RMS Voltage Calculator

Enter a peak or peak-to-peak voltage to calculate the RMS voltage of a sine wave.

How to Use the RMS Voltage Calculator

Select "From Peak" or "From Peak-to-Peak," enter that value, and the RMS voltage comes back instantly. As with the rest of this trio, the math here assumes a clean sine wave.

From peak:          Vrms = Vpeak ÷ √2
From peak-to-peak:  Vrms = Vpp ÷ (2√2)

RMS — root mean square — isn't an average in the ordinary sense; it's the DC-equivalent voltage that would deliver the same heating effect in a resistor as the AC waveform does over a full cycle. That's a deliberately chosen definition, not an arbitrary one, and it's why every multimeter, utility bill, and appliance nameplate voltage is quoted as RMS rather than peak: RMS is the number that actually predicts how much work the electricity does.

A 169.7 V peak sine wave has an RMS value of exactly 120 V — the wave everyone calls "120-volt power" never actually sits at 120 V except twice per cycle, in passing, on its way between roughly −169.7 V and +169.7 V. Divide a peak-to-peak reading of 339.4 V by 2√2 (≈2.828) and the same 120 V falls out.

Have RMS already and need to go the other way? The Peak Voltage and Peak-to-Peak Voltage calculators both start from an RMS figure and derive the other two.