Calculators
Root Mean Square Calculator
Calculate the root mean square (RMS) of signed numeric data privately in your browser.
Calculate the quadratic mean of a dataset.
Enter up to 10000 finite values separated by spaces, commas, semicolons, or newlines. RMS = √(Σ(x²) / n). For 3 and 4, RMS is √12.5 ≈ 3.535534. Negative values contribute the same squared magnitude as positive values, and an all-zero dataset returns zero. Use consistent units; the result has those same units. RMS describes magnitude and differs from standard deviation because it does not subtract the mean. Values are equally weighted samples; this tool does not integrate continuous waveforms. Results use floating-point arithmetic rounded to 12 significant digits. All processing stays in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
What is root mean square?
RMS is the square root of the arithmetic mean of squared values: √(Σ(x²) / n). For 3 and 4, the result is approximately 3.535534.
Can I enter negative numbers or zero?
Yes. Negative and positive values of the same magnitude contribute equally. An all-zero dataset returns zero. Empty input and nonfinite values are rejected.
Is RMS the same as standard deviation?
No. Standard deviation measures spread around the mean, while RMS measures magnitude relative to zero. They coincide for a population dataset whose mean is zero.
How should samples be weighted?
Each entered value has equal weight. For a time signal, use equally spaced samples. This calculator does not integrate a continuous waveform or apply custom sample weights.
What input formats are supported?
Separate up to 10000 values with spaces, commas, semicolons, or newlines. Use decimal points and optional scientific notation without thousands separators. Calculations run locally and display 12 significant digits.