Math Calculators

Root Mean Square (RMS) Calculator

Calculate the root mean square (quadratic mean) of a list of numbers.

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About the Root Mean Square (RMS) Calculator

The root mean square (RMS) is found by squaring every value, averaging the squares, then taking the square root. Because squaring removes negative signs, RMS is useful for measuring the typical magnitude of values that vary in both directions.

Formula: RMS = √((x₁² + x₂² + ... + xₙ²) ÷ n)

RMS is widely used in electrical engineering to describe AC voltage and current, as well as in statistics to measure error and variability.