AC foundations
RMS voltage
- where
- RMS voltage (V)
- peak voltage (V)
Explain this equation
Works out the RMS voltage of a sine wave from its peak. Use it when reading a peak off a scope.
Vᵣₘₛ is the root-mean-square voltage: the equivalent steady value for heating. Vₚ is the peak voltage.
For a sine wave, the effective value comes out at the peak divided by √2, so about 0.707 times the peak.
Sense check: a 100 V peak gives about 70.7 V RMS. A 325 V peak is mains at 230 V RMS.
Watch out: only true for a pure sine wave. The average of a sine wave over a cycle is zero, but its RMS is not.
Divide a sine wave’s peak voltage by √2 to find RMS voltage. RMS is not the arithmetic average over a complete AC cycle.
A symmetric sine wave has zero full-cycle mean while still delivering heating power into a resistor.
Enter your values to see the result.
Common mistake
Confusing zero average with zero RMS.
Limits
Sine wave centred on zero.
Sources
The tools calculate the displayed equation. They do not automatically choose cable sizes, approve installations, supply current regulatory tables, certify equipment or replace inspection and testing.