Half-Wave Rectified RMS Voltage

Vrms = Vpeak / 2

Quick answer

This calculator solves Vrms = Vpeak / 2 (half-wave rectified) for RMS Voltage. With Peak Voltage 26.4 V, the result is 13.2 V. It solves in 2 directions, so you can enter the values you have and get the one you need.

Calculator

RMS Voltage (V)
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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.

Symbols and units

Symbol Meaning Default unit Accepted units
Vrms RMS Voltage V pV, nV, µV, mV, V, kV
Vpeak Peak Voltage V pV, nV, µV, mV, V, kV

Step by step

  1. 1. What you know: Peak Voltage 26.4 V
  2. 2. The relation: Vrms = Vpeak / 2 (half-wave rectified)
  3. 3. Substitute: Vpeak = 26.4 V
  4. 4. Result: RMS Voltage = 13.2 V

Worked examples

Minimum range

Given: Peak Voltage 0.726 V

Result: RMS Voltage = 0.363 V

Low range

Given: Peak Voltage 7.26 V

Result: RMS Voltage = 3.63 V

Typical

Given: Peak Voltage 26.4 V

Result: RMS Voltage = 13.2 V

High range

Given: Peak Voltage 0.506 kV

Result: RMS Voltage = 0.253 kV

Maximum range

Given: Peak Voltage 5.06 kV

Result: RMS Voltage = 2.53 kV

Solving for each variable

Solve for RMS Voltage

Peak Voltage 0.726 V → 0.363 V

Solve for Peak Voltage

RMS Voltage 0.33 V → 0.66 V

How RMS Voltage changes with Peak Voltage

Peak Voltage (input) RMS Voltage (result)
5.81 V 2.905 V
14.53 V 7.263 V
29.05 V 14.53 V
43.58 V 21.79 V
58.1 V 29.05 V
87.15 V 43.58 V
116.2 V 58.1 V
0.2324 kV 116.2 V
0.4067 kV 0.2034 kV
0.581 kV 0.2905 kV

The same result in other units

Unit Value
mV 13200
V 13.2
kV 0.0132

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Frequently asked questions

How do you calculate Half-Wave Rectified RMS Voltage?

Use Vrms = Vpeak / 2 (half-wave rectified). With Peak Voltage 26.4 V, RMS Voltage works out to 13.2 V.

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

The formula is 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.

How do you find Peak Voltage when you know the other values?

Rearrange for Peak Voltage: with RMS Voltage 0.33 V, Peak Voltage is 0.66 V.

What units does Half-Wave Rectified RMS Voltage use?

RMS Voltage is shown in mV, V, kV. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

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