Efficiency and sensitivity conversion - loudspeaker percent and dB loudspeaker efficiency versus sensitivity vs

• Conversion of sensitivity in dB per watt and meter •
to energy efficiency in percent for passive loudspeakers Loudspeaker efficiency versus sensitivity

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In loudspeaker data you never find the real efficiency in percent,
but usually there is the sensitivity in dB per 1W/1m instead.

Efficiency is not the same as sensitivity

- but it is possible to convert efficiency to sensitivity and vice versa:

Sensitivity dB /W/m   |   Efficiency

  |

        ↓   |           ↓

  |

Efficiency   |   Sensitivity dB /W/m

in percent   |

Sensitivity in dB = 112 + 10 log (efficiency)

Efficiency = 10^{(Sensitivity in dB – 112)/10}

Loudspeaker data

Efficiency Percent Sensitivity

0.2        20 % 105 dB

0.1        10 % 102 dB

0.05       5 % 99 dB

0.02       2 % 95 dB

0.01       1 % 92 dB

  0.005     0.5 % 89 dB

  0.002     0.2 % 85 dB

  0.001     0.1 % 82 dB

105 dB is very efficient and 82 dB is very inefficient

The sensitivity of a loudspeaker is the sound pressure between 125 Hz (250 Hz) to 4 kHz
(8 kHz) at a specific distance - when you have a constant voltage - measured in dB per watt
and meter. Mostly it is the voltage of constant 2.83 volts, the distance is 1 meter, at 8 ohms
nominal impedance. For instance the sensitivity of a good 8 ohms loudspeaker is:
92 dB / 2.83 volts / 1 meter. Herewith is the power P = V ² / R = 2.83² / 8 = 1 watt. With a
4 ohms loudspeaker you generate 2 watts. To get the reference value of 1 watt, you have
to subtract from the sensitivity 3 dB.
It is not the efficiency you get here, it is the sensitivity.
The very small value of the efficiency is never shown by a manufacturer. Usual values for HiFi
speakers and studio monitors are between 0.2 % and maximum 2 % − that is an efficiency
of 0.002 to 0.02.
There is no connection between the efficiency and the sound quality.

Efficiency
The efficiency of a system is defined as the ratio between the useful delivered
power output divided by the input power, denoted by the Greek letter small eta (η).

Acoustic efficiency η (eta) of a loudspeaker is:

Acoustic power output P_ak watts

Electric power input P_e watts

       ↓

Energy efficiency η

in percent: %

Where does the 112 dB come from? The 0 dB reference level for sound is 10⁻¹² watts.
1 acoustical watt means 120 dBSPL.
The standard measurement for loudspeakers is done with an infinite baffle sounding in a half room with a distance of r = 1 m.
The resultant factor 2 π × r² (area of a half sphere) equals −8 dB. Therefore we get for an efficiency of 1 = 100 % a sensitivity of 120 − 8 = 112 dB.

This calculation works correct if the loudspeaker radiates in a half circle 2 π. Otherwise you must add the Q factor because of directionality.

      Many car and disco freaks need for their huge loudspeakers:
The Big Power Formulas
        Electrical and mechanical power calculation.

To get a high loudness from loudspeakers you should know:
How many decibels (dB) is twice (double, half) or three times as loud?

Studio monitors have a small energy efficiency arround 1 %, but that gives a very high
uncolored sound quality.

If you are looking for big party loudspeakers with high efficiency you have really to think
of impedance matching (power matching) and megaphones. They have always an
efficiency of more than 10 %, but with the well known distortions and giving a strange
colored sound. That comes really through and has "pressure" and you can hear the
"power".

If you need even more efficiency you have to think of a siren on emergency vehicles. But
the frequency bandwidth is very limited.
Extremes:
dB Drag Racing (racer) is a competition rewarding the person who can produce the
loudest sound inside a vehicle with a car's sound system. Current world record is over
177 dB-SPL. These audio gear does not play usual wideband pop music, like black
metal or gangsta rap, but a single (!) audio frequency. Only by this way an extremely
high efficiency can be achieved; see emergency horn.

Typical Question: Calculate the maximum sound pressure level of a loudspeaker in 1 m
distance, when the sensivity level of 98 dB/1W/1m is given and the wattage is 300 W.
Answer: At 1 Watt you get 98 dBSPL in 1 m distance. At 300 W there is:
10 × log 300/1 = 24.77 dB more level, that means 122.77 dBSPL.

Sometimes the efficiency is given in decibel instead of percent.

Enter simply the value to the left or the right side. The calculator works in both
directions of the ↔ sign. The damping value in dB must begin with a minus sign.

Percent value k:
% ↔ Damping value a:
dB

         k = THD

100 percent = 1 ≡ 0 dB

Decibel to Percentage Converter

Decibel Table - Comparison Chart - dB Scale

Loudspeaker: "Volume" and amplifier power

Sensitivity in dB per 1 watt and 1 meter: dB/W/m

Amplifier power of each loudspeaker: watts

Number of loudspeakers:

Distance to loudspeakers: meters

"Loudness" (volume): dB

A doubling of the listening distance from a loudspeaker gives a reduction of
sound pressure by 6 dB. In practice, that is, in a room with walls, the sound
pressure reduction is less. A doubling of the number of loudspeakers is an
increase of sound pressure by 3 dB.

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Loudspeaker data
Efficiency	Percent	Sensitivity
0.2	20 %	105 dB
0.1	10 %	102 dB
0.05	5 %	99 dB
0.02	2 %	95 dB
0.01	1 %	92 dB
0.005	0.5 %	89 dB
0.002	0.2 %	85 dB
0.001	0.1 %	82 dB

Percent value k: %	↔	Damping value a: dB
k = THD
100 percent = 1 ≡ 0 dB