Audio calculator
Decibel (SPL) Addition Calculator
Decibels do not add arithmetically: two 100 dB sources together make 103 dB, not 200 dB. This calculator performs the correct power summation for up to four incoherent sources, the case that covers most stacked cabinets, generators, and noise sources.
Formulas
Incoherent power sum
Ltot = 10 × log10(10^(L1/10) + 10^(L2/10) + ...)- Li:
- each individual level in dB SPL
- Ltot:
- combined level in dB SPL
How it works
Sound levels combine as power, not as numbers. Converting each level out of decibels, summing the powers, and converting back gives the combined level. Two equal sources add 3 dB; ten equal sources add 10 dB.
That is the incoherent case, which applies when the sources are uncorrelated or arrive with varying phase: different instruments, a speaker plus its room reflections at a listener moving around, machinery noise. Coherent summation, where identical signals arrive exactly in phase, doubles pressure rather than power and yields +6 dB. Coupled subwoofer arrays live in that regime at low frequencies, which is why sub arrays grow so much faster than the cabinet count suggests.
A useful corollary: a source more than about 10 dB below another contributes essentially nothing to the total. Chasing the third-loudest noise source on a quiet corporate show is usually wasted effort until the loudest two are handled.
Worked example: Two ground-stacked cabinets each doing 98 dB SPL at FOH
- 1.Powers: 10^(98/10) + 10^(98/10) = 2 × 10^9.8.
- 2.Combined: 10 × log10(2 × 10^9.8) = 98 + 10 × log10(2) = 98 + 3.0.
- 3.If they were fully coherent at the measurement point, pressure doubling would give 98 + 6 = 104 dB instead.
101 dB SPL incoherent, up to 104 dB where the arrivals are coherent.
Adding two levels by their difference
| Difference between sources | Add to the louder source |
|---|---|
| 0 dB | +3.0 dB |
| 1 dB | +2.5 dB |
| 2 dB | +2.1 dB |
| 3 dB | +1.8 dB |
| 6 dB | +1.0 dB |
| 10 dB | +0.4 dB |
Field notes
- The difference-based shortcut table below is worth memorizing: equal levels +3, a 10 dB quieter source adds only 0.4 dB.
- Meter placement dominates measured combination effects; a 1 m move can swing comb-filtered summation by several dB at a single frequency.
Frequently asked questions
What is 100 dB plus 100 dB?
103 dB for uncorrelated sources (power addition), or up to 106 dB if the two signals are identical and arrive perfectly in phase (pressure addition).
Why do two speakers only add 3 dB?
Because the acoustic powers add, and doubling power is 10 × log10(2) = 3.01 dB. The +6 dB figure requires coherent pressure summation, which only holds where wavelengths are long or arrivals are matched.
How many extra decibels do I get from doubling the number of boxes?
Between +3 dB (uncoupled) and +6 dB (fully coupled), frequency dependent. Subwoofers at 40 Hz couple; two mains covering different zones do not.