Root Mean Square Calculator Formula

Understand the math behind the root mean square calculator. Each variable explained with a worked example.

Use the Root Mean Square Calculator

Formulas Used

Root Mean Square

rms = sqrt(sq_mean)

Arithmetic Mean (for comparison)

arithmetic_mean = (v1 + v2 + v3) / 3

Mean of Squares

mean_of_squares = sq_mean

Variables

VariableDescriptionDefault
v1Value 13
v2Value 24
v3Value 35
sq_meanDerived value= (pow(v1, 2) + pow(v2, 2) + pow(v3, 2)) / 3calculated

How It Works

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.

Worked Example

Compute the RMS of 3, 4, 5.

v1 = 3v2 = 4v3 = 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

Ready to run the numbers?

Open Root Mean Square Calculator