Root Mean Square Calculator

Root mean square and interpretation

RMS is nonnegative and uses the original sample unit. Mean square uses the squared unit. The arithmetic mean can be zero even when the samples have a positive RMS magnitude.

To calculate sample or population standard deviation from raw observations, use the Standard Deviation Calculator and follow its own input conventions.

The formula

Square each sample, average those squares, and take the square root. The arithmetic mean is reported separately; the RMS calculation does not subtract it from the samples.

How to use this calculator

1. Enter numerical samples separated by spaces, commas, or new lines.
2. Use samples with equal weights and the same measurement unit.
3. Compare RMS with mean square and arithmetic mean; they summarize different aspects of the list.

Root Mean Square input conventions

Squaring removes the sign of each sample, so opposite values do not cancel. After averaging the squares, taking a square root restores the original measurement unit. Mean square uses the square of that unit. For a sampled waveform, the entries must represent equal time intervals for this unweighted calculation to approximate its time-averaged RMS.

Interpreting root mean square

RMS includes both a constant offset and variation around that offset. It is therefore different from the standard deviation unless the appropriate mean and divisor conditions are satisfied. A short or unrepresentative set of signal samples can miss peaks and yield a misleading result. This page computes a supplied list; it does not record audio, read oscilloscope files, or integrate a continuous waveform.

Assumptions & limitations

What this calculation assumes

• The supplied samples have equal weights; time-series samples represent equal time intervals.

What to keep in mind

• Equal sample weights only; no waveform capture or unequal-time integration.

Common questions