Case 1
- Peak voltage (V)
- 325V
229.809704V
Open with these valuesRMS Voltage Calculator
229.809704V
Result: 229.809704 VFor a sine wave the RMS voltage is the peak divided by √2, about 70.7 % of it. European mains peaks at roughly 325 V, which is why it is quoted as 230 V. The factor holds for a pure sine only — a square wave has an RMS equal to its peak.
The numbers at a glance
| Peak voltage (V) (V) | Result (V) |
|---|---|
| 0.00 | 0.000000 |
| 100.00 | 70.710678 |
| 200.00 | 141.421356 |
| 300.00 | 212.132034 |
| 325.00Your value | 229.809704 |
| 400.00 | 282.842712 |
| 500.00 | 353.553391 |
| 600.00 | 424.264069 |
Worked examples
Case 2
- Peak voltage (V)
- 170V
120.208153V
Open with these valuesCase 3
- Peak voltage (V)
- 12V
8.485281V
Open with these valuesHow it's calculated
V_rms = V_peak ÷ √2
- StepEnter the peak voltage, measured from zero to the crest of the wave.
- StepRead the RMS voltage — the DC voltage that would deliver the same power.
- ResultDouble the peak instead if you need the peak-to-peak swing.
Reference table
| Peak voltage | Peak-to-peak | RMS voltage in V |
|---|---|---|
| 12 | 24 V | 8.485281 |
| 100 | 200 V | 70.710678 |
| 170 | 340 V | 120.208153 |
| 325 | 650 V | 229.809704 |
| 650 | 1300 V | 459.619408 |
Questions
How do I calculate RMS voltage from peak voltage?
Divide the peak voltage by the square root of two, which leaves about 70.7 % of the peak. A sine wave peaking at 325 V therefore has an RMS voltage of 229.81 V.
What is RMS voltage?
RMS, or root mean square, is the effective voltage of an AC signal — the steady DC voltage that would deliver the same average power to a resistor. That is why mains is quoted as 230 V even though it peaks far higher on every cycle.
What is the difference between peak, RMS and peak-to-peak?
Peak is the amplitude, measured from zero to the crest. RMS is the effective value, peak ÷ √2 for a sine. Peak-to-peak is the full swing from lowest trough to highest crest, twice the peak — for a 325 V peak that is 229.81 V RMS and 650 V peak-to-peak.
Why divide by the square root of two?
RMS means root mean square: square the wave, average it over a full cycle, then take the square root. For a pure sine the mean of the square works out to half the peak squared, and the square root of one half is 1 ÷ √2, roughly 0.707.
Does the formula work for any waveform?
No, the √2 factor applies to a pure sine wave only. A square wave has an RMS equal to its peak, a triangle wave divides by √3 instead, and clipped or distorted signals have their own form factors.
Sources and last check
Information, not professional advice.