Root Mean Square Calculator

About this calculator

The root mean square (RMS), also called the quadratic mean, is calculated by squaring every value, averaging those squares, and taking the square root of the result: RMS = √((x₁² + x₂² + ... + xₙ²) / n). Because squaring removes the sign of negative values before averaging, RMS gives a magnitude-based average that's always at least as large as the simple arithmetic mean — it's especially sensitive to values with large magnitude, which is exactly the property that makes it useful.

RMS is the standard way electrical engineers describe alternating current and voltage: household "120V AC" is actually an RMS value — the voltage that would deliver the same power to a resistive load as a constant 120V DC source, even though the instantaneous voltage swings both above and below that number in a sine wave. Beyond electronics, RMS is used in audio engineering to measure signal loudness and speaker power ratings, in statistics and signal processing to quantify error magnitude (root mean square error, RMSE, is a standard model-accuracy metric), and in mechanical engineering to characterize vibration and surface roughness.

This calculator takes up to five values and computes their root mean square directly, giving you the magnitude-based average used across these engineering and statistical applications.