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Root Mean Square ○◂｜Definition｜1st｜20251119205401-00-⌔

Root mean square - Wikipedia

Root mean square

In mathematics, the root mean square (abbrev. RMS, rms or rms) of a set of values is the square root of the set’s mean square.¹ Given a set $x_i$, its RMS is denoted as either $x_{\mathrm{RMS}}$ or ${\mathrm{RMS}}_x$. The RMS is also known as the quadratic mean (denoted $M_2$),²³ a special case of the generalized mean. The RMS of a continuous function is denoted $f_{\mathrm{RMS}}$ and can be defined in terms of an integral of the square of the function. In estimation theory, the root-mean-square deviation of an estimator measures how far the estimator strays from the data.

Printed 2026-06-28.

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Footnotes

1. “Root-mean-square value”. A Dictionary of Physics (6 ed.). Oxford University Press. 2009. ISBN 9780199233991. ↩

2. Thompson, Sylvanus P. (1965). Calculus Made Easy. Macmillan International Higher Education. p. 185. ISBN 9781349004874. Retrieved 5 July 2020. ↩

3. Jones, Alan R. (2018). Probability, Statistics and Other Frightening Stuff. Routledge. p. 48. ISBN 9781351661386. Retrieved 5 July 2020. ↩

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