Decibel

The decibel (symbol: dB) is a unit used to express the ratio between two measurements, typically power or intensity. The decibel is not an absolute unit like the meter or kilogram; it is a relative measure, meaning that a dB value always requires a known reference level.

The decibel is one tenth of a bel (B). The bel was named after Alexander Graham Bell, whose work involved the transmission of sound and electrical signals over telephone lines. The bel alone is too large for practical use, so the decibel became the standard form.

Calculation

When comparing power, the decibel is calculated by taking the base-10 logarithm of the ratio and then multiplying by 10: L = 10 × log₁₀(P/P₀). When using quantities that are field or amplitude measures—those for which power depends on the square—the multiplication factor becomes 20: L = 20 × log₁₀(p/p₀). Consequently, a doubling of power corresponds to an increase of about 3 dB, while a tenfold increase equals 10 dB.

Reference levels

Because the decibel is a ratio, it is expressed with letters or subscripts indicating the reference used. For example, dB SPL refers to sound pressure level relative to an agreed reference pressure in air, while dBm denotes power relative to one milliwatt. The notations dBW, dBV, and dBi are also standard in electrical engineering, radio, and antenna technology.

Applications

The decibel is used to measure loudness and sound intensity, to quantify loss (attenuation) in cables and fiber optic lines, to measure amplification (gain) in amplifiers, and to express signal-to-noise ratio. The primary advantage of the logarithmic scale is that it compresses a very wide range of small and large numbers into a manageable form, and it also approximates how the human ear perceives changes in sound loudness.