RMS measures the typical size of quantities that can be positive or negative. Mains electricity of 230 V RMS delivers the same power as 230 V DC, although its peak is about 325 V. In statistics, the root mean square error summarises prediction errors.
How to use the Root Mean Square Calculator
- Type the numbers separated by commas, spaces or new lines.
- Read the result – it updates as you type.
Results update as you type, and everything is calculated in your browser.
How it works
Each value is squared (so signs do not cancel), the squares are averaged and the square root brings the result back to the original units.
Tips
- Estimate the answer first so you can spot an impossible result.
- Work with whole numbers where possible and place the decimal point at the end.
- Use the order of operations: brackets, powers, multiplication and division, then addition and subtraction.
- For large integers, the calculator works with exact whole-number arithmetic in your browser.
Common mistakes to avoid
- Misaligning decimal points when adding or subtracting.
- Forgetting the remainder in whole-number division.
- Rounding too early in a multi-step calculation.
What each result means
- Root mean square = rms([Values])
- Arithmetic mean (for comparison) = mean([Values])
Formula
RMS = √((x₁² + x₂² + … + xₙ²) ÷ n)
Worked example
Inputs — Values: 3, -4, 5, -2, 6.
Results — Root mean square = 4.24264069; Arithmetic mean (for comparison) = 1.6.
Key terms
- Quadratic mean
- Another name for the root mean square.
Frequently asked questions
Why use RMS instead of the mean?
Positive and negative values cancel in the mean; RMS measures magnitude.
What is the RMS of a sine wave?
Its peak divided by √2 ≈ 0.707 × peak.
Is RMS always at least the mean?
It is always at least the mean of the absolute values.
What is RMSE?
Root mean square error – the RMS of prediction errors.
What formula does the Root Mean Square Calculator use?
RMS = √((x₁² + x₂² + … + xₙ²) ÷ n).