The root mean square or rms is a statistical measure of the magnitude of a varying quantity. It can be calculated for a series of discrete values or for a continuously varying function. The name comes from the fact that it is the square root of the mean of the squares of the values.
The rms for a collection of N values {x1, x2, ... , xN} is:
Uses
The rms value of a function is often used in physics. For example, we may wish to calculate the power P dissipated by an electrical conductor of resistance R. It is easy to do the calculation when a constant current I flows through the conductor. It is simply,
- (1)
- (2)
The rms value can be calculated using equation (2) for any waveform, for example an audio or radio signal. This allows us to calculate the mean power delivered into a specified load.
It is important to note that rms is a mean value and not an instantaneous measurement. Therefore expressions such as "peak rms power", sometimes used in advertisements for audio amplifiers, are misleading. See also PMPO.