Decibels

The decibel (dB) is a unit used to express ratios of physical quantities, typically power or amplitude, on a logarithmic scale. It is one tenth of a bel, a unit named for Alexander Graham Bell. Because it expresses a ratio w.r.t. a reference value, the decibel is a dimensionless quantity.

For quantities proportional to power, such as electrical or acoustic power, the decibel is defined as dB = 10 log10(P1/P0). For quantities that are proportional to amplitude, such as voltage, current, or pressure, the decibel is dB = 20 log10(A1/A0) when the same impedance or medium applies. In acoustics, sound pressure level uses p0 = 20 microPascals in air at 1 kHz, giving Lp = 20 log10(p/p0). The corresponding intensity level uses I0 = 1e-12 W/m^2.

Decibels are commonly used with various reference values, producing units such as dBm (relative to 1 milliwatt), dBV (relative to 1 volt), or dB re 1 μPa in acoustics. Because the scale is logarithmic, large changes in physical quantity correspond to comparatively small changes in dB, and the same dB value can represent different absolute magnitudes depending on the reference chosen.

In practice, decibels convey relative loudness, gain, or loss rather than an absolute quantity. Interpretation depends on context and reference. In environmental acoustics, sound levels are reported as dB re p0, with typical conversational levels around 60 dB and occupational limits around 85 dB over an eight-hour exposure. See also bel, sound pressure level, A-weighting, and dBm for related concepts.