RMS ↔ Peak Converter
Convert RMS, peak and peak-to-peak for sine waveforms.
valid for a pure sine wave, zero DC offset
Vpk = √2 · Vrms · Vpp = 2 · Vpk
This tool converts between the four ways a sine wave's amplitude gets quoted: RMS, peak, peak-to-peak and rectified average. Enter whichever one you have — a multimeter's RMS, a scope cursor's peak-to-peak — and read the others instantly. Reference: 230 Vrms ↔ 325.27 Vpk ↔ 650.54 Vpp.
How it works
For a pure sinusoid v(t) = Vpk·sin(ωt) the levels are fixed ratios of each other: RMS (the equivalent-heating value) is Vpk/√2, peak-to-peak is 2·Vpk, and the rectified average is 2·Vpk/π. Instruments disagree about which one they report — multimeters speak RMS, oscilloscopes speak peak and peak-to-peak — so reconciling readings between them is a division or multiplication by √2 away.
The ratios above are only valid for clean sines with no DC offset. Distorted or non-sinusoidal signals need a true-RMS measurement; converting their peak by √2 understates or overstates the power depending on the crest factor.
Worked example
peak = 230 × √2 = 325.27 V
peak-to-peak = 650.54 V · rectified avg = 207.07 V
Parameters
| Parameter | Value | Notes |
|---|---|---|
| RMS | Vpk / √2 | ≈ 0.7071 · Vpk |
| Peak | √2 · Vrms | |
| Peak-to-peak | 2 · Vpk | |
| Rectified average | 2·Vpk / π | ≈ 0.6366 · Vpk |
| Validity | pure sine, no DC offset |
Python implementation
import math
# Sine-wave level relationships
def levels_from_rms(vrms: float):
vpk = vrms * math.sqrt(2)
return {"rms": vrms, "peak": vpk,
"pp": 2 * vpk, "avg_rect": 2 * vpk / math.pi}
lv = levels_from_rms(230)
assert round(lv["peak"], 2) == 325.27
assert round(lv["pp"], 2) == 650.54FAQ
▸Why is mains '230 V' actually 325 V at its peak?
Mains voltage is specified as RMS, the value that delivers the same heating power as an equal DC voltage. For a sine, peak = √2 × RMS, so 230 Vrms swings to ±325 V — the number that matters when choosing capacitor and semiconductor voltage ratings.
▸Do these ratios hold for square or triangle waves?
No — they are sine-specific. A square wave has RMS equal to its peak; a triangle wave's RMS is peak/√3. Applying √2 to a non-sinusoidal signal is precisely the mistake cheap 'average-responding' meters make on distorted waveforms.
▸What is the rectified average and why show it?
The mean of the absolute value: 2·Vpk/π ≈ 0.637·Vpk for a sine. Average-responding multimeters actually measure this and multiply by 1.111 (the sine form factor) to display 'RMS' — correct only for clean sines, which is why the value is worth knowing.
▸Which level does an oscilloscope show?
Scopes measure instantaneous voltage, so cursors naturally give peak and peak-to-peak; most scopes also compute true RMS numerically. Multimeters display RMS. This converter is the bridge when comparing the two instruments' readings.
▸Is my data uploaded?
No. All conversion runs locally in your browser.