root mean square

In mathematics, value obtained by taking the square root of the mean of the squares of a set of values; for example the rms value of four quantities a, b, c, and d is

√[(a2 + b2 + c2 + d2)/4].

For an alternating current (AC), the rms value is equal to the peak value divided by the square root of 2.

root mean square

Measure of the effective magnitude of a cyclic or randomly varying quantity whose average value is zero. For a cyclic quantity, it is equal to the square root of the average of the squares of the quantity at each instant over a complete cycle; where the variation is a sine wave, the rms value is equal to the peak value divided by √2. In electrical engineering, for example, the rms value of the current or voltage in an AC circuit is used in power calculations. The rms value is also used as a measure of the amplitude of randomly varying quantities, such as the noise in a telecommunications channel.