Root Mean Square Calculator

Calculate the root mean square (RMS) of a set of values, used in physics and signal processing.

Root Mean Square

4.082483

Arithmetic Mean (for comparison)4.000000
Mean of Squares16.666667

Root Mean Square vs Value 1

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Formule

## How to Calculate the Root Mean Square ### Formula **RMS = sqrt( (v1^2 + v2^2 + ... + vn^2) / n )** 1. Square each value 2. Compute the arithmetic mean of the squares 3. Take the square root The RMS is always greater than or equal to the absolute value of the arithmetic mean. In electrical engineering, RMS voltage represents the equivalent DC voltage that delivers the same power.

Exemple Résolu

Compute the RMS of 3, 4, 5.

  1. 01Squares: 9, 16, 25
  2. 02Mean of squares = (9 + 16 + 25) / 3 = 50 / 3 ≈ 16.6667
  3. 03RMS = sqrt(16.6667) ≈ 4.0825
  4. 04Compare: Arithmetic mean = (3 + 4 + 5) / 3 = 4