Root mean square

In mathematics and its applications, the root mean square of a set of numbers ${\displaystyle x_{i}}$ (abbreviated as RMS, RMS or rms and denoted in formulas as either ${\displaystyle x_{\mathrm {RMS} }}$ or ${\displaystyle \mathrm {RMS} _{x}}$) is defined as the square root of the mean square (the arithmetic mean of the squares) of the set. The RMS is also known as the quadratic mean (denoted ${\displaystyle M_{2}}$) and is a particular case of the generalized mean. The RMS of a continuously varying function (denoted ${\displaystyle f_{\mathrm {RMS} }}$) can be defined in terms of an integral of the squares of the instantaneous values during a cycle.

For alternating electric current, RMS is equal to the value of the constant direct current that would produce the same power dissipation in a resistive load. In estimation theory, the root-mean-square deviation of an estimator is a measure of the imperfection of the fit of the estimator to the data.