RMS, peak and peak-to-peak
An AC voltage can be described in several ways:
- Peak (Vp): the maximum value above zero.
- Peak-to-peak (Vpp): from the lowest to the highest point, twice the peak for a symmetrical wave.
- RMS (root mean square): the DC voltage that would deliver the same power to a resistor. It is the value printed on outlets and read by true-RMS meters.
- Average rectified: the average of the absolute value, which cheap meters measure and then scale.
Conversion factors
| Waveform | RMS ÷ peak | Average ÷ peak | Crest factor | Form factor |
|---|---|---|---|---|
| Sine | 1/√2 ≈ 0.707 | 2/π ≈ 0.637 | 1.414 | 1.111 |
| Square | 1 | 1 | 1 | 1 |
| Triangle or sawtooth | 1/√3 ≈ 0.577 | 0.5 | 1.732 | 1.155 |
The crest factor is peak ÷ RMS and the form factor is RMS ÷ average.
Example: US outlets
US household outlets supply 120 V RMS at 60 Hz:
- peak: 120 × √2 ≈ 170 V;
- peak-to-peak: about 339 V;
- average rectified: about 108 V.
In Europe, 230 V RMS outlets peak at about 325 V.
Why it matters
- Component ratings: capacitors, diodes and insulation must withstand the peak voltage, not the RMS. A rectifier filter capacitor on 120 V charges to about 170 V.
- Power: P = V_RMS² ÷ R. A 120 V RMS supply into 12 Ω delivers 1,200 W.
- Meters: an average-responding meter assumes a sine wave and multiplies the average by 1.111. On square waves, dimmer outputs or inverter outputs, it can be wrong by 10% or more; use a true-RMS meter.
- Audio: amplifier power and signal levels are usually given in RMS. Oscilloscopes show peak-to-peak.
DC offsets
The calculator assumes a waveform centered on zero. If the signal has a DC offset, the true RMS is √(V_DC² + V_AC,RMS²).