In more detail
A decibel expresses a ratio on a logarithmic scale: 10 × log₁₀(P₁ / P₀) for power and 20 × log₁₀(A₁ / A₀) for amplitudes such as voltage or sound pressure. Doubling power adds 3.01 dB, doubling amplitude adds 6.02 dB, and halving amplitude is −6.02 dB. A dB figure always needs a reference: dB SPL is relative to 20 µPa, roughly the threshold of hearing; dBm to 1 milliwatt; dBFS to digital full scale, so real digital levels are 0 or below. A recording that touches 0 dBFS may clip, which flattens the waveform and sounds distorted.
Why it matters
Because the scale is logarithmic, small numbers hide large changes: +10 dB is ten times the power and is heard as roughly twice as loud. Hearing-protection guidance such as the NIOSH limit allows 85 dBA for 8 hours and halves the time for every 3 dB more. When recording, setting the input gain so peaks stay well below 0 dBFS leaves headroom and avoids clipping.
Example
Halve the amplitude: 20 × log₁₀(0.5) = −6.02 dB
Double the power: 10 × log₁₀(2) = +3.01 dB
Two equal 85 dB sources: 10 × log₁₀(2 × 10^8.5) = 88.0 dB (not 170)
16-bit audio range: 20 × log₁₀(65,536) = 96.3 dB