About the RMS Voltage Calculator
This RMS voltage calculator converts any one measurement of an AC waveform — peak, peak-to-peak, RMS or average — into all the others. Choose the waveform shape (sine, square, triangle, sawtooth, half-wave or full-wave rectified sine) and the tool applies the right ratios, then reports the crest factor, form factor and the power the voltage would deliver into a resistive load.
It is for students, technicians and hobbyists who read a peak-to-peak value off an oscilloscope but need the RMS value for power calculations, or who need to know the peak voltage behind a mains or transformer RMS rating — 120 V RMS mains, for example, actually peaks at about 170 V, which matters when choosing capacitor and diode voltage ratings.
“Average” here means the average of the rectified (absolute) waveform, which is what average-responding meters measure; the true mathematical average of a symmetrical AC wave is zero. The waveforms are ideal and have no DC offset, except the rectified ones, which are always positive.
With the default inputs, the rms voltage is 120.2082 V. Change any value above to recalculate instantly.
How to use the rms voltage calculator
- 1Select the waveform shape.
- 2Choose which value you know: peak, peak-to-peak, RMS or average.
- 3Enter the voltage.
- 4Optionally enter a load resistance to see the power delivered.
- 5Read all four voltage values plus the crest and form factors.
Formula and method
RMS (root mean square) is the square root of the average of the squared voltage over one cycle. It is the DC voltage that would produce the same heating in a resistor, which is why AC mains and power calculations use it. Integrating each ideal waveform gives a fixed ratio to its peak: 1/√2 ≈ 0.7071 for a sine, 1 for a square wave, 1/√3 ≈ 0.5774 for triangle and sawtooth, and 1/2 for a half-wave rectified sine.
The calculator first converts your known value to peak voltage, then multiplies by each ratio. Peak-to-peak is twice the peak for symmetrical AC waves and equal to the peak for rectified waves. Crest factor = peak ÷ RMS; form factor = RMS ÷ rectified average (1.111 for a sine). Power into a resistor is Vrms² ÷ R.
- Vp
- Peak voltage (zero to maximum)
- Vpp
- Peak-to-peak voltage
- Vrms
- Root-mean-square voltage
- Vavg
- Average of the rectified waveform
- R
- Load resistance
Worked examples
170 V peak sine wave (US mains)
Vrms = 170 ÷ √2 ≈ 120.2 V, which is why US mains is called 120 V. Peak-to-peak is 340 V and the rectified average is 2 × 170 ÷ π ≈ 108.2 V. Into 100 Ω it delivers 120.2² ÷ 100 ≈ 144.5 W.
120 V RMS to peak
Vp = 120 × √2 ≈ 169.7 V and Vpp ≈ 339.4 V. A capacitor across 120 V AC mains must therefore be rated well above 170 V.
Triangle wave of 20 V peak-to-peak
A 20 Vpp triangle has a 10 V peak. Its RMS value is 10 ÷ √3 ≈ 5.77 V and its rectified average is 5 V, giving a crest factor of √3 ≈ 1.73.
Frequently asked questions
How do I convert peak voltage to RMS?+
For a sine wave multiply the peak by 0.7071 (divide by √2). For a square wave RMS equals the peak, and for a triangle or sawtooth wave divide the peak by √3 (multiply by 0.5774).
How do I convert RMS to peak-to-peak?+
For a sine wave, Vpp = Vrms × 2√2 ≈ Vrms × 2.828. So 230 V RMS mains swings about 650 V peak-to-peak, and 120 V RMS swings about 339 V peak-to-peak.
Why do we use RMS voltage?+
RMS is the equivalent DC voltage that would produce the same power in a resistor. It lets you use P = V²/R and other DC formulas directly with AC, which is why mains voltage and audio power are quoted as RMS.
What is the difference between average and RMS voltage?+
The average of a symmetrical AC wave is zero, so meters use the average of the rectified wave (0.637 × peak for a sine). RMS (0.707 × peak for a sine) is always higher for non-square waves, and their ratio is the form factor.
Why does my multimeter read the wrong RMS on non-sine waves?+
Cheaper meters measure the rectified average and multiply by 1.111, the sine form factor. That is only correct for sine waves; for square, triangle or distorted waves you need a true-RMS meter.