Definition

RMS voltage and current

V_{rms} = \frac{V _{m a x}}{2}, I_{rms} = \frac{I _{m a x}}{2}

Statement

The root-mean-square value of a sinusoidal voltage or current — the effective steady value that dissipates the same average power as a DC source of that value.

Symbols and units

$V_{rms}, I_{rms}$	root-mean-square voltage, current	V, A
$V_{m a x}, I_{m a x}$	peak voltage, current	V, A

When it applies

Any sinusoidal voltage or current — the factor 1/√2 is specific to a sine wave.

Don't use when

The factor 1/√2 is specific to a pure sine wave — a different waveform (square wave, triangle wave) has a different RMS-to-peak ratio.

Derivation

Defined so that P_avg = I_rms²R takes the identical form as DC power — averaging sin²(ωt) over a full cycle gives exactly ½, which is where the factor 1/√2 comes from.

V_{rms} = \frac{V _{m a x}}{2}

Worked examples

Peak voltage of household AC power

For a quoted RMS value of 230 V:

V_{m a x} = V_{rms} 2 \approx 325 V

The quoted 'voltage' is always the RMS value — the actual peak reached each cycle is noticeably higher.

Watch out for

RMS values are what meters read and what power calculations use directly — mixing peak and RMS values in the same calculation is a frequent source of error.

Connects to

AC voltage