What RMS Means and Why It Is Not the Average
RMS stands for root mean square, and the name is a literal recipe: square the waveform, take the mean of those squares, then take the square root. The reason for that apparently odd procedure is that heating depends on the square of voltage, so squaring first is what makes the result physically meaningful.
The RMS value of an AC waveform is the DC voltage that would produce the same heating in a resistor. That is why mains is described as 230 V even though its instantaneous voltage spends most of the cycle somewhere else entirely, and why a 230 V RMS supply and a 230 V DC supply deliver identical power to a heater.
The simple average would be useless
The arithmetic mean of a symmetrical sine wave is zero, since the negative half cancels the positive. A measure that reports zero for a supply capable of electrocution is not a useful one — which is precisely why RMS exists.
The √2 factor applies only to sine waves
For a sine, VRMS = Vpeak/√2, so nominal 230 V mains peaks at about 325 V. This relationship is specific to the sine shape, and applying it to anything else gives the wrong answer:
| Waveform | VRMS relative to peak |
|---|
| Sine | 0.707 × Vpeak |
| Square (symmetrical) | 1.000 × Vpeak |
| Triangle / sawtooth | 0.577 × Vpeak |
Why true-RMS meters cost more
Cheap meters rectify the signal, measure its average, and multiply by 1.11 — the form factor that converts average to RMS for a sine wave. On a distorted waveform, such as the current drawn by a switch-mode supply or the output of a phase-angle dimmer, that assumption fails and the reading is wrong, usually low. A true-RMS instrument performs the actual squaring and averaging, and is essential anywhere electronic loads are involved.