity;

3. The value adopted in the International Service of Weights and Measures for the

standard acceleration due to gravity is 980.665 cm/s

, value already stated in the laws

of some countries.

7th CGPM, 1927

■

Definition of the meter by the international Prototype

(CR, 49)*

The unit of length is the meter, defined by the distance, at 0°, between the axes of the two
central lines marked on the bar of platinum-iridium kept at the Bureau International des
Poids et Mesures and declared Prototype of the meter by the 1st Conférence Générale
des Poids et Mesures, this bar being subject to standard atmospheric pressure and
supported on two cylinders of at least one centimeter diameter, symmetrically placed in
the same horizontal plane at a distance of 571 mm from each other.

CIPM, 1946

■

Definitions of photometric units

(PV,

, 119-122)*

Resolution

…

4. The photometric units may be defined as follows:

New candle

(unit of luminous intensity). — The value of the new candle is such that the

brightness of the full radiator at the temperature of solidification of platinum is 60 new
candles per square centimeter.

New lumen

(unit of luminous flux). — The new lumen is the luminous flux emitted in unit

solid angle (steradian) by a uniform point source having a luminous intensity of 1 new
candle.

5. …

Editors’ note:

In the

United States the term
“weight” is used to mean
both force and mass. In
science and technology
this declaration is usually
followed, with the newton
(N) the SI unit of force and
thus weight. In commercial
and everyday use, and
especially in common
parlance, weight is often
(but incorrectly) used as a
synonym for mass, the SI
unit of which is the
kilogram (kg).

This value of

was the

conventional reference for
calculating the now
obsolete unit kilogram
force.

* This definition was
abrogated in 1960 by the
11th CGPM (Resolution 6,
see p. 57).

* The two definitions
contained in this
Resolution were
ratified in 1948 by the
9th CGPM, which also
approved the name
candela given to the
“new candle” (CR,
54). For the lumen the
qualifier “new” was
later abandoned.
This definition was
modified in 1967 by
the 13th CGPM
(Resolution 5, see
p. 63).

Appendix 1

•

■

Definitions of electric units

(PV,

, 132-133)

Resolution 2

...

4. (A) Definitions of the mechanical units which enter the definitions of electric units:

Unit of force

. — The unit of force [in the MKS (meter, kilogram, second) system] is the

force which gives to a mass of 1 kilogram an acceleration of 1 meter per second, per
second.

Joule

(unit of energy or work). — The joule is the work done when the point of application

of 1 MKS unit of force [newton] moves a distance of 1 meter in the direction of the
force.

Watt

(unit of power). — The watt is the power which in one second gives rise to energy of

1 joule.

(B) Definitions of electric units. The Comité International des Poids et Mesures (CIPM)
accepts the following propositions which define the theoretical value of the electric
units:

Ampere

(unit of electric current). — The ampere is that constant current which, if

maintained in two straight parallel conductors of infinite length, of negligible circular
cross-section, and placed 1 meter apart in vacuum, would produce between these
conductors a force equal to 2

−

MKS unit of force [newton] per meter of length.

Volt

(unit of potential difference and of electromotive force). — The volt is the potential

difference between two points of a conducting wire carrying a constant current of
1 ampere, when the power dissipated between these points is equal to 1 watt.

Ohm

(unit of electric resistance). — The ohm is the electric resistance between two points

of a conductor when a constant potential difference of 1 volt, applied to these points,
produces in the conductor a current of 1 ampere, the conductor not being the seat of
any electromotive force.

Coulomb

(unit of quantity of electricity). — The coulomb is the quantity of electricity

carried in 1 second by a current of 1 ampere.

Farad

(unit of capacitance). — The farad is the capacitance of a capacitor between the

plates of which there appears a potential difference of 1 volt when it is charged by a
quantity of electricity of 1 coulomb.

Henry

(unit of electric inductance). — The henry is the inductance of a closed circuit in

which an electromotive force of 1 volt is produced when the electric current in the
circuit varies uniformly at the rate of 1 ampere per second.

Weber

(unit of magnetic flux). — The weber is the magnetic flux which, linking a circuit of

one turn, would produce in it an electromotive force of 1 volt if it were reduced to zero
at a uniform rate in 1 second.

9th CGPM, 1948

■

Triple point of water; thermodynamic scale with a single fixed point;

unit of quantity of heat (joule)

(CR, 55 and 63)

Resolution 3

1. With present-day techniques, the triple point of water is capable of providing a

thermometric reference point with an accuracy higher than can be obtained from the
melting point of ice.

The definitions contained
in this Resolution were
ratified in 1948 by the
9th CGPM (CR, 49),
which also adopted the
name newton

(Resolution 7) for the
MKS unit of force.

•

Appendix 1

In consequence the Comité Consultatif de Thermométrie et Calorimétrie (CCTC)
considers that the zero of the centesimal thermodynamic scale must be defined as the
temperature 0.0100 degree below that of the triple point of water.

2. The CCTC accepts the principle of an absolute thermodynamic scale with a single

fundamental fixed point, at present provided by the triple point of pure water, the
absolute temperature of which will be fixed at a later date.

The introduction of this new scale does not affect in any way the use of the
International Scale, which remains the recommended practical scale.

3. The unit of quantity of heat is the joule.

Note:

It is requested that the results of calorimetric experiments be as far as possible

expressed in joules. If the experiments are made by comparison with the rise of
temperature of water (and that, for some reason, it is not possible to avoid using the
calorie), the information necessary for conversion to joules must be provided. The CIPM,
advised by the CCTC, should prepare a table giving, in joules per degree, the most
accurate values that can be obtained from experiments on the specific heat of water.

A table, prepared in response to this request, was approved and published by the
CIPM in 1950 (PV,

, 92).

■

Adoption of “degree Celsius”

[

CIPM, 1948

(PV,

, 88)

and 9th CGPM,

1948

(CR, 64)]

From three names (“degree centigrade,” “centesimal degree,” “degree Celsius”)
proposed to denote the degree of temperature, the CIPM has chosen “degree
Celsius” (PV,

, 88).

This name is also adopted by the 9th CGPM (CR, 64).

■

Proposal for establishing a practical system of units of measurement

(CR, 64)

Resolution 6

The Conférence Générale des Poids et Mesures (CGPM),

considering

•

that the Comité International des Poids et Mesures (CIPM) has been requested by the

International Union of Physics to adopt for international use a practical Système
International d’Unités; that the International Union of Physics recommends the MKS
system and one electric unit of the absolute practical system, but does not
recommend that the CGS system be abandoned by physicists;

•

that the CGPM has itself received from the French Government a similar request,

accompanied by a draft to be used as basis of discussion for the establishment of a
complete specification of units of measurement;

instructs

the CIPM:

•

to seek by an energetic, active, official enquiry the opinion of scientific, technical and

educational circles of all countries (offering them, in fact, the French document as
basis);

•

to gather and study the answers;

•

to make recommendations for a single practical system of units of measurement,

suitable for adoption by all countries adhering to the Meter Convention.

Appendix 1

•

■

Writing and printing of unit symbols and of numbers

(CR, 70)*

Resolution 7

Principles

Roman (upright) type, in general lower-case, is used for symbols of units; if, however, the
symbols are derived from proper names, capital roman type is used. These symbols are
not followed by a full stop.

In numbers, the comma (French practice) or the dot (British practice) is used only to
separate the integral part of numbers from the decimal part. Numbers may be divided in
groups of three in order to facilitate reading; neither dots nor commas are ever inserted in
the spaces between groups.

Unit

Symbol

Unit

Symbol

•

meter

ampere

•

square meter

volt

•

cubic meter

watt

•

micron

ohm

•

liter

coulomb

•

gram

farad

•

metric ton

henry

second s

hertz

erg

poise

dyne

dyn

newton

degree Celsius

°C

•

candela (new candle)

•

degree absolute

°K

lux

calorie

cal

lumen

bar

stilb

hour

Notes

1. The symbols whose unit names are preceded by dots are those which had already

been adopted by a decision of the CIPM.

2. The symbol for the stere, the unit of volume for firewood, shall be “st” and not “s,”

which had been previously assigned to it by the CIPM.

3. To indicate a temperature interval or difference, rather than a temperature, the word

“degree” in full, or the abbreviation “deg,” must be used.

10th CGPM, 1954

■

Definition of the thermodynamic temperature scale

(CR, 79)*

Resolution 3

The 10th Conférence Générale des Poids et Mesures decides to define the
thermodynamic temperature scale by choosing the triple point of water as the

* The CGPM abrogated
certain decisions on units
and terminology, in
particular: micron, degree
absolute, and the terms
“degree,” and “deg,”
13th CGPM, 1967/68
(Resolutions 7 and 3,
see pp. 64 and 62,
respectively), and the liter;
16th CGPM, 1979
(Resolution 6, see p. 69).

Editors’ note

: The name

“tonne” appears in the
original text, not “metric
ton”; see footnote (

) of

Table 6, p. 32.

* The 13th CGPM in 1967
explicitly defined the
kelvin (Resolution 4, see
p. 63).

•

Appendix 1

fundamental fixed point, and assigning to it the temperature 273.16 degrees Kelvin,
exactly.

■

Definition of the standard atmosphere

(CR, 79)

Resolution 4

The 10th Conférence Générale des Poids et Mesures (CGPM), having noted that the
definition of the standard atmosphere given by the 9th CGPM when defining the
International Temperature Scale led some physicists to believe that this definition of the
standard atmosphere was valid only for accurate work in thermometry,

declares

that it adopts, for general use, the definition:

1 standard atmosphere = 1 013 250 dynes per square centimeter,

i.e., 101 325 newtons per square meter.

■

Practical system of units

(CR, 80)*

Resolution 6

In accordance with the wish expressed by the 9th Conférence Générale des Poids et
Mesures (CGPM) in its Resolution 6 concerning the establishment of a practical system of
units of measurement for international use, the 10th CGPM

decides

to adopt as base units of the system, the following units:

length

meter

mass

kilogram

time

second

electric current

ampere

thermodynamic temperature

degree Kelvin

luminous intensity

candela

CIPM, 1956

■

Definition of the unit of time (second)

(PV,

, 77)*

Resolution 1

In virtue of the powers invested in it by Resolution 5 of the 10th Conférence Générale des
Poids et Mesures, the Comité International des Poids et Mesures,

considering

1. that the 9th General Assembly of the International Astronomical Union (Dublin, 1955)

declared itself in favour of linking the second to the tropical year,

2. that, according to the decisions of the 8th General Assembly of the International

Astronomical Union (Rome, 1952), the second of ephemeris time (ET) is the fraction

496

986

408

813

276

960

−

of the tropical year for 1900 January 0 at 12 h ET,

decides

* The unit name “degree
kelvin” was changed to
“kelvin” in 1967 by the
13th CGPM (Resolution 3,
see p. 62).

* This definition was
abrogated in 1967 by the
13th CGPM (Resolution 1,
see p. 62).

Appendix 1

•

“The second is the fraction 1/31 556 925.9747 of the tropical year for 1900 January 0 at
12 hours ephemeris time.”

■

Système International d’Unités

(PV,

, 83)

Resolution 3

The Comité International des Poids et Mesures,

considering

•

the task entrusted to it by Resolution 6 of the 9th Conférence Générale des Poids et

Mesures (CGPM) concerning the establishment of a practical system of units of
measurement suitable for adoption by all countries adhering to the Meter Convention,

•

the documents received from twenty-one countries in reply to the enquiry requested by

the 9th CGPM,

•

Resolution 6 of the 10th CGPM, fixing the base units of the system to be established,

recommends

1. that the name “Système International d’Unités” be given to the system founded on the

base units adopted by the 10th CGPM, viz.:

[This is followed by the list of the six base units with their symbols, reproduced
in Resolution 12 of the 11th CGPM (1960)].

2. that the units listed in the table below be used, without excluding others which might

be added later:

[This is followed by the table of units reproduced in paragraph 4 of Resolution
12 of the 11th CGPM (1960)].

11th CGPM, 1960

■

Definition of the meter

(CR, 85)*

Resolution 6

The 11th Conférence Générale des Poids et Mesures (CGPM),

considering

•

that the international Prototype does not define the meter with an accuracy adequate

for the present needs of metrology,

•

that it is moreover desirable to adopt a natural and indestructible standard,

decides

1. The meter is the length equal to 1 650 763.73 wavelengths in vacuum of the radiation

corresponding to the transition between the levels 2p

and 5d

of the krypton 86

atom.

2. The definition of the meter in force since 1889, based on the international Prototype of

platinum-iridium, is abrogated.

3. The international Prototype of the meter sanctioned by the 1st CGPM in 1889 shall be

kept at the BIPM under the conditions specified in 1889.

* This definition was
abrogated in 1983 by the
17th CGPM (Resolution 1,
see p. 70).

•

Appendix 1

■

Definition of the unit of time (second)

(CR, 86)*

Resolution 9

The 11th Conférence Générale des Poids et Mesures (CGPM),

considering

•

the powers given to the Comité International des Poids et Mesures (CIPM) by the

10th CGPM to define the fundamental unit of time,

•

the decision taken by the CIPM in 1956,

ratifies

the following definition:

“The second is the fraction 1/31 556 925.9747 of the tropical year for 1900 January 0 at
12 hours ephemeris time.”

■

Système International d’Unités

(CR, 87)*

Resolution 12

The 11th Conférence Générale des Poids et Mesures (CGPM),

considering

•

Resolution 6 of the 10th CGPM, by which it adopted six base units on which to

establish a practical system of measurement for international use:

length

meter

mass

kilogram

time

second

electric

current

ampere

thermodynamic

temperature degree

Kelvin °K

luminous

intensity

candela

•

Resolution 3 adopted by the Comité International des Poids et Mesures (CIPM) in

1956,

•

the recommendations adopted by the CIPM in 1958 concerning an abbreviation for the

name of the system, and prefixes to form multiples and submultiples of the units,

decides

1. the system founded on the six base units above is called the “Système International

d’Unités”;

2. the international abbreviation of the name of the system is: SI;

3. names of multiples and submultiples of the units are formed by means of the following

prefixes:

Multiplying factor

Prefix Symbol

Multiplying factor Prefix

Symbol

1 000 000 000 000 = 10

tera

0.1 = 10

−

deci

1 000 000 000 = 10

giga

0.01 = 10

−

centi

1 000 000 = 10

mega

0.001 = 10

−

milli

1 000 = 10

kilo

0.000 001 = 10

−

micro

100 = 10

hecto

0.000 000 001 = 10

−

nano

10 = 10

deka

0.000 000 000 001 = 10

−

pico

* This definition was
abrogated in 1967 by the
13th CGPM (Resolution 1,
see p. 62).

* The CGPM later
abrogated certain of its
decisions and extended the
list of prefixes, see notes
below.

A seventh base unit, the
mole, was adopted by the
14th CGPM in 1971
(Resolution 3, see p. 66)

The name and symbol for
the unit of thermodynamic
temperature was modified
by the 13th CGPM in 1967
(Resolution 3, see p. 62).

Further

prefixes were

adopted by the 12th CGPM
in 1964 (Resolution 8,
see p. 61),
the 15th CGPM in 1975
(Resolution 10, see p. 67)
and the 19th CGPM in
1991 (Resolution 4,
see p. 74).

Appendix 1

•

4. the units listed below are used in the system, without excluding others which might be

added later.

Supplementary units

plane angle

radian

rad

solid angle

steradian

Derived units

area

square

meter

volume

cubic

meter

frequency

hertz

1/s

mass density (density)

kilogram per cubic meter

kg/m

speed, velocity

meter per second

m/s

angular velocity

radian per second

rad/s

acceleration

meter per second squared

m/s

angular acceleration

radian per second squared

rad/s

force

newton

kg · m/s

pressure (mechanical stress) newton per square meter

N/m

kinematic viscosity

square meter per second

dynamic viscosity

newton-second per square

meter

N · s/m

work, energy, quantity of heat joule

N · m

power

watt

J/s

quantity of electricity (side bar) coulomb

A · s

tension (voltage),
potential difference,
electromotive force

volt

W/A

electric field strength

volt per meter

V/m

electric resistance

ohm

V/A

capacitance

farad

A · s/V

magnetic flux

weber

V · s

inductance

henry

V · s/A

magnetic flux density

tesla

Wb/m

magnetic field strength

ampere per meter

A/m

magnetomotive force

ampere

luminous flux

lumen

cd · sr

luminance

candela per square meter

cd/m

illuminance

lux

lx lm/m

The 20th CGPM in 1995
abrogated the class of
supplementary units in the
SI (Resolution 8, see
p. 74). These are now
considered as derived
units.

The 13th CGPM in 1967
(Resolution 6, see p. 64)
specified other units which
should be added to the list.
In principle, this list of
derived units is without
limit.

Modern practice is to use
the phrase “amount of
heat” rather than “quantity
of heat,” because the word
quantity has a different
meaning in metrology.

Modern practice is to use
the phrase “amount of
electricity” rather than
“quantity of electricity”
(see note above).

•

Appendix 1

■

Cubic decimeter and liter

(CR, 88)

Resolution 13

The 11th Conférence Générale des Poids et Mesures (CGPM),

considering

•

that the cubic decimeter and the liter are unequal and differ by about 28 parts in 10

•

that determinations of physical quantities which involve measurements of volume are

being made more and more accurately, thus increasing the risk of confusion between
the cubic decimeter and the liter,

requests

the Comité International des Poids et Mesures to study the problem and submit

its conclusions to the 12th CGPM.

CIPM, 1961

■

Cubic decimeter and liter

(PV,

, 34)

Recommendation

The Comité International des Poids et Mesures recommends that the results of accurate
measurements of volume be expressed in units of the International System and not in
liters.

CIPM, 1964

■

Atomic and molecular frequency standards

(PV,

, 26 and CR, 93)

Declaration

The Comité International des Poids et Mesures,

empowered

by Resolution 5 of the 12th Conférence Générale des Poids et Mesures to

name atomic or molecular frequency standards for temporary use for time measurements
in physics,

declares

that the standard to be employed is the transition between the hyperfine levels

= 4

, M =

0 and

F =

= 0 of the ground state

1/2

of the cesium 133 atom,

unperturbed by external fields, and that the frequency of this transition is assigned the
value 9 192 631 770 hertz.

12th CGPM, 1964

■

Atomic standard of frequency

(CR, 93)

Resolution 5

The 12th Conférence Générale des Poids et Mesures (CGPM),

considering

•

that the 11th CGPM noted in its Resolution 10 the urgency, in the interests of accurate

metrology, of adopting an atomic or molecular standard of time interval,

•

that, in spite of the results already obtained with cesium atomic frequency standards,

the time has not yet come for the CGPM to adopt a new definition of the second, base

Appendix 1

•

unit of the Système International d’Unités, because of the new and considerable
improvements likely to be obtained from work now in progress,

considering also

that it is not desirable to wait any longer before time measurements in

physics are based on atomic or molecular frequency standards,

empowers

the Comité International des Poids et Mesures to name the atomic or

molecular frequency standards to be employed for the time being,

requests

the organizations and laboratories knowledgeable in this field to pursue work

connected with a new definition of the second.

■

Liter

(CR, 93)

Resolution 6

The 12th Conférence Générale des Poids et Mesures (CGPM)

considering

Resolution 13 adopted by the 11th CGPM in 1960 and the Recommendation

adopted by the Comité International des Poids et Mesures in 1961,

abrogates

the definition of the liter given in 1901 by the 3rd CGPM,

declares

that the word “liter” may be employed as a special name for the cubic

decimeter,

recommends

that the name liter should not be employed to give the results of high-

accuracy volume measurements.

■

Curie

(CR, 94)*

Resolution 7

The 12th Conférence Générale des Poids et Mesures,

considering

that the curie has been used for a long time in many countries as unit of

activity for radionuclides,

recognizing

that in the Système International d’Unités (SI), the unit of this activity is the

second to the power of minus one (s

−

accepts

that the curie be still retained, outside SI, as unit of activity, with the value

3.7

−

. The symbol for this unit is Ci.

■

SI prefixes femto and atto

(CR, 94)*

Resolution 8

The 12th Conférence Générale des Poids et Mesures (CGPM)

decides

to add to the list of prefixes for the formation of names of multiples and sub-

multiples of units, adopted by the 11th CGPM, Resolution 12, paragraph 3, the following
two new prefixes:

Multiplying factor

Prefix

Symbol

−

femto

−

atto a

* The name “becquerel”
(Bq) was adopted by the
15th CGPM in 1975
(Resolution 8, see p. 67)
for the SI unit of activity:
1 Ci = 3.7

Bq.

* New prefixes were added
by the 15th CGPM in 1975
(Resolution 10, see p. 67).

•

Appendix 1

CIPM, 1967

■

Decimal multiples and submultiples of the unit of mass

(PV,

, 29 and

Metrologia

, 1968,

, 45)

Recommendation 2

The Comité International des Poids et Mesures,

considering

that the rule for forming names of decimal multiples and submultiples of the

units of paragraph 3 of Resolution 12 of the 11th Conférence Générale des Poids et
Mesures (CGPM) (1960) might be interpreted in different ways when applied to the unit of
mass,

declares

that the rules of Resolution 12 of the 11th CGPM apply to the kilogram in the

following manner: the names of decimal multiples and submultiples of the unit of mass are
formed by attaching prefixes to the word “gram.”

13th CGPM, 1967/68

■

SI unit of time (second)

(CR, 103 and

Metrologia

, 1968,

, 43)

Resolution 1

The 13th Conférence Générale des Poids et Mesures (CGPM),

considering

•

that the definition of the second adopted by the Comité International des Poids et

Mesures (CIPM) in 1956 (Resolution 1) and ratified by Resolution 9 of the 11th CGPM
(1960), later upheld by Resolution 5 of the 12th CGPM (1964), is inadequate for the
present needs of metrology,

•

that at its meeting of 1964 the CIPM, empowered by Resolution 5 of the 12th CGPM

(1964), recommended, in order to fulfil these requirements, a cesium atomic frequency
standard for temporary use,

•

that this frequency standard has now been sufficiently tested and found sufficiently

accurate to provide a definition of the second fulfilling present requirements,

•

that the time has now come to replace the definition now in force of the unit of time of

the Système International d’Unités by an atomic definition based on that standard,

decides

1. The SI unit of time is the second defined as follows:

“The second is the duration of 9 192 631 770 periods of the radiation corresponding to
the transition between the two hyperfine levels of the ground state of the cesium 133
atom”;

2. Resolution 1 adopted by the CIPM at its meeting of 1956 and Resolution 9 of the

11th CGPM are now abrogated.

■

SI unit of thermodynamic temperature (kelvin)

(CR, 104 and

Metrolog

1968,

, 43)*

Resolution 3

The 13th Conférence Générale des Poids et Mesures (CGPM),

considering

At its 1997 meeting, the
CIPM affirmed that this
definition refers to a
cesium atom at rest at a
thermodynamic
temperature of 0 K.

* At its 1980 meeting, the
CIPM approved the report
of the 7th meeting of the
CCU, which requested that
the use of the symbols
“°K” and “deg” no longer
be permitted.

Appendix 1

•

the names “degree Kelvin” and “degree,” the symbols “°K” and “deg” and the rules for

their use given in Resolution 7 of the 9th CGPM (1948), in Resolution 12 of the
11th CGPM (1960), and the decision taken by the Comité International des Poids et
Mesures in 1962 (PV,

, 27),

•

that the unit of thermodynamic temperature and the unit of temperature interval are

one and the same unit, which ought to be denoted by a single name and a single
symbol,

decides

1. the unit of thermodynamic temperature is denoted by the name “kelvin” and its symbol

is “K”;**

2. the same name and the same symbol are used to express a temperature interval;

3. a temperature interval may also be expressed in degrees Celsius;

4. the decisions mentioned in the opening paragraph concerning the name of the unit of

thermodynamic temperature, its symbol and the designation of the unit to express an
interval or a difference of temperatures are abrogated, but the usages which derive
from these decisions remain permissible for the time being.

■

Definition of the SI unit of thermodynamic temperature (kelvin)

(CR, 104

and

Metrologia

, 1968,

, 43)*

Resolution 4

The 13th Conférence Générale des Poids et Mesures (CGPM),

considering

that it is useful to formulate more explicitly the definition of the unit of

thermodynamic temperature contained in Resolution 3 of the 10th CGPM (1954),

decides

to express this definition as follows:

“The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the
thermodynamic temperature of the triple point of water.”

■

SI unit of luminous intensity (candela)

(CR, 104 and

Metrologia

, 1968,

43-44)*

Resolution 5

The 13th Conférence Générale des Poids et Mesures (CGPM),

considering

•

the definition of the unit of luminous intensity ratified by the 9th CGPM (1948) and

contained in the “Resolution concerning the change of photometric units” adopted by
the Comité International des Poids et Mesures in 1946 (PV,

, 119) in virtue of the

powers conferred by the 8th CGPM (1933),

•

that this definition fixes satisfactorily the unit of luminous intensity, but that its wording

may be open to criticism,

decides

to express the definition of the candela as follows:

“The candela is the luminous intensity, in the perpendicular direction, of a surface of
1/600 000 square meter of a black body at the temperature of freezing platinum under a
pressure of 101 325 newtons per square meter.”

* See Recommendation 5
(CI-1989) of the CIPM on
the International
Temperature Scale of
1990, p. 73.

* This definition was
abrogated by the
16th CGPM in 1979
(Resolution 3, see p. 68).

** See Recommendation 2
(CI-2005) of the CIPM on
the isotopic composition of
water entering in the
definition of the kelvin,
p. 80.

•

Appendix 1

■

SI derived units

(CR, 105 and

Metrologia

, 1968,

, 44)*

Resolution 6

The 13th Conférence Générale des Poids et Mesures (CGPM),

considering

that it is useful to add some derived units to the list of paragraph 4 of

Resolution 12 of the 11th CGPM (1960),

decides

to add:

wave number

1 per meter

−

entropy

joule per kelvin

J/K

specific heat capacity

joule per kilogram kelvin

J/(kg · K)

thermal conductivity

watt per meter kelvin

W/(m · K)

radiant intensity

watt per steradian

W/sr

activity (of a radioactive source)

1 per second

−

■

Abrogation of earlier decisions (micron and new candle)

(CR, 105 and

Metrologia

, 1968,

, 44)

Resolution 7

The 13th Conférence Générale des Poids et Mesures (CGPM),

considering

that subsequent decisions of the General Conference concerning the

Système International d’Unités are incompatible with parts of Resolution 7 of the
9th CGPM (1948),

decides

accordingly to remove from Resolution 7 of the 9th Conference:

1. the unit name “micron,” and the symbol “

” which had been given to that unit but which

has now become a prefix;

2. the unit name “new candle.”

CIPM, 1969

■

Système International d’Unités, Rules for application of Resolution 12 of

the 11th CGPM (1960)

(PV,

30 and

Metrologia

, 1970,

, 66)*

Recommendation 1

The Comité International des Poids et Mesures,

considering

that Resolution 12 of the 11th Conférence Générale des Poids et Mesures

(CGPM) (1960), concerning the Système International d’Unités, has provoked discussions
on certain of its aspects,

declares

1. the base units, the supplementary units and the derived units of the Système

International d’Unités, which form a coherent set, are denoted by the name “SI
units”;**

2. the prefixes adopted by the CGPM for the formation of decimal multiples and

submultiples of SI units are called “SI prefixes”;

and

recommends

3. the use of SI units and of their decimal multiples and submultiples whose names are

formed by means of SI prefixes.

* The unit of activity was
given a special name and
symbol by the

15th CGPM

in 1975 (Resolution 8, see
p. 67).

* The 20th CGPM in 1995
decided to abrogate the
class of supplementary
units in the SI
(Resolution 8, see p. 74).

** The CIPM approved in
2001 a proposal of the
CCU to clarify the
definition of “SI units” and
“units of the SI,”
see p. 76.

Appendix 1

•

Note:

The name “supplementary units,” appearing in Resolution 12 of the 11th CGPM

(and in the present Recommendation) is given to SI units for which the General
Conference declines to state whether they are base units or derived units.

CCDS, 1970 (

CIPM, 1970)

■

Definition of TAI

(PV,

, 110-111 and

Metrologia

, 1971,

, 43)

Recommendation S 2

International Atomic Time (TAI) is the time reference coordinate established by the
Bureau International de l'Heure on the basis of the readings of atomic clocks operating in
various establishments in accordance with the definition of the second, the unit of time of
the International System of Units.

In 1980, the definition of TAI was completed as follows (declaration of the CCDS,

BIPM Com. Cons. Déf. Seconde

, 1980,

, S 15 and

Metrologia

, 1981,

, 70):

TAI is a coordinate time scale defined in a geocentric reference frame with the SI second
as realized on the rotating geoid as the scale unit.

14th CGPM, 1971

■

Pascal and siemens

(CR, 78)

The 14th Conférence Générale des Poids et Mesures adopted the special names “pascal”
(symbol Pa), for the SI unit newton per square meter, and “siemens” (symbol S), for the SI
unit of electric conductance [reciprocal ohm].

■

International Atomic Time, function of CIPM

(CR, 77-78 and

Metrologia

1972,

, 35)

Resolution 1

The 14th Conférence Générale des Poids et Mesures (CGPM),

considering

•

that the second, unit of time of the Système International d’Unités, has since 1967

been defined in terms of a natural atomic frequency, and no longer in terms of the time
scales provided by astronomical motions,

•

that the need for an International Atomic Time (TAI) scale is a consequence of the

atomic definition of the second,

•

that several international organizations have ensured and are still successfully

ensuring the establishment of the time scales based on astronomical motions,
particularly thanks to the permanent services of the Bureau International de l'Heure
(BIH),

•

that the BIH has started to establish an atomic time scale of recognized quality and

proven usefulness,

•

that the atomic frequency standards for realizing the second have been considered

and must continue to be considered by the Comité International des Poids et Mesures
(CIPM) helped by a Consultative Committee, and that the unit interval of the
International Atomic Time scale must be the second realized according to its atomic
definition,

This definition was further
amplified by the
International Astronomical
Union in 1991,
Resolution A4:
“TAI is a realized time
scale whose ideal form,
neglecting a constant offset
of 32.184 s, is Terrestrial
Time (TT), itself related to
the time coordinate of the
geocentric reference frame,
Geocentric Coordinate
Time (TCG), by a constant
rate.”
(See Proc. 21st General
Assembly of the IAU,

IAU

Trans.

, 1991, vol.

XXIB,

Kluwer.)

•

Appendix 1

•

that all the competent international scientific organizations and the national

laboratories active in this field have expressed the wish that the CIPM and the CGPM
should give a definition of International Atomic Time, and should contribute to the
establishment of the International Atomic Time scale,

•

that the usefulness of International Atomic Time entails close coordination with the

time scales based on astronomical motions,

requests

the CIPM

1. to give a definition of International Atomic Time,

2. to take the necessary steps, in agreement with the international organizations

concerned, to ensure that available scientific competence and existing facilities are
used in the best possible way to realize the International Atomic Time scale and to
satisfy the requirements of users of International Atomic Time.

■

SI unit of amount of substance (mole)

(CR, 78 and

Metrologia

, 1972,

36)*

Resolution 3

The 14th Conférence Générale des Poids et Mesures (CGPM),

considering

the advice of the International Union of Pure and Applied Physics, of the

International Union of Pure and Applied Chemistry, and of the International Organization
for Standardization, concerning the need to define a unit of amount of substance,

decides

1. The mole is the amount of substance of a system which contains as many elementary

entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is “mol.”

2. When the mole is used, the elementary entities must be specified and may be atoms,

molecules, ions, electrons, other particles, or specified groups of such particles.

3. The mole is a base unit of the Système International d’Unités.

15th CGPM, 1975

■

Recommended value for the speed of light

(CR, 103 and

Metrologia

, 1975,

, 179-180)

Resolution 2

The 15th Conférence Générale des Poids et Mesures,

considering

the excellent agreement among the results of wavelength measurements on

the radiations of lasers locked on a molecular absorption line in the visible or infrared
region, with an uncertainty estimated at ± 4

−

which corresponds to the uncertainty of

the realization of the meter,

considering

also the concordant measurements of the frequencies of several of these

radiations,

recommends

the use of the resulting value for the speed of propagation of

electromagnetic waves in vacuum

= 299 792 458 meters per second.

* At its 1980 meeting, the
CIPM approved the report
of the 7th meeting of the
CCU (1980) specifying
that, in this definition, it is
understood that unbound
atoms of carbon 12, at rest
and in their ground state,
are referred to.

The relative uncertainty
given here corresponds to
three standard deviations
in the data considered.

The definition of TAI was
given by the CCDS in
1970 (now the CCTF), see
p. 65 .

Appendix 1

•

■

Coordinated Universal Time (UTC)

(CR, 104 and

Metrologia

, 1975,

180)

Resolution 5

The 15th Conférence Générale des Poids et Mesures,

considering

that the system called “Coordinated Universal Time” (UTC) is widely used,

that it is broadcast in most radio transmissions of time signals, that this wide diffusion
makes available to the users not only frequency standards but also International Atomic
Time and an approximation to Universal Time (or, if one prefers, mean solar time),

notes

that this Coordinated Universal Time provides the basis of civil time, the use of

which is legal in most countries,

judges

that this usage can be strongly endorsed.

■

SI units for ionizing radiation (becquerel and gray)

(CR, 105 and

Metrologia

, 1975,

, 180)*

Resolutions 8 and 9

The 15th Conférence Générale des Poids et Mesures,

by reason of the pressing requirement, expressed by the International Commission on
Radiation Units and Measurements (ICRU), to extend the use of the Système
International d’Unités to radiological research and applications,

by reason of the need to make as easy as possible the use of the units for nonspecialists,

taking into consideration also the grave risks of errors in therapeutic work,

adopts

the following special name for the SI unit of activity:

becquerel

symbol Bq, equal to one reciprocal second (Resolution 8),

adopts

the following special name for the SI unit of ionizing radiation:

gray

symbol Gy, equal to one joule per kilogram (Resolution 9).

Note:

The gray is the SI unit of absorbed dose. In the field of ionizing radiation, the gray

may be used with other physical quantities also expressed in joules per kilogram: the
Comité Consultatif des Unités has responsibility for studying this matter in collaboration
with the competent international organizations.

■

SI prefixes peta and exa

(CR, 106 and

Metrologia

, 1975,

, 180-181)*

Resolution 10

The 15th Conférence Générale des Poids et Mesures (CGPM)

decides

to add to the list of SI prefixes to be used for multiples, which was adopted by the

11th CGPM, Resolution 12, paragraph 3, the two following prefixes:

Multiplying factor

Prefix

Symbol

peta

exa

* At its 1976 meeting, the
CIPM approved the report
of the 5th meeting of the
CCU (1976), specifying
that, following the advice
of the ICRU, the gray may
also be used to express
specific energy imparted,
kerma and absorbed dose
index.

* New prefixes were added
by the 19th CGPM in 1991
(Resolution 4, see p. 74).

•

Appendix 1

16th CGPM, 1979

■

SI unit of luminous intensity (candela)

(CR, 100 and

Metrologia

, 1980,

56)

Resolution 3

The 16th Conférence Générale des Poids et Mesures (CGPM),

considering

•

that despite the notable efforts of some laboratories there remain excessive

divergences between the results of realizations of the candela based upon the present
black body primary standard,

•

that radiometric techniques are developing rapidly, allowing precisions that are already

equivalent to those of photometry and that these techniques are already in use in
national laboratories to realize the candela without having to construct a black body,

•

that the relation between luminous quantities of photometry and radiometric quantities,

namely the value of 683 lumens per watt for the spectral luminous efficacy of
monochromatic radiation of frequency 540

hertz, has been adopted by the

Comité International des Poids et Mesures (CIPM) in 1977,

•

that this value has been accepted as being sufficiently accurate for the system of

luminous photopic quantities, that it implies a change of only about 3 % for the system
of luminous scotopic quantities, and that it therefore ensures satisfactory continuity,

•

that the time has come to give the candela a definition that will allow an improvement

in both the ease of realization and the precision of photometric standards, and that
applies to both photopic and scotopic photometric quantities and to quantities yet to be
defined in the mesopic field,

decides

1. The candela is the luminous intensity, in a given direction, of a source that emits

monochromatic radiation of frequency 540

hertz and that has a radiant intensity

in that direction of 1/683 watt per steradian.

2. The definition of the candela (at the time called new candle) adopted by the CIPM in

1946 by reason of the powers conferred by the 8th CGPM in 1933, ratified by the
9th CGPM in 1948, then amended by the 13th CGPM in 1967, is abrogated.

■

Special name for the SI unit of dose equivalent (sievert)

(CR, 100 and

Metrologia

, 1980,

, 56)*

Resolution 5

The 16th Conférence Générale des Poids et Mesures,

considering

•

the effort made to introduce SI units into the field of ionizing radiations,

•

the risk to human beings of an underestimated radiation dose, a risk that could result

from a confusion between absorbed dose and dose equivalent,

•

that the proliferation of special names represents a danger for the Système

International d’Unités and must be avoided in every possible way, but that this rule can
be broken when it is a matter of safeguarding human health,

adopts

the special name

sievert

symbol Sv, for the SI unit of dose equivalent in the field

of radioprotection. The sievert is equal to the joule per kilogram.

* The CIPM, in 1984,
decided to accompany
this Resolution with an
explanation
(Recommendation 1,
see p. 71).

Photopic vision is detected
by the cones on the retina
of the eye, which are
sensitive to a high level of
luminance
(

> ca. 10 cd/m

) and are

used in daytime vision.
Scotopic vision is detected
by the rods of the retina,
which are sensitive to low
level luminance
(

< ca. 10

−

cd/m

used in night vision.
In the domain between
these levels of luminance
both cones and rods are
used, and this is described
as mesopic vision.

Appendix 1

•

■

Symbols for the liter

(CR, 101 and

Metrologia

, 1980,

, 56-57)

Resolution 6

The 16th Conférence Générale des Poids et Mesures (CGPM),

recognizing

the general principles adopted for writing the unit symbols in Resolution 7 of

the 9th CGPM (1948),

considering

that the symbol l for the unit liter was adopted by the Comité International

des Poids et Mesures (CIPM) in 1879 and confirmed in the same Resolution of 1948,

considering

also that, in order to avoid the risk of confusion between the letter l and the

number 1, several countries have adopted the symbol L instead of l for the unit liter,

considering

that the name liter, although not included in the Système International

d’Unités, must be admitted for general use with the System,

decides

as an exception, to adopt the two symbols l and L as symbols to be used for the

unit liter,

considering

further that in the future only one of these two symbols should be retained,

invites

the CIPM to follow the development of the use of these two symbols and to give

the 18th CGPM its opinion as to the possibility of suppressing one of them.

CIPM, 1980

■

SI supplementary units (radian and steradian)

(PV,

, 24 and

Metrologia

1981,

, 72)*

Recommendation 1

The Comité International des Poids et Mesures (CIPM),

taking into consideration

Resolution 3 adopted by ISO/TC 12 in 1978 and Recommen-

dation U 1 (1980) adopted by the Comité Consultatif des Unités at its 7th meeting,

considering

•

that the units radian and steradian are usually introduced into expressions for units

when there is need for clarification, especially in photometry where the steradian plays
an important role in distinguishing between units corresponding to different quantities,

•

that in the equations used one generally expresses plane angle as the ratio of two

lengths and solid angle as the ratio between an area and the square of a length, and
consequently that these quantities are treated as dimensionless quantities,

•

that the study of the formalisms in use in the scientific field shows that none exists

which is at the same time coherent and convenient and in which the quantities plane
angle and solid angle might be considered as base quantities,

considering also

•

that the interpretation given by the CIPM in 1969 for the class of supplementary units

introduced in Resolution 12 of the 11th Conférence Générale des Poids et Mesures
(CGPM) in 1960 allows the freedom of treating the radian and the steradian as SI
base units,

•

that such a possibility compromises the internal coherence of the SI based on only

seven base units,

The CIPM, in 1990,
considered that it was still
too early to choose a single
symbol for the liter.

* The class of SI
supplementary units was
abrogated by decision of
the 20th CGPM in 1995
(Resolution 8, see p. 74).

Editors’ note:

The

preferred symbol for
the liter in the United
states is L; see
footnote (

) of Table

6, p. 32.

•

Appendix 1

decides

to interpret the class of supplementary units in the International System as a

class of dimensionless derived units for which the CGPM allows the freedom of using or
not using them in expressions for SI derived units.

17th CGPM, 1983

■

Definition of the meter

(CR, 97 and

Metrologia

, 1984,

, 25)

Resolution 1

The 17th Conférence Générale des Poids et Mesures (CGPM),

considering

•

that the present definition does not allow a sufficiently precise realization of the meter

for all requirements,

•

that progress made in the stabilization of lasers allows radiations to be obtained that

are more reproducible and easier to use than the standard radiation emitted by a
krypton 86 lamp,

•

that progress made in the measurement of the frequency and wavelength of these

radiations has resulted in concordant determinations of the speed of light whose
accuracy is limited principally by the realization of the present definition of the meter,

•

that wavelengths determined from frequency measurements and a given value for the

speed of light have a reproducibility superior to that which can be obtained by
comparison with the wavelength of the standard radiation of krypton 86,

•

that there is an advantage, notably for astronomy and geodesy, in maintaining

unchanged the value of the speed of light recommended in 1975 by the 15th CGPM in
its Resolution 2 (

= 299 792 458 m/s),

•

that a new definition of the meter has been envisaged in various forms all of which

have the effect of giving the speed of light an exact value, equal to the recommended
value, and that this introduces no appreciable discontinuity into the unit of length,
taking into account the relative uncertainty of ± 4

−

of the best realizations of the

present definition of the meter,

•

that these various forms, making reference either to the path travelled by light in a

specified time interval or to the wavelength of a radiation of measured or specified
frequency, have been the object of consultations and deep discussions, have been
recognized as being equivalent and that a consensus has emerged in favour of the
first form,

•

that the Comité Consultatif pour la Définition du Mètre (CCDM) is now in a position to

give instructions for the practical realization of such a definition, instructions which
could include the use of the orange radiation of krypton 86 used as standard up to
now, and which may in due course be extended or revised,

decides

1. The meter is the length of the path travelled by light in vacuum during a time interval of

1/299 792 458 of a second,

2. The definition of the meter in force since 1960, based upon the transition between the

levels 2p

and 5d

of the atom of krypton 86, is abrogated.

The relative uncertainty
given here corresponds to
three standard deviations
in the data considered.

Appendix 1

•

■

On the realization of the definition of the meter

(CR, 98 and

Metrologia

1984,

, 25-26)

Resolution 2

The 17th Conférence Générale des Poids et Mesures,

invites

the Comité International des Poids et Mesures

•

to draw up instructions for the practical realization of the new definition of the meter,

•

to choose radiations which can be recommended as standards of wavelength for the

interferometric measurement of length and to draw up instructions for their use,

•

to pursue studies undertaken to improve these standards.

CIPM, 1984

■

Concerning the sievert

(PV,

31 and

Metrologia

, 1985,

, 90)*

Recommendation 1

The Comité International des Poids et Mesures,

considering

the confusion which continues to exist on the subject of Resolution 5,

approved by the 16th Conférence Générale des Poids et Mesures (1979),

decides

to introduce the following explanation in the brochure “Le Système International

d'Unités (SI)”:

The quantity dose equivalent

is the product of the absorbed dose

of ionizing radiation

and the dimensionless factors

(quality factor) and

(product of any other multiplying

factors) stipulated by the International Commission on Radiological Protection:

H = Q · N · D .

Thus, for a given radiation, the numerical value of

in joules per kilogram may differ from

that of

in joules per kilogram depending upon the values of

and

In order to avoid

any risk of confusion between the absorbed dose

and the dose equivalent

, the

special names for the respective units should be used, that is, the name gray should be
used instead of joules per kilogram for the unit of absorbed dose

and the name sievert

instead of joules per kilogram for the unit of dose equivalent

18th CGPM, 1987

■

Forthcoming adjustment to the representations of the volt and of the

ohm

(CR, 100 and

Metrologia

, 1988,

, 115)

Resolution 6

The 18th Conférence Générale des Poids et Mesures,

considering

•

that worldwide uniformity and long-term stability of national representations of the

electrical units are of major importance for science, commerce and industry from both
the technical and economic points of view,

•

that many national laboratories use the Josephson effect and are beginning to use the

quantum Hall effect to maintain, respectively, representations of the volt and of the
ohm, as these offer the best guarantees of long-term stability,

See Recommendation 1
(CI-2002) of the CIPM on
the revision of the practical
realization of the definition
of the meter, p. 76.

* The CIPM, in 2002,
decided to change the
explanation of the
quantity dose equivalent
in the SI Brochure
(Recommendation 2,
see p. 78).

•

Appendix 1

•

that because of the importance of coherence among the units of measurement of the

various physical quantities the values adopted for these representations must be as
closely as possible in agreement with the SI,

•

that the results of recent and current experiment will permit the establishment of an

acceptable value, sufficiently compatible with the SI, for the coefficient which relates
each of these effects to the corresponding electrical unit,

invites

the laboratories whose work can contribute to the establishment of the quotient

voltage/frequency in the case of the Josephson effect and of the quotient voltage/current
for the quantum Hall effect to vigorously pursue these efforts and to communicate their
results without delay to the Comité International des Poids et Mesures, and

instructs

the Comité International des Poids et Mesures to recommend, as soon as it

considers it possible, a value for each of these quotients together with a date for them to
be put into practice simultaneously in all countries; these values should be announced at
least one year in advance and would be adopted on 1 January 1990.

CIPM, 1988

■

Representation of the volt by means of the Josephson effect

(PV,

, 44

and

Metrologia

, 1989,

, 69)

Recommendation 1

The Comité International des Poids et Mesures,

acting

in accordance with instructions given in Resolution 6 of the 18th Conférence

Générale des Poids et Mesures concerning the forthcoming adjustment of the
representations of the volt and the ohm,

considering

•

that a detailed study of the results of the most recent determinations leads to a value

of 483 597.9 GHz/V for the Josephson constant,

that is to say, for the quotient of

frequency divided by the potential difference corresponding to the

n =

1 step in the

Josephson effect,

•

that the Josephson effect, together with this value of

can be used to establish a

reference standard of electromotive force having a one-standard-deviation uncertainty
with respect to the volt estimated to be 4 parts in 10

, and a reproducibility which is

significantly better,

recommends

•

that 483 597.9 GHz/V exactly be adopted as a conventional value, denoted by

J-90

for

the Josephson constant,

•

that this new value be used from 1 January 1990, and not before, to replace the

values currently in use,

•

that this new value be used from this same date by all laboratories which base their

measurements of electromotive force on the Josephson effect, and

•

that from this same date all other laboratories adjust the value of their laboratory

reference standards to agree with the new adopted value,

is of the opinion

that no change in this recommended value of the Josephson constant

will be necessary in the foreseeable future, and

draws the attention

of laboratories to the fact that the new value is greater by

3.9 GHz/V, or about 8 parts in 10

, than the value given in 1972 by the Comité Consultatif

d'Électricité in its Declaration E-72.

Appendix 1

•

■

Representation of the ohm by means of the quantum Hall effect

(PV,

45 and

Metrologia

, 1989,

, 70)

Recommendation 2

The Comité International des Poids et Mesures,

acting

in accordance with instructions given in Resolution 6 of the 18th Conférence

Générale des Poids et Mesures concerning the forthcoming adjustment of the
representations of the volt and the ohm,

considering

•

that most existing laboratory reference standards of resistance change significantly

with time,

•

that a laboratory reference standard of resistance based on the quantum Hall effect

would be stable and reproducible,

•

that a detailed study of the results of the most recent determinations leads to a value

of 25 812.807

for the von Klitzing constant,

that is to say, for the quotient of the

Hall potential difference divided by current corresponding to the plateau

= 1 in the

quantum Hall effect,

•

that the quantum Hall effect, together with this value of

, can be used to establish a

reference standard of resistance having a one-standard-deviation uncertainty with
respect to the ohm estimated to be 2 parts in 10

, and a reproducibility which is

significantly better,

recommends

•

that

812.807

exactly be adopted as a conventional value, denoted by

K-90

, for

the von Klitzing constant,

•

that this value be used from 1 January 1990, and not before, by all laboratories which

base their measurements of resistance on the quantum Hall effect,

•

that from this same date all other laboratories adjust the value of their laboratory

reference standards to agree with

K-90

•

that in the use of the quantum Hall effect to establish a laboratory reference standard

of resistance, laboratories follow the most recent edition of the technical guidelines for
reliable measurements of the quantized Hall resistance drawn up by the Comité
Consultatif d'Électricité and published by the Bureau International des Poids et
Mesures, and

is of the opinion

that no change in this recommended value of the von Klitzing constant

will be necessary in the foreseeable future.

CIPM, 1989

■

The International Temperature Scale of 1990

(PV,

, 115 and

Metrologia

1990,

, 13)

Recommendation 5

The Comité International des Poids et Mesures (CIPM) acting in accordance with
Resolution 7 of the 18th Conférence Générale des Poids et Mesures (1987) has adopted
the International Temperature Scale of 1990 (ITS-90) to supersede the International
Practical Temperature Scale of 1968 (IPTS-68).

The CIPM

notes

that, by comparison with the IPTS-68, the ITS-90

At its 89th meeting in
2000, the CIPM approved
the declaration of the
22nd meeting of the
CCEM on the use of the
value of the von Klitzing
constant, see p. 76.

•

Appendix 1

•

extends to lower temperatures, down to 0.65 K, and hence also supersedes the

EPT-76,

•

is in substantially better agreement with corresponding thermodynamic temperatures,

•

has much improved continuity, precision and reproducibility throughout its range and

•

has subranges and alternative definitions in certain ranges which greatly facilitate its

use.

The CIPM also

notes

that, to accompany the text of the ITS-90 there will be two further

documents, the

Supplementary Information for the ITS-90

and

Techniques for

Approximating the ITS-90

. These documents will be published by the BIPM and

periodically updated.

The CIPM

recommends

•

that on 1 January 1990 the ITS-90 come into force and

•

that from this same date the IPTS-68 and the EPT-76 be abrogated.

19th CGPM, 1991

■

SI prefixes zetta, zepto, yotta and yocto

(CR, 185 and

Metrologia

, 1992,

, 3)

Resolution 4

The 19th Conférence Générale des Poids et Mesures (CGPM)

decides

to add to the list of SI prefixes to be used for multiples and submultiples of units,

adopted by the 11th CGPM, Resolution 12, paragraph 3, the 12th CGPM, Resolution 8
and the 15th CGPM, Resolution 10, the following prefixes:

Multiplying factor

Prefix

Symbol

zetta

−

zepto

yotta

−

yocto

20th CGPM, 1995

■

Elimination of the class of supplementary units in the SI

(CR, 223 and

Metrologia

, 1996,

, 83)

Resolution 8

The 20th Conférence Générale des Poids et Mesures (CGPM),

considering

•

that the 11th Conférence Générale in 1960 in its Resolution 12, establishing the

Système International d’Unités, SI, distinguished between three classes of SI units:
the base units, the derived units, and the supplementary units, the last of these
comprising the radian and the steradian,

•

that the status of the supplementary units in relation to the base units and the derived

units gave rise to debate,

•

that the Comité International des Poids et Mesures, in 1980, having observed that the

ambiguous status of the supplementary units compromises the internal coherence of

The names zepto and zetta
are derived from septo
suggesting the number
seven (the seventh power
of 10

) and the letter “z” is

substituted for the letter
“s” to avoid the duplicate
use of the letter “s” as a
symbol. The names yocto
and yotta are derived from
octo, suggesting the
number eight (the eighth
power of 10

); the letter

“y” is added to avoid the
use of the letter “o” as a
symbol because it may be
confused with the number
zero.

Appendix 1

•

the SI, has in its Recommendation 1 (CI-1980) interpreted the supplementary units, in
the SI, as dimensionless derived units,

approving

the interpretation given by the Comité International in 1980,

decides

•

to interpret the supplementary units in the SI, namely the radian and the steradian, as

dimensionless derived units, the names and symbols of which may, but need not, be
used in expressions for other SI derived units, as is convenient,

•

and, consequently, to eliminate the class of supplementary units as a separate class

in the SI.

21st CGPM, 1999

■

The definition of the kilogram

(CR, 331 and

Metrologia

, 2000,

, 94)

Resolution 7

The 21st Conférence Générale des Poids et Mesures,

considering

•

the need to assure the long-term stability of the International System of Units (SI),

•

the intrinsic uncertainty in the long-term stability of the artifact defining the unit of

mass, one of the base units of the SI,

•

the consequent uncertainty in the long-term stability of the other three base units of

the SI that depend on the kilogram, namely, the ampere, the mole and the candela,

•

the progress already made in a number of different experiments designed to link the

unit of mass to fundamental or atomic constants,

•

the desirability of having more than one method of making such a link,

recommends

that national laboratories continue their efforts to refine experiments that

link the unit of mass to fundamental or atomic constants with a view to a future redefinition
of the kilogram.

■

Special name for the SI derived unit mole per second, the katal, for the

expression of catalytic activity

(CR, 334-335 and

Metrologia

, 2000,

, 95)

Resolution 12

The 21st Conférence Générale des Poids et Mesures,

considering

•

the importance for human health and safety of facilitating the use of SI units in the

fields of medicine and biochemistry,

•

that a non-SI unit called “unit,” symbol U, equal to 1

mol

min

–1

, which is not coherent

with the International System of Units (SI), has been in widespread use in medicine
and biochemistry since 1964 for expressing catalytic activity,

•

that the absence of a special name for the SI coherent derived unit mole per second

has led to results of clinical measurements being given in various local units,

•

that the use of SI units in medicine and clinical chemistry is strongly recommended by

the international unions in these fields,

•

Appendix 1

•

that the International Federation of Clinical Chemistry and Laboratory Medicine has

asked the Consultative Committee for Units to recommend the special name katal,
symbol kat, for the SI unit mole per second,

•

that while the proliferation of special names represents a danger for the SI, exceptions

are made in matters related to human health and safety (15th General Conference,
1975, Resolutions 8 and 9, 16th General Conference, 1979, Resolution 5),

noting

that the name katal, symbol kat, has been used for the SI unit mole per second for

over thirty years to express catalytic activity,

decides

to adopt the special name katal, symbol kat, for the SI unit mole per second to

express catalytic activity, especially in the fields of medicine and biochemistry,

and

recommends

that when the katal is used, the measurand be specified by reference

to the measurement procedure; the measurement procedure must identify the indicator
reaction.

CIPM, 2000

■

“use of the von Klitzing constant to express the value of a reference

standard of resistance as a function of quantum Hall effect”

(PV,

101)

At its 89th meeting in 2000, the CIPM approved the following declaration of the
22nd meeting of the CCEM (CCEM,

, 90):

“The CCEM, having reviewed the 1998 CODATA least squares adjustment of the
fundamental constants, is now of the opinion that the quantum Hall effect, together with
the value of

K-90

, can be used to establish a reference standard of resistance having a

relative one standard deviation uncertainty with respect to the ohm, estimated to be
1

−

, and a reproducibility which is significantly better. This represents a reduction in

the uncertainty of a factor of two compared with the 1988 recommendation.”

CIPM, 2001

■

“SI units” and “units of the SI”

(PV,

120)

The CIPM approved in 2001 the following proposal of the CCU regarding “SI
units” and “units of the SI”:

“We suggest that “SI units” and “units of the SI” should be regarded as names that include
both the base units and the coherent derived units, and also all units obtained by
combining these with the recommended multiple and sub-multiple prefixes.

We suggest that the name “coherent SI units” should be used when it is desired to restrict
the meaning to only the base units and the coherent derived units.”

CIPM, 2002

■

Revision of the practical realization of the definition of the meter

(PV,

194-204 and

Metrologia

, 103-133)

Recommendation 1

The International Committee for Weights and Measures,

recalling

Appendix 1

•

that in 1983 the 17th General Conference (CGPM) adopted a new definition of the

meter;

•

that in the same year the CGPM invited the International Committee (CIPM)

•

to draw up instructions for the practical realization of the meter,

•

to choose radiations which can be recommended as standards of wavelength for

the interferometric measurement of length and draw up instructions for their use,

•

to pursue studies undertaken to improve these standards and in due course to

extend or revise these instructions;

•

that in response to this invitation the CIPM adopted Recommendation 1 (CI-1983)

(

mise en pratique

of the definition of the meter) to the effect

•

that the meter should be realized by one of the following methods:

(a) by means of the length

of the path travelled in vacuum by a plane

electromagnetic wave in a time

; this length is obtained from the measured time

using the relation

l = c

and the value of the speed of light in vacuum

299 792 458 m/s,

(b) by means of the wavelength in vacuum

of a plane electromagnetic wave of

frequency

; this wavelength is obtained from the measured frequency

using the

relation

= c

and the value of the speed of light in vacuum

299 792 458 m/s,

vacuum or whose stated frequency can be used with the uncertainty shown,
provided that the given specifications and accepted good practice are followed;

•

that in all cases any necessary corrections be applied to take account of actual

conditions such as diffraction, gravitation or imperfection in the vacuum;

•

that in the context of general relativity, the meter is considered a unit of proper

length. Its definition, therefore, applies only within a spatial extent sufficiently small
that the effects of the non-uniformity of the gravitational field can be ignored (note
that, at the surface of the Earth, this effect in the vertical direction is about 1 part in
10

per meter). In this case, the effects to be taken into account are those of

special relativity only. The local methods for the realization of the meter
recommended in (b) and (c) provide the proper meter but not necessarily that
given in (a). Method (a) should therefore be restricted to lengths

which are

sufficiently short for the effects predicted by general relativity to be negligible with
respect to the uncertainties of realization. For advice on the interpretation of
measurements in which this is not the case, see the report of the Consultative
Committee for Time and Frequency (CCTF) Working Group on the Application of
General Relativity to Metrology (Application of general relativity to metrology,

Metrologia

, 1997,

, 261-290);

•

that the CIPM had already recommended a list of radiations for this purpose;

recalling

also that in 1992 and in 1997 the CIPM revised the practical realization of the

definition of the meter;

considering

•

that science and technology continue to demand improved accuracy in the realization

of the meter;

•

that since 1997 work in national laboratories, in the BIPM and elsewhere has identified

new radiations and methods for their realization which lead to lower uncertainties;

•

that there is an increasing move towards optical frequencies for time-related activities,

and that there continues to be a general widening of the scope of application of the
recommended radiations of the

mise en pratique

to cover not only dimensional

•

Appendix 1

metrology and the realization of the meter, but also high-resolution spectroscopy,
atomic and molecular physics, fundamental constants and telecommunication;

•

that a number of new frequency values with reduced uncertainties for radiations of

high-stability cold atom and ion standards already listed in the recommended
radiations list are now available, that the frequencies of radiations of several new cold
atom and ion species have also recently been measured, and that new improved
values with substantially reduced uncertainties for a number of optical frequency
standards based on gas cells have been determined, including the wavelength region
of interest to optical telecommunications;

•

that new femtosecond comb techniques have clear significance for relating the

frequency of high-stability optical frequency standards to that of the frequency
standard realizing the SI second, that these techniques represent a convenient
measurement technique for providing traceability to the International System of Units
(SI) and that comb technology also can provide frequency sources as well as a
measurement technique;

recognizes

comb techniques as timely and appropriate, and recommends further

research to fully investigate the capability of the techniques;

welcomes

validations now being made of comb techniques by comparison with other

frequency chain techniques;

urges

national metrology institutes and other laboratories to pursue the comb technique

to the highest level of accuracy achievable and also to seek simplicity so as to encourage
widespread application;

recommends

•

that the list of recommended radiations given by the CIPM in 1997 (Recom-