Peak & RMS Voltage Calculator

RMS (root mean square) voltage is the effective value of an AC waveform: an AC supply at a given rms voltage delivers the same heating power into a resistive load as a DC supply of that voltage. It is what a standard multimeter displays and what equipment ratings refer to. UK mains is 230 V rms, even though the sine wave actually peaks at about 325 V.

For a sine wave, divide the peak by the square root of 2: Vrms = Vpeak / 1.4142, or about 0.707 × Vpeak. Going the other way, Vpeak = Vrms × 1.4142. Peak-to-peak is simply twice the peak for a symmetrical waveform. These ratios only hold for sinusoidal waveforms, which is the case for grid-supplied power in the UK.

Because 230 V is the rms figure, the instantaneous voltage on a UK mains circuit swings up to about plus and minus 325 V every cycle, 650 V peak-to-peak. Insulation, capacitors and semiconductor devices experience that peak stress 100 times a second on a 50 Hz supply, so components connected across the mains are selected for the peak voltage plus a safety margin, not the rms value.

No. The square root of 2 ratio between peak and rms applies only to pure sine waves. A square wave has equal rms and peak values, while the output of many inverters, dimmers and variable speed drives is chopped and needs a true-rms meter to measure correctly. A basic averaging multimeter assumes a sine wave and can read significantly wrong on distorted waveforms.

It is the rectified average of the sine wave, equal to about 0.9 times the rms value. It matters because low-cost averaging multimeters actually measure this quantity and scale it up assuming a sine wave. On a clean sinusoid that approach works; on a distorted waveform an averaging meter and a true-rms meter will disagree, sometimes by 10% or more, which often explains conflicting readings on drive outputs.