The root mean square of a real function or data set is the square root of its mean square. A sinusoid of amplitude has root mean square . For orthogonal or uncorrelated zero-mean components, the squared root mean square of their sum is the sum of their mean squares; this follows by expanding the square and observing that all cross terms average to zero.
The raw root mean square of a random variable is , whereas its r.m.s. fluctuation about its mean is the standard deviation . The former cannot be smaller than . Experimental phrases such as r.m.s. noise or temperature spread usually refer to the latter and should state the reference level.
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Root Mean Square (RMS) is a statistical measure used to quantify the magnitude of a varying quantity. It is especially useful in contexts where alternating values are present, such as in electrical engineering, signal processing, and physics. The RMS value provides a way to express the average of a set of values, where all values are taken into account without regard to their sign (positive or negative).