bel

bel

Non-SI unit accepted for use with SI
Name Symbol Quantity Value in SI units
bel B logarithmic ratio

Definition

The bel, symbol B, is a non-SI unit accepted for use with the SI.

One bel, is equal to the decadic logarithm of a ratio between two power quantities of 10:1, or the decadic logarithm of a ratio between two root-power quantities of √10:1

The bel, symbol B, is a relative unit of measurement used to express the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by 0.1 B have a power ratio of 10110, or root-power ratio of 10120.

The bel expresses a change in value (e.g. +1 B or −1 B) or an absolute value.

When expressing a power ratio, it is defined as being equal to the logarithm in base 10. That is, a change in power by a factor of 10 corresponds to a 1 B change in level.

When expressing root-power quantities, a change in amplitude by a factor of 10 corresponds to a 2 B change in level.

The bel scales differ by a factor of two, so that the related power and root-power levels change by the same value in linear systems, where power is proportional to the square of amplitude.