RMS to Peak Voltage Converter
For a pure sine wave there is a fixed relationship between the RMS voltage that meters and power ratings use and the peak voltage that components must withstand. Peak is RMS times the square root of 2, and peak-to-peak is twice that. This converter takes an RMS voltage and returns the peak, peak-to-peak, and average (rectified mean) values for a sinusoid. Knowing the peak matters because capacitors, insulation, and semiconductors must survive the peak, not just the RMS, of an AC signal.
Sine-wave RMS to peak formula
Peak Vp = Vrms * sqrt(2) (sqrt 2 approx 1.41421)
Peak-to-peak Vpp = 2 * Vp = Vrms * 2 * sqrt(2)
Average (full-wave rectified) = Vp * 2 / pi = Vrms * 0.90032
Crest factor = Vp / Vrms = sqrt(2)
To go back: Vrms = Vp / sqrt(2)
These factors hold only for a pure sine wave. Other waveforms have different ratios set by their own crest factor.
AC voltage context
- RMS is the DC-equivalent heating value, which is why power ratings use it.
- Components must withstand the peak, which is about 1.41 times the RMS for a sine.
- Peak-to-peak is the full swing from negative peak to positive peak.
- The rectified average is what a simple non-RMS meter reads, lower than the RMS.
- These ratios apply to sine waves only; square and triangle waves differ.
RMS to peak: frequently asked questions
How do I convert RMS voltage to peak for a sine wave?
For a pure sine wave, peak voltage equals RMS voltage times the square root of 2 (about 1.41421). Peak-to-peak is twice the peak, so it equals RMS times 2 times the square root of 2 (about 2.82843). For example, 120 V RMS gives about 169.7 V peak and 339.4 V peak-to-peak.
How do I convert peak back to RMS?
Divide the peak voltage by the square root of 2 (about 1.41421), which is the same as multiplying by 0.70711. So a 170 V peak sine wave has an RMS value of about 120.2 V. This is the figure a true-RMS meter would read.
Does this only work for sine waves?
Yes. The square-root-of-2 factor applies only to a pure sinusoid. Square waves have a peak equal to their RMS, triangle waves use the square root of 3, and arbitrary waveforms need the crest factor of that specific shape. This converter assumes a clean sine wave.
What is the crest factor of a sine wave?
Crest factor is the ratio of peak to RMS. For a sine wave it is the square root of 2, about 1.414. A square wave has a crest factor of 1, and sharper or more peaky waveforms have larger crest factors. It tells you how spiky a signal is.
Why is mains voltage quoted as RMS?
RMS is the equivalent steady DC voltage that would deliver the same heating power to a resistor, so it is the most useful single number for power. A 120 V RMS supply heats a resistor exactly as a 120 V DC supply would, even though its peak swings to about 170 V.
Official sources
- NIST: SI electrical units and constants.
- IEEE Standards Association: AC quantity definitions and standards.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.