RMS Voltage Calculator
Alternating voltage swings up and down, so quoting a single number for it takes a little care. The figure that matters for power is the root-mean-square voltage, the steady direct-current voltage that would heat a resistor at exactly the same rate as the alternating signal does. That is why mains supplies are always labeled by their RMS value rather than their peak, and why RMS is the number engineers reach for first. This calculator converts between the peak voltage of a sine wave and its RMS value. For a clean sinusoid, the relationship is fixed: the RMS voltage is the peak divided by the square root of two, roughly 0.7071 times the peak. Enter the peak voltage of your sine wave and the tool returns the RMS voltage, and it also shows the conversion factor so the arithmetic is transparent. Remember that the square-root-of-two factor is specific to sine waves; square and triangle waves convert differently. This is the everyday tool for relating a measured peak on an oscilloscope to the RMS value your power calculations actually need, whether you are checking a mains supply or rating a component for the voltage it must withstand. A worked example below reconciles exactly to the calculator default.
For a sine wave the RMS voltage is the peak scaled down by the square root of two: Vrms = Vpeak / sqrt(2). A peak of 170 V gives an RMS voltage of 120.21 V, the familiar mains figure.
RMS voltage formula
Vrms = Vpeak / sqrt(2) = 0.7071 x Vpeak
Vpeak = peak (amplitude) voltage
valid for a pure sine wave only
rearranged: Vpeak = Vrms x sqrt(2)
The square root of two comes from averaging the square of a sine over a full cycle and taking the root. It applies only to sinusoidal signals.
Worked example
A sine wave with a peak voltage of 170 V.
- Conversion factor = 1 / sqrt(2) = 0.7071.
- Vrms = 170 x 0.7071.
- Vrms = 120.21 V.
These are the calculator's default inputs, so the result above matches the widget exactly.
RMS voltage calculator: frequently asked questions
What is RMS voltage?
Root-mean-square voltage is the steady DC voltage that would deliver the same average power to a resistor as a given AC waveform. It is the most useful single number for an alternating signal, because power depends on the RMS value, not the peak. AC mains voltages are always quoted as RMS.
Why divide the peak by the square root of two?
For a pure sine wave, averaging the square of the instantaneous voltage over a cycle and taking the square root gives the peak divided by the square root of two, about 0.707 times the peak. This factor is specific to sine waves; other waveform shapes have different peak-to-RMS ratios.
Does this work for any waveform?
No. The square-root-of-two factor applies only to a sinusoidal voltage. Square waves, triangle waves and distorted signals each have their own conversion factor between peak and RMS. Use this calculator only when the signal is a clean sine wave.
How does RMS relate to mains voltage?
When a supply is described as 120 V or 230 V, that is the RMS value. The actual peak voltage is higher, the RMS times the square root of two, so a 120 V RMS supply peaks at about 170 V. Insulation and component ratings must account for the higher peak.
What is the RMS voltage formula?
For a sine wave, RMS voltage equals the peak voltage divided by the square root of two, which is the peak times about 0.7071. Rearranged, the peak voltage equals the RMS voltage times the square root of two.
Official sources
- Electrical units, AC quantities and measurement standards: US National Institute of Standards and Technology (NIST). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.