Statistics & probability

Root mean square calculator

Calculate the quadratic magnitude of positive and negative values.

Root mean square calculator
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Your inputs

Up to 50,000 values. No thousands separators. Absolute values up to 1 trillion; non-zero values must be at least 1e-100 in magnitude.

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A clear answer. Here’s how.

RMS = sqrt(mean(x²)). Scales values by their largest absolute magnitude before squaring to avoid avoidable overflow. Reports RMS, arithmetic mean and population standard deviation, which satisfy RMS²=mean²+population variance apart from floating-point rounding.

See a worked example

Worked example

A fixed demonstration, separate from the values you enter above.

Values, separated by commas or new lines
-3, 3, -4, 4

Example result

Root mean square
3.53553390593
Arithmetic mean
0
Population standard deviation
3.53553390593
Count
4

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