untitled

The BIPM
and the Metre Convention

The International Bureau of Weights and Measures (BIPM) was set up by the Metre
Convention signed in Paris on 20 May 1875 by seventeen States during the final
session of the diplomatic Conference of the Metre. 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 Metre 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 Metre 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 Metre Convention. The principal task of the CIPM is to ensure
worldwide uniformity in units of measurement. It does this by direct action or by
submitting proposals to the CGPM.

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.

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 in 1876

-1878, were enlarged in

1929; new buildings were constructed in 1963-1964 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 Metre (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
Metre Convention.

The International System of Units

Contents

The BIPM and the Metre Convention

Preface to the 8th edition

101

1 Introduction

103

1.1 Quantities and units

103

1.2 The International System of Units (SI) and the corresponding

system of quantities

104

1.3 Dimensions of quantities

105

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

106

1.5 SI units in the framework of general relativity

107

1.6 Units for quantities that describe biological effects

107

1.7 Legislation on units

108

1.8 Historical

note

108

2 SI units

111

2.1 SI base units

111

2.1.1 Definitions

111

2.1.1.1 Unit of length (metre)

112

2.1.1.2 Unit of mass (kilogram)

112

2.1.1.3 Unit of time (second)

112

2.1.1.4 Unit of electric current (ampere)

113

2.1.1.5 Unit of thermodynamic temperature (kelvin)

113

2.1.1.6 Unit of amount of substance (mole)

114

2.1.1.7 Unit of luminous intensity (candela)

115

2.1.2 Symbols for the seven base units

116

2.2 SI derived units

116

2.2.1 Derived units expressed in terms of base units

116

2.2.2 Units with special names and symbols; units that incorporate

special names and symbols

117

2.2.3 Units for dimensionless quantities, also called

quantities of dimension one

120

3 Decimal multiples and submultiples of SI units

121

3.1 SI

prefixes

121

3.2 The

kilogram

122

4 Units outside the SI

123

4.1 Non-SI units accepted for use with the SI, and units based

on fundamental constants

123

4.2 Other non-SI units not recommended for use

129

5 Writing unit symbols and names, and expressing the values

of quantities

130

5.1 Unit

symbols

130

5.2 Unit

names

131

5.3 Rules and style conventions for expressing values of quantities

131

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

quantity

calculus

131

5.3.2 Quantity symbols and unit symbols

132

5.3.3 Formatting the value of a quantity

133

5.3.4 Formatting numbers, and the decimal marker

133

5.3.5 Expressing the measurement uncertainty in the value of a quantity

133

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

numbers

134

5.3.7 Stating values of dimensionless quantities, or quantities of

dimension one

134

Appendix 1. — Decisions of the CGPM and the CIPM

137

Appendix 2. — Practical realization of the definitions of some important

units

172

Appendix 3. — Units for photochemical and photobiological quantities

173

List of acronyms

175

Index

177

103

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 metre, m, and
the second, s, may be
chosen as base units. Speed

is then taken as a derived

quantity, with the derived
unit metre 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 metre per second

and kilometre 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 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

104

•

Introduction

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 metre, 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 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

* Acronyms used in this Brochure are listed with their meaning on p. 175.

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

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

•

105

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

d and d

, is written

)

(

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, CGS-EMU, 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
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

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

−

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.

106

•

Introduction

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. 118). 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. 119).

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. 121, 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. 155) 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 SI units, the
resulting units are no longer coherent, because a prefix on a derived unit effectively
introduces a numerical factor in the expression for the derived 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. 122).
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 SI

Note, however, that the decimal multiples and submultiples of the SI units do not
form a coherent set.

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

−

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

The metre per second,
symbol m/s, is the coherent
SI unit of speed. The
kilometre per second, km/s,
the centimetre per second,
cm/s, and the millimetre per
second, mm/s, are also SI
units, but they are not
coherent SI units.

Introduction

•

107

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 metre 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
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

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).

108

•

Introduction

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

Convention du Mètre

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 metre
and the kilogram, on 22 June 1799, in the Archives de la République in Paris can

Introduction

•

109

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

millimetre, 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 centimetre, 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.

•

After the signing of the

Convention du Mètre

on 20 May 1875, which created the

BIPM and established the CGPM and the CIPM, work began on the construction
of new international prototypes of the metre and kilogram. In 1889 the first
CGPM sanctioned the international prototypes for the metre and the kilogram.
Together with the astronomical second as the unit of time, these units constituted
a three-dimensional mechanical unit system similar to the CGS system, but with
the base units metre, kilogram, and second, the MKS system.

•

In 1901 Giorgi showed that it is possible to combine the mechanical units of this
metre-kilogram-second system with the practical electrical units to form a single
coherent four-dimensional system by adding to the three base units a fourth unit,
of an electrical nature such as the ampere or the ohm, and rewriting the equations
occurring in electromagnetism in the so-called rationalized form. Giorgi’s
proposal opened the path to a number of new developments.

•

After the revision of the

Convention du Mètre

by the 6th CGPM in 1921, which

extended the scope and responsibilities of the BIPM to other fields in physics,
and the subsequent creation of the Consultative Committee for Electricity (CCE)
by the 7th CGPM in 1927, the Giorgi proposal was thoroughly discussed by the
IEC, the International Union of Pure and Applied Physics (IUPAP), and other
international organizations. This led the CCE to propose, in 1939, the adoption of
a four-dimensional system based on the metre, kilogram, second, and ampere, the
MKSA system, a proposal approved by the CIPM in 1946.

111

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,

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. 163 and 166, 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 metre, kilogram, second, ampere, kelvin, mole, and candela – are in a
number of instances interdependent. Thus the definition of the metre incorporates the
second; the definition of the ampere incorporates the metre, kilogram, and second; the
definition of the mole incorporates the kilogram; and the definition of the candela
incorporates the metre, kilogram, and second.

112

•

SI units

2.1.1.1 Unit of length (metre)

The 1889 definition of the metre, 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 metre 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 metre 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 metres per second,

= 299 792 458 m/s.

The original international prototype of the metre, 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 artefact 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. 143.

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).

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

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

•

113

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 caesium 133 atom.

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

(hfs Cs) = 9 192 631 770 Hz.

At its 1997 meeting the CIPM affirmed that:

This definition refers to a caesium 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 caesium 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 metre apart in vacuum, would produce between these
conductors a force equal to 2 × 10

−

newton per metre of length.

It follows that the magnetic constant,

, also known as the permeability of free

space, is exactly 4

−7

henries per metre,

= 4

−7

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 symbol,

(hfs Cs), is

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

114

•

SI units

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

O 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).

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

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

(X),

where the atomic entity X
should be specified, and for
relative molecular mass of a
molecule (molecular
weight) it is

(X), where

the molecular entity X
should be specified.

The symbol,

tpw

, is used to

denote the thermodynamic
temperature of the triple
point of water.

SI units

•

115

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

(X) denotes the number of entities

X in a specified sample, and if

(X) denotes the amount of substance of entities X in

the same sample, the relation is

(X) =

(X)/

Note that since

(X) is dimensionless, and

(X) 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

The molar mass of an atom
or molecule X is denoted

(X) or

, and is the mass

per mole of X.

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

116

•

SI units

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,

= 683 lm/W

= 683 cd sr/W.

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)).

Table 1. SI base units

Base quantity

SI base unit

_________________________________

___________________________

Name

Symbol

Name

Symbol

length

l, x, r

etc.

metre

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. 106).

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

•

117

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

metre

volume

cubic

metre

speed, velocity

metre per second

m/s

acceleration

metre per second squared

m/s

wavenumber

reciprocal

metre

−

density, mass density

kilogram per cubic metre

kg/m

surface density

kilogram per square metre

kg/m

specific volume

cubic metre per kilogram

/kg

current density

ampere per square metre

A/m

magnetic field strength

ampere per metre

A/m

amount concentration

(

)

mole per cubic metre

mol/m

concentration
mass concentration

kilogram per cubic metre

kg/m

luminance

candela per square metre

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.

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.

118

•

SI units

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

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.

(

) 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.

(

)

See CIPM Recommendation 2 (CI-2002), p. 168, on the use of the sievert (PV, 2002,

, 205).

SI units

•

119

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 metre

N m

kg s

−

surface tension

newton per metre

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 metre

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 metre kelvin

W/(m K) m kg s

−

energy density

joule per cubic metre

J/m

−1

kg s

−

electric field strength

volt per metre

V/m

m kg s

−

electric charge density

coulomb per cubic metre

C/m

−

s A

surface charge density

coulomb per square metre

C/m

−

s A

electric flux density,

coulomb per square metre

C/m

−

s A

electric

displacement

permittivity

farad per metre

F/m

−

permeability

henry per metre

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 metre steradian

W/(m

sr) m

−

kg s

−

= kg s

−

catalytic activity

katal per cubic metre

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. 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 metre, or kilogram metre 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

120

•

SI units

may be thought of as the cross product of force and distance, suggesting the unit
newton metre, 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 2π 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

is length. For all these cases the unit may be considered as the number one, which is a
dimensionless derived unit.

Another class of dimensionless quantities are numbers that represent a count, such as
a number of molecules, degeneracy (number of energy levels), and partition function
in statistical thermodynamics (number of thermally accessible states). All of these
counting quantities are also described as being dimensionless, or of dimension one,
and are taken to have the SI unit one, although the unit of counting quantities cannot
be described as a derived unit expressed in terms of the base units of the SI. For such
quantities, the unit one may instead be regarded as a further base unit.

In a few cases, however, a special name is given to the unit one, in order to facilitate
the identification of the quantity involved. This is the case for the radian and the
steradian. The radian and steradian have been identified by the CGPM as special
names for the coherent derived unit one, to be used to express values of plane angle
and solid angle, respectively, and are therefore included in Table 3.

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: Recommenda-
tion 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. 161 and 168,
respectively.

121

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

by 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

deca 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
(deca), 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.

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

−

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 (picometre)
mmol (millimole)
GΩ (gigaohm)
THz (terahertz)

124

•

Units outside the SI

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 litre, and the 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

litre

(

)

L, l

1 L = 1 l = 1 dm

= 10

−

mass

tonne

(

)

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 centre 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 as or

″

, milliarcseconds, microarcseconds, and picoarcseconds, denoted mas,

µas, 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 litre, 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).

(

) 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

•

125

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 three 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 2π, 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

ħ/m

. 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

/(4π

∞

), where

is the fine-structure

constant and

∞

is the Rydberg constant; and

/(4π

) = 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 and atomic physics, and quantum chemistry,
respectively. Standard uncertainties in the least significant digits are shown in
parenthesis after each numerical value.

126

•

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

ħ/

(

)

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

ħ/E

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. 133).

(

) 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
metres 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).

Units outside the SI

•

127

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 neperian (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

millimetre of mercury

(

)

mmHg

1 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 25 bar,
or 101 325 Pa.

(

) The millimetre 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.

(

) 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 centre of the Earth, which is convenient when latitude and longitude are
measured in degrees and minutes of angle.

128

•

Units outside the SI

(

) 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 neperian logarithmic amplitude ratio, or the neperian amplitude

level difference.

(

) The

statement

dB = (

/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 (centimetre-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 centimetre, 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.).

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.

Units outside the SI

•

129

(

) 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

www.bipm.org/en/si/si_brochure/chapter4/conversion_factors.html

130

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 litre, in order to avoid possible confusion between
the numeral 1 (one) and the lower-case letter l (el).
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 (centred) 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 millimetre), cc (for either

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

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.

m, metre
s, second
Pa, pascal
Ω, ohm

L or l, litre

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 metre

m/s or

or m s

–1

for metre per second

ms, millisecond
m s, metre times second

m kg/(s

A),

or m kg s

–3

–1

but not

m kg/s

nor

m kg/s

Writing unit symbols and names

•

131

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.
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

milligram,

but not

milli-gram

kilopascal,

but not

kilo-pascal

pascal second, or
pascal-second

metre per second squared,
square centimetre,
cubic millimetre,
ampere per square metre,
kilogram per cubic metre.

unit name symbol

joule

hertz

metre

second    s
ampere    A
watt   W

2.6 m/s,
or 2.6 metres 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 metres per second, and
90 is the numerical value of
the speed in the unit
kilometres per hour.

132

•

Writing unit symbols and names

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/

(

)

Algebraically equivalent forms may be used in place of 10

, such as kK/

, or

(

/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.

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

•

133

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 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

= 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 kΩ resistor

a 35-millimetre film

= 12.3 g where

is used

as a symbol for the quantity
mass, but

= 30° 22′ 8″,

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

134

•

Writing unit symbols and names

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

−

When multiplying the value of quantities either a multiplication sign,

, or brackets

should be used, not a half-high (centred) 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. 127).
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.
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

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

= 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

= 1.51,

but not

= 1.51 × 1,

where

is the quantity

symbol for refractive index.

138

•

Appendix 1

Table of Contents of Appendix 1

Decisions relating to the establishment of the SI

page

9th

CGPM, 1948:

decision to establish the SI

145

10th CGPM, 1954:

decision on the first six base units

147

CIPM 1956:

decision to adopt the name “Système International d’Unités”

148

11th CGPM, 1960:

confirms the name and the abbreviation “SI”,

149

names prefixes from tera to pico,

149

establishes the supplementary units rad and sr,

149

lists some derived units

150

CIPM, 1969:

declarations concerning base, supplementary,

derived and coherent units, and the use of prefixes

155

CIPM, 2001

“SI units” and “units of the SI”

166

Decisions relating to the base units of the SI

Length

1st CGPM, 1889:

sanction of the prototype metre

142

7th CGPM, 1927:

definition and use of the prototype metre

143

11th CGPM, 1960:

redefinition of the metre in terms of krypton 86 radiation

148

15th CGPM, 1975:

recommends value for the speed of light

157

17th CGPM, 1983:

redefinition of the metre using the speed of light,

160

ealization of the definition of the metre

161

CIPM, 2002:

specifies the rules for the practical realization of the

definition of the metre

166

CIPM, 2003:

revision of the list of recommended radiations

169

CIPM, 2005:

revision of the list of recommended radiations

171

Mass

1st CGPM, 1889:

sanction of the prototype kilogram

142

3rd CGPM, 1901:

declaration on distinguishing mass and weight,

and on the conventional value of

143

CIPM, 1967:

declaration on applying prefixes to the gram

152

21st CGPM, 1999:

future redefinition of the kilogram

165

Time

CIPM, 1956:

definition of the second as a fraction of the

tropical year 1900

147

11th CGPM, 1960:

ratifies the CIPM 1956 definition of the second

148

Appendix 1

•

139

page

CIPM, 1964:

declares the caesium 133 hyperfine transition

to be the recommended standard

151

12th CGPM, 1964:

empowers CIPM to investigate atomic

and molecular frequency standards

151

13th CGPM, 1967/68: defines the second in terms of the caesium transition

153

CCDS, 1970:

defines International Atomic Time, TAI

155

4th CGPM, 1971:

requests the CIPM to define and establish

International Atomic Time, TAI

156

15th CGPM, 1975:

endorses the use of Coordinated Universal Time, UTC

157

Electrical units

CIPM, 1946:

definitions of mechanical and electrical units in the SI

144

14th CGPM, 1971:

adopts the name siemens, symbol S, for electrical

conductance

156

18th CGPM, 1987:

forthcoming adjustment to the representations of

the volt and of the ohm

161

CIPM, 1988:

Josephson effect

162

CIPM, 1988:

quantum Hall effect

163

CIPM, 2000:

realization of the ohm using the value of the

von Klitzing constant

166

Thermodynamic temperature

9th CGPM, 1948:

adopts the triple point of water as the thermodynamic

reference point,

144

adopts the zero of Celsius temperature to be

0.01 degree below the triple point

144

CIPM, 1948:

adopts the name degree Celsius for the Celsius

temperature

scale

145

10th CGPM, 1954:

defines thermodynamic temperature such that the

triple point of water is 273.16 degrees Kelvin exactly,

146

defines standard atmosphere

147

13th CGPM, 1967/68: decides formal definition of the kelvin, symbol K

154

CIPM, 1989:

the International Temperature Scale of 1990, ITS-90

163

CIPM, 2005:

note added to the definition of the kelvin concerning the

isotopic composition of water

170

Amount of substance

14th CGPM, 1971:

definition of the mole, symbol mol, as a seventh

base unit, and rules for its use

156

21st CGPM, 1999:

adopts the special name katal, kat

165

140

•

Appendix 1

Luminous

intensity

page

CIPM, 1946:

definition of photometric units, new candle and new lumen

143

13th CGPM, 1967/68: defines the candela, symbol cd, in terms of a black body

154

16th CGPM, 1979:

redefines the candela in terms of monochromatic radiation

158

Decisions relating to SI derived and supplementary units

SI derived units

12th CGPM, 1964:

accepts the continued use of the curie as a non-SI unit

152

13th CGPM, 1967/68: lists some examples of derived units

154

15th CGPM, 1975:

adopts the special names becquerel, Bq, and gray, Gy

157

16th CGPM, 1979:

adopts the special name sievert, Sv

159

CIPM, 1984:

decides to clarify the relationship between absorbed dose

(SI unit gray) and dose equivalent (SI unit sievert)

161

CIPM, 2002:

modifies the relationship between absorbed dose

and dose equivalent

168

Supplementary units

CIPM, 1980:

decides to interpret supplementary units

as dimensionless derived units

159

20th CGPM, 1995:

decides to abrogate the class of supplementary units,

and confirms the CIPM interpretation that they are

dimensionless derived units

164

Decisions concerning terminology and the acceptance of units for use with the SI

SI prefixes

12th CGPM, 1964:

decides to add femto and atto to the list of prefixes

152

15th CGPM, 1975:

decides to add peta and exa to the list of prefixes

158

19th CGPM, 1991:

decides to add zetta, zepto, yotta, and yocto to the

list of prefixes

164

Unit symbols and numbers

9th CGPM, 1948:

decides rules for printing unit symbols

146

Unit names

13th CGPM, 1967/68: abrogates the use of the micron and new candle

155

as units accepted for use with the SI

The decimal marker

22nd CGPM, 2003:

decides to allow the use of the point or the comma

on the line as the decimal marker

169

142

•

Appendix 1

1st CGPM, 1889

Sanction of the international prototypes of the metre 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 Metre Commission and of the CIPM, the
fundamental measurements of the international and national prototypes of the metre
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 metre 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 Metre and the equality in mass of the

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

•

that the differences between the national Metres and the international Metre lie within

0.01 millimetre 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 Metre and Kilogram and the national Metres and Kilograms fulfil

the requirements of the Metre Convention,

sanctions

A. As regards international prototypes:

1. The Prototype of the metre 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 Metres have been established.

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

…

3rd CGPM, 1901

Declaration concerning the definition of the litre

(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 “litre”.

2. …

* The definition of the
metre was abrogated in
1960 by the 11th CGPM
(Resolution 6,
see p. 148).

* This definition was
abrogated in 1964 by the
12th CGPM (Resolution 6,
see p. 152).

Appendix 1

•

143

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 metre by the international Prototype

(CR, 49)

The unit of length is the metre, 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 metre 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 centimetre 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 centimetre.

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. …

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. 148).

* 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. 154).

144

•

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 (metre, kilogram, second) system] is the

force which gives to a mass of 1 kilogram an acceleration of 1 metre 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 metre 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 metre apart in vacuum, would produce between these
conductors a force equal to 2

−

MKS unit of force [newton] per metre 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.

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.

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

•

145

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

, 21,

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 Metre Convention.

146

•

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

•

metre

ampere

•

square metre

volt

•

cubic metre

watt

•

micron

ohm

Ω

•

litre

coulomb

•

gram

farad

•

tonne

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

* 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. 155 and 153,
respectively), and the litre;
16th CGPM, 1979
(Resolution 6, see p. 159).

* The 13th CGPM in 1967
explicitly defined the
kelvin (Resolution 4, see
p. 154).

Appendix 1

•

147

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 centimetre,

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

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

metre

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

* The unit name “degree
kelvin” was changed to
“kelvin” in 1967 by the
13th CGPM (Resolution 3,
see p. 153).

* This definition was
abrogated in 1967 by the
13th CGPM (Resolution 1,
see p. 153).

148

•

Appendix 1

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 Metre 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 metre

(CR, 85)

Resolution 6

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

considering

•

that the international Prototype does not define the metre 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 metre 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 metre in force since 1889, based on the international Prototype of

platinum-iridium, is abrogated.

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

kept at the BIPM under the conditions specified in 1889.

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,

* This definition was
abrogated in 1983 by the
17th CGPM (Resolution 1,
see p. 160).

* This definition was
abrogated in 1967 by the
13th CGPM (Resolution 1,
see p. 153).

Appendix 1

•

149

•

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

metre

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

deca

0.000 000 000 001 = 10

−

pico

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

* 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. 156)

The name and symbol for
the unit of thermodynamic
temperature was modified
by the 13th CGPM in 1967
(Resolution 3, see p. 153).

Further

prefixes were

adopted by the 12th CGPM
in 1964 (Resolution 8,
see p. 152),
the 15th CGPM in 1975
(Resolution 10, see p. 158)
and the 19th CGPM in
1991 (Resolution 4,
see p. 164).

The 20th CGPM in 1995
abrogated the class of
supplementary units in the
SI (Resolution 8, see
p. 164). These are now
considered as derived
units.

150

•

Appendix 1

Derived units

area

square

metre

volume

cubic

metre

frequency

hertz

1/s

mass density (density)

kilogram per cubic metre

kg/m

speed, velocity

metre per second

m/s

angular velocity

radian per second

rad/s

acceleration

metre per second squared

m/s

angular acceleration

radian per second squared

rad/s

force

newton

kg · m/s

pressure (mechanical stress) newton per square metre

N/m

kinematic viscosity

square metre per second

dynamic viscosity

newton-second per square

metre

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 metre

V/m

electric resistance

ohm

Ω

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 metre

A/m

magnetomotive force

ampere

luminous flux

lumen

cd · sr

luminance

candela per square metre

cd/m

illuminance

lux

lx lm/m

Cubic decimetre and litre

(CR, 88)

Resolution 13

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

considering

•

that the cubic decimetre and the litre 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 decimetre and the litre,

requests

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

its conclusions to the 12th CGPM.

The 13th CGPM in 1967
(Resolution 6, see p. 154)
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

•

151

CIPM, 1961

Cubic decimetre and litre

(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
litres.

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 caesium 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 caesium atomic frequency standards,

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

152

•

Appendix 1

Litre

(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 litre given in 1901 by the 3rd CGPM,

declares

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

decimetre,

recommends

that the name litre 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

CIPM, 1967

Decimal multiples and submultiples of the unit of mass

(PV,

35,

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”.

* The name “becquerel”
(Bq) was adopted by the
15th CGPM in 1975
(Resolution 8, see p. 157)
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. 158).

Appendix 1

•

153

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 caesium 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 caesium 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

Metrologia

1968,

, 43)

Resolution 3

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

considering

•

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.

At its 1997 meeting, the
CIPM affirmed that this
definition refers to a
caesium 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.

** See Recommendation 2
(CI-2005) of the CIPM on
the isotopic composition of
water entering in the
definition of the kelvin,
p. 170.

154

•

Appendix 1

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 metre of a black body at the temperature of freezing platinum under a
pressure of 101 325 newtons per square metre.”

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 metre

−

entropy

joule per kelvin

J/K

specific heat capacity

joule per kilogram kelvin

J/(kg · K)

thermal conductivity

watt per metre kelvin

W/(m · K)

radiant intensity

watt per steradian

W/sr

activity (of a radioactive source)

1 per second

−

* See Recommendation 5
(CI-1989) of the CIPM on
the International
Temperature Scale of
1990, p. 163.

* This definition was
abrogated by the
16th CGPM in 1979
(Resolution 3, see p. 158).

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

15th CGPM

in 1975 (Resolution 8, see
p. 157).

Appendix 1

•

155

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.

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.

* The 20th CGPM in 1995
decided to abrogate the
class of supplementary
units in the SI
(Resolution 8, see p. 164).

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.)

** The CIPM approved in
2001 a proposal of the
CCU to clarify the
definition of « SI units »
and « units of the SI »,
see p. 166.

156

•

Appendix 1

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 metre, 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,

•

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,

* 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 definition of TAI was
given by the CCDS in
1970 (now the CCTF), see
p. 155.

Appendix 1

•

157

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 metre,

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 metres per second.

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).

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

* 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.

158

•

Appendix 1

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

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.

* New prefixes were added
by the 19th CGPM in 1991
(Resolution 4, see p. 164).

Photopic vision is detected
by the cones on the retina
of the eye, which are
sensitive to a high level of
luminance
(L > 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
(L < ca. 10

−3

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

•

159

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.

Symbols for the litre

(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 litre 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 litre,

considering

that the name litre, 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 litre,

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,

* The CIPM, in 1984,
decided to accompany
this Resolution with an
explanation
(Recommendation 1,
see p. 161).

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

* The class of SI
supplementary units was
abrogated by decision of
the 20th CGPM in 1995
(Resolution 8, see p. 164).

160

•

Appendix 1

•

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,

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 metre

(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 metre

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 metre,

•

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 metre 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 metre,

•

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,

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

Appendix 1

•

161

decides

1. The metre 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 metre in force since 1960, based upon the transition between the

levels 2p

and 5d

of the atom of krypton 86, is abrogated.

On the realization of the definition of the metre

(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 metre,

•

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,

See Recommendation 1
(CI-2002) of the CIPM on
the revision of the practical
realization of the definition
of the metre, p. 166.

* The CIPM, in 2002,
decided to change the
explanation of the
quantity dose equivalent
in the SI Brochure
(Recommendation 2,
see p. 168).

162

•

Appendix 1

•

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,

•

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

•

163

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

Ω

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 25 812.807

Ω

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

•

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,

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. 166.

164

•

Appendix 1

•

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,

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 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,

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

•

165

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 artefact 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,

•

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),

166

•

Appendix 1

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 metre

(PV

194-204 and

Metrologia

, 103-133)

Recommendation 1

The International Committee for Weights and Measures,

recalling

•

that in 1983 the 17th General Conference (CGPM) adopted a new definition of the

metre;

•

that in the same year the CGPM invited the International Committee (CIPM)

•

to draw up instructions for the practical realization of the metre,

•

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;

Appendix 1

•

167

•

that in response to this invitation the CIPM adopted Recommendation 1 (CI-1983) (

mise

en pratique

of the definition of the metre) to the effect

•

that the metre 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 metre 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 metre). In this case, the effects to be taken into account are those of

special relativity only. The local methods for the realization of the metre
recommended in (b) and (c) provide the proper metre 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 metre;

considering

•

that science and technology continue to demand improved accuracy in the realization of

the metre;

•

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

metrology and the realization of the metre, 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

168

•

Appendix 1

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-

mendation 1 (CI-1997)) be replaced by the list of radiations given below*, including

•

updated frequency values for cold Ca atom, H atom and the trapped Sr

ion,

•

frequency values for new cold ion species including trapped Hg

ion, trapped In

ion

and trapped Yb

ion,

•

updated frequency values for Rb-stabilized lasers, I

-stabilized Nd:YAG and He-Ne

lasers, CH

-stabilized He-Ne lasers and OsO

-stabilized CO

lasers at 10

•

frequency values for standards relevant to the optical communications bands,

including Rb- and C

-stabilized lasers.

. . .

Dose equivalent

(PV

205)

Recommendation 2

The International Committee for Weights and Measures,

considering

that

•

the current definition of the SI unit of dose equivalent (sievert) includes a factor “

”

(product of any other multiplying factors) stipulated by the International Commission on
Radiological Protection (ICRP), and

•

both the ICRP and the International Commission on Radiation Units and Measurements

(ICRU) have decided to delete this factor

as it is no longer deemed to be necessary,

and

•

the current SI definition of

including the factor

is causing some confusion,

decides

to change the explanation in the brochure “Le Système International d'Unités (SI)”

to the following:

The quantity dose equivalent

is the product of the absorbed dose

of ionizing radiation

and the dimensionless factor

(quality factor) defined as a function of linear energy

transfer by the ICRU:

H = Q · D

Thus, for a given radiation, the numerical value of

in joules per kilogram may differ from

that of

in joules per kilogram depending on the value of

The Committee further

decides

to maintain the final sentence in the explanation as follows:

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

* The list of recommended
radiations,
Recommendation 1
(CI-2002), is given in PV,

, 197-204 and

Metrologia

, 2003,

104-115.
Updates are available on
the BIPM website at

www.bipm.org/en/
publications/mep.html

Document Outline