Decibels express amplitude on a log scale because human loudness perception is logarithmic

The decibel converts raw amplitude or power ratios into a scale matched to how human hearing works. Because the ear responds to the log of intensity (spanning roughly 12 orders of magnitude of power), decibels compress this huge range into a workable 120-dB span. The formula is: dB = 20 log10(input level / reference level) when working with amplitudes. One practical rule: doubling amplitude equals +6 dB; successive gain multiplications correspond to additions of decibels. A common error is adding decibels where adding amplitudes is needed (e.g. mixing two equal signals). Return to linear amplitude for mixing, use decibels for display and metering.

Examples

A mixer working from +9 dB to negative infinity. Full scale 0 dBFS in digital audio. The 98 dB dynamic range of 16-bit audio (6 dB per bit times 16 bits is roughly 96-98 dB).

Assessment

A signal doubles in amplitude three times in a row. What is the total dB gain? Why can you not directly add decibel values to find the sum of two audio signals?