bels

The bel is a logarithmic unit used to express the ratio between two quantities, typically power or intensity. It is defined as the base-10 logarithm of the ratio of the two quantities: B = log10(Q/Q0), where Q is a quantity such as power or intensity and Q0 is a reference value. Because the bel tends to produce large numbers in practical measurements, in everyday use it is usually replaced by the decibel, which is one-tenth of a bel.

The bel is named after Alexander Graham Bell. It originated in the early development of telecommunication and measurement technology, but in most modern contexts it has largely been superseded by the decibel, which provides a more convenient range of values for audible and other signals. In specialized fields—such as some areas of optics, radio engineering, and certain scientific measurements—the bel may still appear in historical references or when expressing ratios in a larger, less-compressed unit.

Relationship to the decibel: one bel equals ten decibels, so dB = 10 × log10(Q/Q0) for a given ratio. In acoustics and related disciplines, decibels are the standard unit because they conveniently align with human perception and numerical ranges. Nonetheless, the bel remains a valid, if rarely used, unit for expressing logarithmic ratios, with the decibel serving as its practical subdivision.