Definition

Sound level

(W3.2.1) W3.2 · Intensity and Decibels →

β = 10 lo g_{10} (\frac{I}{I _{0}}) dB

Statement

Sound level in decibels, referenced to the threshold of hearing intensity I₀ = 10⁻¹² W/m².

Symbols and units

$β$	sound level	dB
$I$	sound intensity	W/m²
$I_{0}$	reference intensity	10⁻¹² W/m²

When it applies

Any sound intensity I compared against the reference threshold I₀.

Derivation

Human hearing responds roughly logarithmically to intensity, so a logarithmic scale compresses the enormous range of audible intensities into a manageable one:

β = 10 lo g_{10} (I / I_{0}) dB

Worked examples

A 3 dB increase, as a ratio

1 0^{3/10} \approx 2.0

A rule of thumb worth keeping: +3 dB means roughly double the intensity, +10 dB means exactly tenfold.

Watch out for

A 10 dB increase is a TENFOLD increase in intensity, not a doubling — decibels are logarithmic, not linear.