What this calculator does
An alternating voltage spends most of its time below its peak, so quoting the peak overstates what it can actually deliver. The RMS value is the equivalent steady voltage that would produce the same heating in a resistor, which is why it is the figure used everywhere in practice.
For a sine wave the RMS is the peak divided by the square root of two. A 230 V mains supply therefore has a peak of about 325 V, which is why components in mains equipment must be rated well above the nominal figure.
The formula
Divide the peak by the square root of two for the RMS value. The rectified average is two over π times the peak. Form factor is RMS divided by average, and crest factor is peak divided by RMS.
| Term | Meaning |
|---|---|
| RMS (root mean square) | The equivalent DC value that delivers the same power into a resistive load. |
| Crest factor | Peak divided by RMS, equal to √2 for a sine wave. |
| Form factor | RMS divided by rectified average, about 1.111 for a sine wave. |
The inputs explained
| Field | What to enter |
|---|---|
| Peak value (V (or A)) | The peak value, in volts or amps. The same arithmetic applies to either. |
When to use it
Rating components for mains
Insulation and capacitors must withstand the peak, not the nominal RMS, which is over 40 per cent higher.
Interpreting an oscilloscope trace
A scope shows peak or peak-to-peak directly, and converting to RMS is what allows comparison with a meter reading.
Calculating power
Power in a resistive load uses RMS values. Using peak values instead overstates the power by a factor of two.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What RMS values do common peak voltages give?
A range of peak values and the figures they correspond to.
Questions
Why not just use the average?
Because the simple average of a sine wave over a full cycle is zero, the positive and negative halves cancelling. Even the rectified average does not predict heating correctly, because power depends on the square of voltage, which is exactly what RMS accounts for.
Does the square root of two apply to every waveform?
No, only to a pure sine wave. Square waves have an RMS equal to their peak, and triangular waves divide by the square root of three. Non-sinusoidal waveforms need their own crest factors.
Why does mains equipment need higher-rated parts?
Because the insulation sees the peak, not the RMS. A 230 V supply peaks at about 325 V, and transient spikes go higher still, so parts are usually rated at 400 V or more.
Do multimeters read RMS?
Most read RMS, but many cheaper ones measure the average and scale it assuming a sine wave. On a distorted waveform those give the wrong answer, which is why true-RMS meters exist.
For the power a circuit actually delivers, see the AC power factor calculator. For the DC relationship between voltage and current, see the Ohm's law calculator.