Overview

The decibel (symbol: dB) is a logarithmic unit used to express ratios of power, intensity, or amplitude. Because it is based on a logarithm, the decibel compresses very large or small ratios into a compact scale. Engineers and scientists use decibels across fields such as audio, acoustics, radio, and telecommunications to describe gains, losses, signal strengths and relative levels. The decibel is actually one tenth of a bel, a larger unit named for Alexander Graham Bell and introduced within the Bell System; however, the bel itself is rarely used.

Definition and calculation

The decibel describes a ratio. For power quantities the level difference in decibels is given by the formula: L(dB) = 10 × log10(P2 / P1). For quantities proportional to amplitude (voltage, pressure, or field strength) where power is proportional to the square of amplitude, the corresponding formula is: L(dB) = 20 × log10(A2 / A1). The logarithm is base 10, so equal multiplicative factors become simple additive decibel amounts. For example, doubling power corresponds to about +3.01 dB, while doubling amplitude corresponds to about +6.02 dB. Because it expresses a ratio, a decibel value must usually include a reference to be fully informative.

Common reference units and examples

When a decibel measurement refers to an absolute level it is paired with a reference. Widely encountered forms include:

  • dBm — decibels relative to 1 milliwatt. This is common in radio and system power budgets. See dBm reference.
  • dBW — decibels relative to 1 watt.
  • dBV / dBu — decibels referenced to particular voltage levels (used in audio).
  • dB SPL — decibels of sound pressure level, referenced to 20 micropascals in air (a conventional threshold near human hearing at 1 kHz).

Because decibels are ratios, they add easily for cascaded systems: a +10 dB amplifier followed by −3 dB filter yields a net +7 dB change. They are also handy for describing attenuation (losses) and gains in cables, filters and antennas.

History and common applications

The bel and decibel arose in telephony and early electrical engineering to manage large dynamic ranges and to simplify link budget arithmetic. They became widespread in the 20th century within telecommunications and audio engineering. Modern use spans signal processing, RF engineering, acoustics, and many measurement disciplines where relative changes matter more than absolute linear values. In telecommunications, for example, decibels are used to express link loss, amplifier gain, and signal-to-noise ratios; see discussions of telecommunication signal applications for context.

Perception, acoustics, and notable facts

In acoustics the decibel scale approximates human perception: equal increments can correspond to roughly similar perceptual steps over parts of the audible range. The conventional zero point for dB SPL (sound pressure level) is 20 μPa, often associated with a young listener's threshold near 1 kHz; for details consult sources on the Absolute threshold of hearing. Small changes (1 dB or so) may be just perceptible in controlled conditions, whereas changes of 10 dB are commonly perceived as about a doubling or halving of loudness.

Practical considerations and cautions

Because a decibel is fundamentally a dimensionless ratio, values reported without a reference can be ambiguous. Always check whether a dB value is relative (e.g., dB gain between two ports) or absolute (e.g., dBm, dB SPL). Also note the distinction between power-based and amplitude-based formulas — using 10 × log10 versus 20 × log10 — which depends on whether the measured quantity is proportional to power or to field/voltage. For mathematical and historical background see general references to power ratios and the logarithmic or exponential function basis of the decibel.