Decibel & Power Calculator
Convert between decibels, power ratio, voltage ratio and perceived loudness; find the watts needed for a given dB change.
Inputs
Cheat sheet
How it works
The decibel is a logarithmic ratio. It compresses the enormous range of human hearing (a factor of 1,000,000 in pressure) into a manageable scale, and because hearing itself is roughly logarithmic, equal dB steps sound like equal loudness steps.
Power: dB = 10 · log₁₀(P₂ / P₁) Voltage: dB = 20 · log₁₀(V₂ / V₁) (also pressure, SPL) P₂ = P₁ · 10^(dB/10) Loudness ≈ 2^(dB/10) (each +10 dB sounds about twice as loud)
Rules of thumb every installer should know: +3 dB = double the power (barely, but noticeably, louder); +6 dB = double the voltage = 4× power; +10 dB = 10× power = “twice as loud”; +1 dB is the smallest change most people can detect. That is why going from a 500 W to a 1000 W amp gives only +3 dB, but adding a second identical sub (which doubles the output pressure) gives +6 dB.
The two curves show why: for the same ratio, the voltage (20·log) curve climbs twice as fast as the power (10·log) curve. SPL and voltage are “field” quantities (20 log); watts and acoustic power are “power” quantities (10 log).