Decibel Calculator

A decibel is a ratio expressed logarithmically, not a quantity. That is why a bare decibel figure is meaningless without a reference — sound pressure levels are quoted against the threshold of hearing, which is what the dB SPL scale means, and a gain of 6 dB says something about amplification rather than absolute loudness.

The formula depends on what you are comparing, and getting it wrong puts you out by a factor of two. Power uses 10·log₁₀ and amplitude uses 20·log₁₀. They agree physically because power goes as the square of amplitude, and squaring inside a logarithm becomes a factor of two outside it. Doubling power is +3 dB; doubling voltage or sound pressure is +6 dB.

Decibels do not add arithmetically, which surprises people constantly. Two 60 dB sources together give 63 dB, not 120 — the underlying powers add and the logarithm is applied afterwards. The practical consequence is that a quiet source next to a loud one contributes almost nothing: adding 40 dB to 80 dB changes the total by well under a thousandth of a decibel.

Level falls with distance because a point source spreads its energy over a sphere, and a sphere's area grows with the square of its radius. That gives 6 dB lost per doubling of distance — so moving from one metre to two costs the same 6 dB as moving from ten metres to twenty.

The landmarks are worth knowing for a reason that is not academic. Sustained exposure above about 85 dB risks permanent hearing damage, and the time it takes falls sharply as level rises — a nightclub at 100 dB does damage in around fifteen minutes.