RMS Voltage Calculator

What Is RMS Voltage?

RMS (root mean square) voltage is the effective AC voltage that would dissipate the same power in a resistive load as an equivalent DC voltage. Household mains in the United States is rated at 120 V RMS, even though the peak voltage is about 170 V.

RMS Voltage Formula

For a periodic waveform with DC offset \(V_0\), the total RMS voltage is:

For a pure sine wave with peak voltage \(V_p\) and no DC offset, \(V_{\text{ac,RMS}} = V_p / \sqrt{2}\). Square, triangle, sawtooth, and rectified sine waves each have their own conversion factors from peak, peak-to-peak, or average voltage.

Waveform Conversion Factors

A sine wave: \(V_{\text{RMS}} = V_p / \sqrt{2}\). A square wave: \(V_{\text{RMS}} = V_p\). Triangle and sawtooth waves: \(V_{\text{RMS}} = V_p / \sqrt{3}\). Half-wave rectified sine: \(V_{\text{RMS}} = V_p / 2\). Full-wave rectified sine: \(V_{\text{RMS}} = V_p / \sqrt{2}\).

Related tools: HP to Amps Calculator and Ohm's Law Calculator.