The quietest sound a young healthy ear can hear and a jet engine up close differ in pressure by a factor of millions and in intensity by a factor of a million million million. Writing numbers like that is awkward, so we squeeze them with a logarithm. The result is the decibel (dB).

For intensity I (power per square metre): L = 10 × log₁₀(I / I₀), with the reference I₀ = 10⁻¹² W/m².

For pressure p: L = 20 × log₁₀(p / p₀), with the reference p₀ = 20 micropascals (20 µPa). Compare that with the air pressure around you, about 101,325 Pa: the quietest audible sound is only about two parts in ten billion of that. A sound of 1 pascal is about 94 dB, and 20 Pa is about 120 dB.

Two rules of thumb are all you need:

• +10 dB means 10 times the intensity. +20 dB means 100 times, +30 dB means 1,000 times.
• +3 dB means double the intensity (and +6 dB means double the pressure).

0 dB is not silence. It is the reference near the threshold of hearing. Very quiet rooms can have negative levels.