What is the formula for Half-Wave Rectified RMS Voltage?

The Half-Wave Rectified RMS Voltage formula is Vrms = Vpeak / 2 (half-wave rectified), where Vrms—RMS of the half-wave rectified waveform (V); Vpeak—Peak voltage (V).

What does Vrms mean in the Half-Wave Rectified RMS Voltage formula?

Vrms is RMS of the half-wave rectified waveform (V).

Half-Wave Rectified RMS Voltage

Q: How do you calculate Half-Wave Rectified RMS Voltage?

Use the formula Vrms = Vpeak / 2 (half-wave rectified). The RMS value of a half-wave rectified sine is exactly half its peak, because the waveform is zero for half of every cycle. Enter the values you know in the calculator above and it solves for the remaining variable.

Vrms = Vpeak / 2

Calculator

RMS Voltage

Peak Voltage

Result

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Formula

Vrms = Vpeak / 2 (half-wave rectified)

Description

The RMS value of a half-wave rectified sine is exactly half its peak, because the waveform is zero for half of every cycle. This RMS value—not the average—determines the heating and true power delivered to a resistive load and the rating of components carrying the rectified current. It contrasts with a full sine (Vpeak/√2) and a full-wave rectified output (also Vpeak/√2).

Variables

Vrms — RMS of the half-wave rectified waveform (V)
Vpeak — Peak voltage (V)

Practical Notes

Power into a resistor is Vrms²/R, so a half-wave signal delivers only a quarter of the power of a full sine of the same peak. Full-wave rectified RMS is Vpeak/√2 ≈ 0.707·Vpeak.

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