RMS and Peak Voltage

Also known as root mean square voltage · peak to RMS

V_{rms} = \frac{V_{peak}}{\sqrt{2}}

V_rms =

V_peak =

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Constant used — built into this formula, no need to enter

\sqrt{2} = 1.4142135623730951

Square Root of Two · exact

Learning zone

AC voltage spends most of its time below its peak, so which number is "the" voltage? The fair answer is the DC level that would heat a resistor equally — the root-mean-square — and for a sine wave that works out to peak/√2. "120 V" mains actually swings to ±170 V; European "230 V" reaches ±325 V. Power formulas like P = V²/R work unmodified with RMS values, which is exactly why the convention exists — and why capacitors in mains equipment must be rated for the peak, not the label.

RMS and Peak Voltage

V_{rms} = \frac{V_{peak}}{\sqrt{2}}

Where

$V_{rms}$ = RMS voltage
$V_{peak}$ = Peak voltage

Missing one of these? Work it out first, then come back

RMS voltage — Ohm's Law, Electrical Power (P = VI)
Peak voltage — Ohm's Law, Electrical Power (P = VI)

Part of this formula set

Reactance, resonance and time constants

7 formulasHow capacitors and inductors oppose alternating current, the frequency at which they cancel, and the RC and RL constants that set switching speed.