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The decibel is a logarithmic unit used to describe the ratio of a signal level - like power, intensity or amplitude - to a reference level.

  • the decibel express the level of a value relative to a reference value

Two types of decibel are normally used:

  • for power ratios - dB is defined as ten times the logarithm in base 10
  • for amplitude ratios - root power quantities - a change in amplitude by a factor of 10 corresponds to 20 dB change in level

Decibel Definition - Power Ratios

The decibel level of a signal can be expressed as

L = 10 log (S / S ref)                (1)


L = signal level (decibel, dB)

S = signal - intensity or power level (signal unit)

S ref = reference signal - intensity or power level (signal unit)

Decibel is a dimensionless value of relative ratios. The signal units depends on the nature of the signal - can be W for power.

A decibel is one-tenth of a Bel - named after Alexander Graham Bell, the inventor of the telephone.

Note! - the decibel value of a signal increases with 3 dB if the signal is doubled (L = 10 log (2) = 3).

dB vs. Signal Ratio
dBPower Ratio
Amplitude Ratio (A/Aref)
-40 0.0001 0.01
-20 0.01 0.1
0 1 1
3 2 √2
6 4 2
10 10 3.162
20 100 10

If the decibel value and reference level are known the absolute signal level can be calculated by transforming (1) to

S = S ref 10 (L / 10)                                                       (2)


Decibel Calculator

Example - Lowest Hearable Sound Power

10 -12 W is normally the lowest sound power possible to hear and this value is normally used as the reference power in sound power calculations.

The sound power in decibel from a source with the lowest sound hearable can be calculated as

L = 10 log ( (10 -12 W ) / (10 -12 W ))

    = 0 dB


Example - Highest Hearable Sound Power

100 W is almost the highest sound power possible to hear. The sound power in decibel from a source with the highest possible to hear sound power can be calculated as

L = 10 log ( (100 W) / (10 -12 W ))

    = 140 dB

Example - Sound Power from a Fan

A fan creates 1 W of sound power. The noise level from the fan in decibel can be calculated as

L = 10 log ((1 W) / (10 -12 W ))

    = 120 dB

Example - Sound Intensity and Decibel

The difference in decibel between sound intensity 10 -8 W/m 2 and sound intensity 10 -4 W/m 2 ( 10000 units) can be calculated as

ΔL = 10 log ((10 -4 W/m 2) / (10 -12 W/m 2)) - 10 log ((10 -8 W/m 2) / (10 -12 W/m 2))

    = 40 dB

Increasing the sound intensity by a factor of

  • 10 raises its level by 10 dB
  • 100 raises its level by 20 dB
  • 1000 raises its level by 30 dB
  • 10000 raises its level by 40 dB and so on

Decibel Ratios - Amplitude Ratios

L = 20 log (A / A ref)                (3)


L = signal level (decibel, dB)

A = amplitude level (signal unit)

A ref = amplitude level level (signal unit)

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