Calculate peak voltage or average rectified voltage from a full-wave rectified sine wave using mV, V, or kV with unit conversion in either direction.

For an ideal full-wave-rectified sine wave. Enter the nonnegative peak magnitude, not RMS or peak-to-peak voltage.

Average (Rectified) Voltage Formula

The calculator uses the average value of a full-wave-rectified sine wave. For an ideal sine wave, the average rectified voltage is exactly 2/π times the peak voltage (approximately 0.636620).

Vₐvg = (2 / π) × Vₚeak
Vₚeak = (π / 2) × Vₐvg
  • V_avg = average rectified voltage
  • V_peak = peak voltage of the sine wave
  • 2/π = full-wave-rectified sine-wave average factor; the calculator uses π rather than a rounded factor

Select the value to solve for, enter the known nonnegative voltage magnitude and select Calculate. Average rectified voltage equals peak voltage multiplied by 2/π; peak voltage equals average rectified voltage multiplied by π/2. Input unit changes convert the entered quantity. Calculations use volts internally and the selected Result unit for display.

Common Rectified Sine Wave Voltage Relationships

These values apply to an ideal sine wave. The calculator uses the average rectified relationship shown in the first row.

Voltage quantity Formula using peak voltage Multiplier
Average rectified voltage, full-wave V_avg = (2/π) × V_peak 2/π ≈ 0.636620
RMS voltage of sine wave V_rms = V_peak / √2 1/√2 ≈ 0.707107
Peak voltage from average rectified voltage V_peak = (π/2) × V_avg π/2 ≈ 1.570796

Voltage Unit Conversions

Unit Meaning Equivalent in volts
mV millivolt 1 mV = 0.001 V
V volt 1 V = 1 V
kV kilovolt 1 kV = 1000 V

Example Calculations

Example 1: Find average rectified voltage from peak voltage

You have a sine wave with a peak voltage of 20 V.

Vₐvg = (2 / π) × 20
Vₐvg ≈ 12.732395 V

The average rectified voltage is approximately 12.732395 V.

Example 2: Find peak voltage from average rectified voltage

You have an average rectified voltage of 5 V.

Vₚeak = 5 × (π / 2)
Vₚeak ≈ 7.853982 V

The peak voltage is approximately 7.853982 V.

FAQ

What does average rectified voltage mean?

Average rectified voltage is the mean value of a waveform after the negative half-cycles have been flipped positive. For an ideal full-wave-rectified sine wave, this average is 2/π times the peak voltage. The signed average of an unrectified zero-offset sine over a full cycle is zero.

Is average rectified voltage the same as RMS voltage?

No. For a sine wave, average rectified voltage is about 0.637 times the peak voltage, while RMS voltage is about 0.707 times the peak voltage. RMS voltage is commonly used for power calculations. Average rectified voltage is the arithmetic average of the rectified waveform.

Does this formula apply to all waveforms?

No. The 2/π factor applies to an ideal full-wave-rectified sine wave, without diode drops, filtering or load regulation. Other waveforms, such as square waves, triangle waves, or distorted AC signals, have different average values.