Decibel Calculator
Add or subtract incoherent dB levels and predict SPL at a new distance.
Overview
The decibel calculator adds incoherent sound sources together and predicts how SPL changes with distance. Add two 80 dB sources and the total is 83 dB — not 160. Halve the distance from a speaker and SPL rises by 6 dB in a free field. The tool spells out both calculations so you can answer real-world questions about noise exposure, PA system coverage, and room sound design.
It's used by live sound engineers planning system gain structure, acousticians estimating noise transfer between rooms, audio educators explaining why "twice as loud" isn't twice the dB number, and safety officers checking whether worker noise exposure stays under regulatory limits. The math underpins almost every loudness conversation in audio.
How it works
Decibels are logarithmic, so you can't just add them. Two incoherent sources combine by power: convert each level to a linear power ratio with 10^(dB/10), sum them, then convert back with 10 x log10. Two equal sources add 3 dB; ten equal sources add 10 dB; a hundred equal sources add 20 dB. For unequal sources, the louder one dominates and the quieter one adds only a fraction of a dB.
Distance follows the inverse-square law in a free field: SPL drops 6 dB for every doubling of distance from a point source. So a speaker reading 100 dB at 1 meter reads 94 dB at 2 m, 88 dB at 4 m, 82 dB at 8 m, and so on. Indoors, reverberant build-up softens the drop-off once you're beyond the critical distance, so the formula is a best-case estimate.
Examples
80 dB + 80 dB → 83 dB (two equal sources)
90 dB + 75 dB → ~90.1 dB (louder source dominates)
100 dB @ 1 m → 94 dB @ 2 m, 82 dB @ 8 m (free field)
Ten 70 dB sources → 80 dB combined
FAQ
Why doesn't 80 + 80 = 160 dB?
Decibels measure on a logarithmic scale of power. Adding two equal incoherent sources doubles the power, which is +3 dB on the log scale.
What's the difference between coherent and incoherent addition?
Two coherent (correlated) sources, like the same signal from two speakers, can add up to +6 dB at the listener or cancel completely depending on phase. Incoherent (uncorrelated) sources like two different musicians always add to +3 dB for equal levels.
When does the inverse-square law break down?
Indoors, once you're past the critical distance, the reverberant field flattens the curve. Line arrays also break the rule near the array because they behave like a line source (3 dB per doubling) rather than a point.
How loud is "twice as loud" subjectively?
About +10 dB. That's a tenfold increase in power but only a doubling of perceived loudness, which is why decibel scales are logarithmic in the first place.
Is 85 dB really the safe limit?
85 dB(A) over an 8-hour workday is the OSHA threshold for hearing conservation. Every 3 dB above that halves the safe duration.