Add Independent Sound Levels

Combine two uncorrelated sound-pressure levels measured at the same receiver.

How this calculation works

Decibels are logarithmic, so two sound-pressure levels cannot be added as ordinary numbers. Enter the separate levels of two independent, incoherent sources as measured at the same receiving position. Both readings must use the same frequency band and weighting. The calculator converts their relative levels into additive mean-square contributions, sums them and converts the result back to decibels. It also reports how much the combined level exceeds the louder source alone. Two equal levels produce an increase of approximately 3.01 dB; a much quieter source makes a smaller contribution. This calculation does not describe coherent tones whose phase relationships can cause reinforcement or cancellation, and it does not evaluate hearing exposure dose or certify a safe noise level.

Inputs and units

Source 1 sound-pressure level (dB): Use the same frequency band and weighting for both levels
Source 2 sound-pressure level (dB)

Method and formula

Ltotal = 10 log10(10^(L1/10) + 10^(L2/10)). Computed relative to the larger level for numerical stability.

Worked example

Example inputs

Source 1 sound-pressure level: 70 dB
Source 2 sound-pressure level: 70 dB

Calculation steps

With both sources at 70 dB, the relative mean-square contribution of the second source is 10^((70 − 70)/10) = 1.
Add the contributions logarithmically: Ltotal = 70 + 10 × log10(1 + 1) = 73.010300 dB.
Subtract the louder individual level: increase = 73.010300 − 70 = 3.010300 dB.

Example results

Combined sound-pressure level: 73.01029996 dB
Increase over louder source: 3.010299957 dB

Assumptions

Independent incoherent sources; both readings at the same position and with matching weighting/bandwidth