Root Mean Square Calculator
Calculate the RMS of comma- or space-separated values. The result includes every squared value, the mean square, and a check against the magnitude of the arithmetic mean.
Written and checked by TheToolNet Editorial Team · Last reviewed: September 19, 2026
Calculate root mean square
How to calculate RMS
Square every value, add the squares, divide by the number of values, and take the square root. For 3, 4, and 5, the squares are 9, 16, and 25. Their mean is 50/3, so RMS = √(50/3) ≈ 4.08248.
RMS versus arithmetic mean
The arithmetic mean averages signed values directly; RMS measures magnitude after squaring. For −3 and 3, the arithmetic mean is 0 while RMS is 3. For any real list, RMS is at least the absolute value of the arithmetic mean, which provides a useful calculation check.
When RMS is useful
RMS commonly describes varying signals, measurement error, velocity, and electrical current or voltage. The input values must represent comparable quantities in the same units. This page calculates the mathematical RMS only; it does not infer sampling weights or convert peak voltage to RMS unless the samples themselves are supplied.
Frequently asked questions
Do negative values affect RMS?
Their magnitudes do, but their signs disappear when squared.
Is RMS always positive?
It is nonnegative. It equals zero only when every input value is zero.
Should I use n or n − 1?
RMS uses n, the number of values. The n − 1 adjustment belongs to sample-variance estimation, not ordinary RMS.