RMS Calculator
The root mean square of a waveform or a list of readings, with peak, average, form factor and crest factor.
Results
What this tool does
RMS is the number that makes alternating current comparable to steady direct current. It is the value that delivers the same power into a resistor, and it is not the average — for a sine wave the average is zero, while the RMS is about seventy-one per cent of the peak. Choose a waveform and give its peak, or paste a list of measured samples, and this page returns the RMS along with the peak-to-peak span, the rectified average that a cheap meter actually measures, and the form and crest factors that connect them.
Formula
sine wave: RMS = peak ÷ √2 · triangular: peak ÷ √3 · square: RMS = peak · samples: √(Σx² ÷ n)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
waveform | Shape of the wave | — |
peak | Peak value | — |
samples | The readings | — |
load | Load resistance | Ω |
RM | RMS value | — |
PK | Peak value | — |
PP | Peak to peak | — |
AV | Rectified average | — |
FF | Form factor | — |
CF | Crest factor | — |
PW | Power into that resistance | W |
NS | Readings used | — |
Worked example
- Shape of the wavesine
- Peak value325.269
- The readings
- Load resistance0 Ω
- RMS value229.999916
- Peak value325.269000
- Peak to peak650.538000
- Rectified average207.072677
- Form factor1.110721
- Crest factor1.414214
- Power into that resistance0.000000 W
- Readings used0
Limitations
- Electrical installations are governed by national wiring rules. Cable sizing also depends on installation method, grouping, ambient temperature and protection devices, which this calculator does not evaluate.
Frequently asked questions
Why not just use the average?
Because the average of a sine wave is zero — it spends as much time below the line as above — and a heater plugged into it plainly does not produce zero heat. Power depends on the square of the voltage, and squaring makes the negative half count just as much as the positive. The RMS value is the one that gets the power right: a 230 volt RMS supply heats a resistor exactly as much as 230 volts of steady direct current would. That is the whole definition, and it is why every mains voltage you have ever seen quoted is an RMS figure.
Why does the waveform change the answer?
Because the RMS value depends on how long the signal spends near its peak. A square wave sits at full amplitude the whole time, so its RMS equals its peak. A sine wave spends most of its time somewhere in the middle, so its RMS is about 71 per cent of the peak. A triangle wave spends even less time high and comes out at 58 per cent. This matters practically: a cheap multimeter measures the rectified average and multiplies by 1.11, which is correct only for a sine wave. On a dimmer output or a switching supply it can be twenty per cent out, which is what "true RMS" on a meter is worth paying for.