Root Mean Square Calculator
Calculate RMS magnitude for a list of signed or unsigned observations.
Loading tool…
How to use Root Mean Square Calculator
RMS is the square root of the mean of squared observations. The calculation scales values before squaring to preserve a useful numeric range.
- Enter numbers.
- Check that the input follows the stated limits and uses consistent units.
- Run the calculator, review the result, then copy or download it.
Good to know
- Up to 1,000 equally weighted observations. This is a discrete RMS, not continuous signal integration or an instrument calibration.
- Decimal inputs have at most 120 characters and magnitude from 1e-100 to 1e15, or zero. Floating-point results are rounded to 12 significant digits; extreme derived results may underflow or be rejected. Exact integer results are identified separately.
Common questions
What calculation does Root Mean Square Calculator perform?
RMS is the square root of the mean of squared observations. The calculation scales values before squaring to preserve a useful numeric range.
Can a negative input make RMS negative?
No. Squaring removes each sign, so the RMS magnitude is always nonnegative.
Keep going with related tools
All math →Descriptive Statistics Calculator
Summarize a numeric list with mean, median, modes, range, count, and sum.
MathFraction Calculator
Add, subtract, multiply, or divide two fractions and reduce the exact result.
MathSampled Signal Spectrum Workbench
Inspect a bounded real-sample DFT with explicit window gain, single-sided amplitude, phase threshold and a Parseval energy check.
MathUncorrelated Measurement Uncertainty Budget
Build a transparent first-order uncertainty budget with standard or bounded-distribution components and an entered coverage factor.
MathIncoherent Sound Level Combiner
Combine same-reference sound levels by adding their incoherent intensity ratios stably.
MathLinear Spring and Oscillator Calculator
Calculate ideal spring restoring force, stored energy and undamped oscillation period.