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Root Mean Square (RMS) Calculator

Find the root mean square of a list of numbers — the quadratic mean used for AC signals, deviations and magnitudes.

Values (comma or space separated)

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How it works

RMS = √( (x₁² + x₂² + … + xₙ²) ÷ n )

The root mean square squares each value, averages the squares, then takes the square root. Squaring makes every contribution positive and weights large-magnitude values more heavily, which is why RMS is the natural measure for the effective magnitude of a fluctuating signal — an AC voltage of 3, 4, 5, 6 has an RMS that describes its equivalent steady power. The RMS is always at least as large as the arithmetic mean of the absolute values, with equality only when all magnitudes are equal.

Worked example

For 3, 4, 5, 6: the squares are 9, 16, 25, 36 summing to 86. Divide by n = 4 to get 21.5, then take the square root: √21.5 = 4.637. That is larger than the plain mean of 4.5 because squaring emphasizes the bigger values.

Sources: Root mean square — Wikipedia

Frequently asked questions

How is RMS different from the average?

The average adds the values directly; RMS averages their squares before rooting. RMS is never smaller than the mean of the magnitudes and reacts more strongly to large values.

Does the sign of a value matter?

No. Each value is squared, so −5 and +5 contribute identically. RMS measures magnitude, not direction.

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This calculator is for educational purposes. Double-check important results before acting on them.