Adding levels in dB
Combine sound levels, add two coherent signals with a phase difference, or subtract background noise.
Combine several levels
- dB
- dB
- Sum of uncorrelated sources
- 83.0103dB
- Increase over loudest source
- 3.0103dB
- Fully correlated, in phase (coherent)
- 86.0206dB
Two coherent signals with a phase difference
dB
dB
°
0° adds +6 dB for equal levels, 180° cancels.
- Sum of the two coherent signals
- 3.0103dB
- Change relative to the louder signal
- 3.0103dB
Subtract a level (remove background noise)
dB
dB
- Level of the source alone
- 83.3491dB
- Correction to subtract
- 1.65089dB
If the total is less than 3 dB above the background, the result is unreliable.
How it works
Two equal, uncorrelated sources (e.g. two different instruments) add 3 dB. Ten add 10 dB. Decibels cannot simply be added arithmetically.
Identical signals in phase add as pressures, giving up to +6 dB for two sources. Real-world results lie between the two cases.
Formulas
- L = 10 · log₁₀( Σ 10^(Lᵢ/10) ) — uncorrelated
- L = 20 · log₁₀ | a₁ + a₂·e^(jφ) | — coherent, phase φ
- L_source = 10 · log₁₀( 10^(L_total/10) − 10^(L_bg/10) )
Read more
Found a mistake or have an idea for this tool?
Suggest a change