RMS Voltage Calculator
Enter the peak voltage of a sine wave to get its RMS (effective) voltage in volts — plus the peak-to-peak voltage — and see why V_rms is the peak divided by the square root of two.
RMS and peak-to-peak at once
Enter the peak voltage and this RMS voltage calculator returns the RMS (effective) voltage and the peak-to-peak voltage together, both in volts.
Sine waves only
The V_peak ÷ √2 relation applies to a pure sine wave — square, triangle, and distorted waveforms use different factors.
What is RMS voltage?
The effective value of an AC signal
This RMS voltage calculator turns the peak voltage of an alternating-current sine wave into its RMS (root-mean-square) value — the effective voltage that does real work. RMS voltage is the equivalent steady DC voltage that would deliver the same average power to a resistor, which is why a "230 V" mains supply is quoted as an RMS figure even though the voltage actually swings far higher at its crest. For a sine wave the RMS value is always the peak divided by the square root of two, roughly 70.7 % of the peak. The calculator also reports the peak-to-peak voltage, the full swing from the lowest trough to the highest crest.
Enter a peak voltage in volts to get the RMS voltage and the peak-to-peak voltage of a sine wave instantly.
The RMS voltage of a sine wave is the peak voltage divided by the square root of two, and the peak-to-peak voltage is simply twice the peak.
V_rms = V_peak / √2Take EU mains, which peaks at about 325 V. Divide by √2 (about 1.4142) and the RMS voltage is 325 ÷ 1.4142 = 229.81 V — the familiar "230 V" rating. The peak-to-peak voltage is 2 × 325 = 650 V, the distance from the negative trough to the positive crest. That single √2 factor is what lets a meter read one effective number for a voltage that is constantly changing.
The conversion is exact, but it rests on one assumption worth keeping in mind.
Pure sine waves only
The V_peak ÷ √2 relation holds only for a pure, undistorted sine wave. Square waves, triangle waves, and clipped or noisy signals each have a different ratio between peak and RMS (the "form factor"), so this calculator should not be used for them. It also assumes a symmetric waveform with no DC offset — a signal riding on top of a DC level needs that offset accounted for separately.