Root Mean Square (RMS) Calculator
Paste your values to get their root mean square.
Your numbers
Separate numbers with commas, spaces or new lines. You can paste a column from a spreadsheet.
Your results
Root mean square
Root mean square
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Mean square
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Arithmetic mean
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Count
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Root Mean Square (RMS) Calculator by TheCalcTools
How the Root Mean Square (RMS) Calculator works
Square every value, take the mean of the squares, then the square root. Because squaring removes the sign, RMS measures the typical magnitude of values that swing positive and negative.
For a pure sine wave the RMS value is the peak divided by √2, which is why mains voltage is quoted as an RMS value.
The formula
RMS = √( (x₁² + x₂² + … + xₙ²) ÷ n )
Worked example
Using the default values shown in the calculator:
| Values | 3, -4, 5, -6 |
|---|
- Squares: 9 + 16 + 25 + 36 = 86.
- Mean square = 86 ÷ 4 = 21.5; RMS = √21.5 = 4.6368.
Result:
| Root mean square | 4.6368 |
|---|---|
| Mean square | 21.5000 |
| Arithmetic mean | -0.5000 |
| Count | 4 |
Frequently asked questions
How is RMS related to standard deviation?
The standard deviation is the RMS of the deviations from the mean. If the mean is zero they are equal.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.