decibel

decibel (dB), unit for expressing the ratio between two physical quantities, usually amounts of acoustic or electric power, or for measuring the relative loudness of sounds. One decibel (0.1 bel) equals 10 times the common logarithm of the power ratio. Expressed as a formula, the intensity of a sound in decibels is 10 log₁₀ (S₁/S₂), where S₁ and S₂ are the intensity of the two sounds; i.e., doubling the intensity of a sound means an increase of a little more than 3 dB. In ordinary usage, specification of the intensity of a sound implies a comparison of the intensity of the sound with that of a sound just perceptible to the human ear. For example, a 60-dB, or 6-bel, sound, such as normal speech, is six powers of 10 (i.e., 10⁶, or 1,000,000) times more intense than a barely detectable sound, such as a faint whisper, of 1 dB. Decibels are also used more generally to express the logarithmic ratio of two magnitudes of any unit, such as two electric voltages or currents (or analogous acoustic quantities). In cases where the ratio is of a squared quantity, 1 dB equals 20 times the common logarithm of the ratio.

The term bel is derived from the name of Alexander Graham Bell, inventor of the telephone. The unit decibel is used because a one-decibel difference in loudness between two sounds is the smallest difference detectable by human hearing.