Root mean square

In statistics, the root mean square (abbreviated RMS or rms), also known as the quadratic mean, is a statistical measure defined as the square root of the arithmetic mean of the squares of a set of numbers.

RMS can also be calculated for a continuously varying function.

In physics it is a characteristic of a continuously varying quantity, such as a cyclically alternating electric current, obtained by taking the mean of the squares of the instantaneous values during a cycle. It is equal to the value of the direct current that would produce the same power dissipation in a resistive load. This is a result of Joule's first law, which states that the power in resistive load is proportional to the square of the current (and, as a consequence of Ohm's law, also to the square of the voltage).

In econometrics the root mean square error of an estimator is a measure of the imperfection of the fit of the estimator to the data.

The root mean square is a particular case of the generalized mean, with exponent 2.