Decibel (dB)

The decibel (dB) is a logarithmic unit expressing the ratio of two quantities of power. Each 10 dB corresponds to a 10× ratio; 20 dB is 100×; 30 dB is 1000×.

Formula: dB = 10 × log₁₀(P₁/P₀) for power, or 20 × log₁₀(A₁/A₀) for amplitude (because power scales as amplitude squared). The 10 comes from the “deci” prefix on the original bel unit (named after Alexander Graham Bell).

Decibels are dimensionless. To make them concrete, the reference point gets a suffix:

• dBSPL — sound pressure level relative to 20 µPa (threshold of human hearing).
• dBm — power relative to 1 milliwatt.
• dBV — voltage relative to 1 volt.
• dBFS — full-scale digital audio (0 dBFS = clipping).

Reference levels for sound: whisper ~30 dBSPL, normal conversation ~60, busy traffic ~80, jet engine at 100 ft ~140. Hearing damage starts around 85 dBSPL for prolonged exposure.