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RMS Voltage Calculator

Find RMS and peak-to-peak voltage.

Result

229.81 V
650.00 V

How it is calculated

From the peak voltage of a pure sine wave the tool computes Vrms = Vpeak ÷ √2 (about 0.7071 × Vpeak) and Vpp = 2 × Vpeak. Peak voltage means the maximum height of the wave measured from zero, in volts. Both results are shown in volts with two decimals.

The √2 factor holds only for a sinusoid. Square waves, triangle waves, rectified signals and distorted waveforms have different ratios between peak and RMS, so this tool gives wrong values for them. The peak must be zero or more; a negative number returns no result, so enter the magnitude. Peak-to-peak is simply the swing from the lowest to the highest point, which for a wave centred on zero is twice the peak.

Worked example

A mains waveform reaches a peak of 325 V. RMS = 325 ÷ √2 = 325 ÷ 1.41421 = 229.81 V, close to the 230 V rating printed on the outlet. Peak-to-peak = 2 × 325 = 650.00 V. This is why an oscilloscope showing a 650 V swing and a multimeter reading about 230 V describe the same supply, one with the full height of the wave and the other with its heating-equivalent value.

Try this example →

Common mistakes

  • Entering the peak-to-peak reading from an oscilloscope in the peak field. The result is then twice too large; halve a peak-to-peak value first.
  • Entering a nominal RMS voltage, such as 230, as the peak. The tool then returns an RMS of about 162.63 V, not 230 V.
  • Applying the √2 factor to a square wave or other non-sine signal. For a square wave the RMS equals the peak.
  • Entering a negative peak voltage to describe the lower half of the wave. The tool needs the positive magnitude.
  • Expecting a DC offset to be included. The tool assumes the wave is centred on 0 V.

About this calculator

For a sinusoidal AC voltage, this calculator finds the RMS (root-mean-square) voltage, Vrms = Vpeak / √2 (≈ 0.707 × Vpeak), and the peak-to-peak voltage, Vpp = 2 × Vpeak. RMS voltage is the value that would deliver the same average power to a resistive load as an equivalent DC voltage — it's derived by squaring the sine wave, averaging over a full cycle, and taking the square root.

RMS is the standard way AC voltage is specified everywhere: a "230V" or "120V" mains outlet is an RMS value, not the actual peak voltage (which is roughly 325V or 170V respectively), and RMS current and voltage are what's used to calculate real power dissipation, P = Vrms × Irms, in any AC circuit.

Electrical engineers and electricians sizing wiring and components for AC power, audio engineers working with amplifier voltage specs, and electronics students converting between peak, peak-to-peak, and RMS readings on an oscilloscope all use this calculator.

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