Index Room & AcousticsAdding Decibels

Adding Decibels

Sum several sound sources the way pressure and power really add.

Combined level88.0dB

Gain over the loudest+3.01dB

Sources2

MethodPower10·log of summed powers

Levels

Source 185.0 dB

Source 285.0 dB

Combined88.0 dB

What a second source adds

The quieter a second source is, the less it matters. Ten decibels down, it adds under half a decibel.

Input

How the sources relate

Source 1dB

Source 2dB

How it works

Decibels do not add

Two 85 dB sources do not make 170 dB. Decibels are logarithms, so levels have to be converted back to a linear quantity, summed, and converted again. Which linear quantity depends on how the sources relate.

Unrelated sources

Different instruments, noise from separate machines, or left and right channels carrying different material have random phase. Their powers add:

L_{\Sigma} = 10\log_{10}\!\left(\sum_i 10^{L_i/10}\right)

Two equal sources give +3 dB, four give +6 dB, ten give +10 dB.

Identical signals in phase

Two drivers fed the same signal and placed close together, or a mono signal from both speakers at the centre seat, add as pressures:

L_{\Sigma} = 20\log_{10}\!\left(\sum_i 10^{L_i/20}\right)

Two equal sources now give +6 dB. This is why doubling up subwoofers side by side gains more than doubling amplifier power.

The shortcut

For two sources differing by $\Delta$ decibels, add this to the louder one:

\delta = 10\log_{10}\!\left(1 + 10^{-\Delta/10}\right)

That curve is the second plot. It explains masking in practical terms: a noise floor 10 dB under the music raises the total by only 0.4 dB.