Root Mean Square Calculator
RMS value of any dataset, waveform or error list.
Enter your values
ⓘ Live results
Results
- Root mean square
- 4.24264
- Mean of squares
- 18
- Peak magnitude
- 6
- Crest factor
- 1.4142
- Count
- 5
- Sine-wave equivalent peak
- 6
Quick answer
RMS is the square root of the mean of the squares — the effective magnitude of a set of values regardless of sign, used for AC voltage and error metrics.
RMS = √(Σxᵢ² ÷ n)
How to use the Root Mean Square Calculator
- 1Enter your values — signs are fine, they get squared away.
- 2Read the RMS as the effective magnitude.
- 3Use the crest factor to see how spiky the data is compared with a pure sine wave (1.414).
Worked example
Using the values the calculator loads with:
Inputs
- Values3, -4, 5, -6, 2
Results
- Root mean square4.24264
- Mean of squares18
- Peak magnitude6
- Crest factor1.4142
- Count5
- Sine-wave equivalent peak6
Frequently asked questions
Is RMS the same as standard deviation?
Only when the mean is zero. Standard deviation is the RMS of the deviations from the mean.
Why is mains voltage quoted as RMS?
Because RMS voltage delivers the same heating power as an equal DC voltage, which is the number that matters for equipment.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.