What Is Root Mean Square?

Root mean square (RMS) is the square root of the mean of the squared values of a set. Squaring every value makes negatives positive, so the RMS captures typical magnitude rather than net direction. It is the standard measure of amplitude for alternating current, audio signals, and vibration.

How to Calculate RMS

RMS = √(Σxᵢ² ÷ n) — square each value, add them, divide by the count, then take the square root. When the values represent a continuous signal like a sine wave, the same idea becomes an integral, but for a finite list of measurements this formula is exact.

Why Household Voltage Is Stated as RMS

Mains electricity alternates between about +170 V and −170 V, averaging to zero. Saying "120 volts" would be meaningless for the average — yet 120 V RMS is exactly right, because a heater connected to that AC runs at the same power as one connected to 120 V DC. The RMS value is the DC equivalent that produces the same heating effect.