Calculate peak amplitude or effective (RMS) voltage for a pure sine wave with zero DC offset, with conversions between V, mV, and kV.

Divide peak amplitude by โˆš2.

Pure sine wave with zero DC offset. Peak means amplitude from zero, not peak-to-peak voltage.

Result unit

Effective Voltage Formula

For a pure sine wave with zero DC offset, the following formula calculates effective (RMS) voltage from peak amplitude (not peak-to-peak voltage).

Veff = (Vโ‚šโ‚‘โ‚โ‚–) / (โˆš(2))

Variables:

  • Veff is the effective voltage
  • Vpeak is the peak voltage

To calculate the effective voltage, divide the peak voltage by the square root of 2. This โˆš2 relationship applies to a pure sine wave with zero DC offset; other waveforms and DC offsets require a different RMS calculation.

What is Effective Voltage?

Effective voltage, also known as RMS (root mean square) voltage, is a measure of the equivalent DC voltage that would produce the same power dissipation in a resistive load. It is a crucial parameter in AC (alternating current) circuits because it allows for the comparison of AC and DC voltages in terms of their ability to deliver power. RMS is the square root of the mean squared instantaneous voltage over a full cycle, not the arithmetic mean voltage. For a zero-offset sine wave, RMS equals peak amplitude divided by โˆš2.

How to Calculate Effective Voltage?

The following steps outline how to calculate the Effective Voltage.

  1. First, determine the peak amplitude (Vpeak) of a pure sine wave with zero DC offset. Select the quantity to solve for in the calculator.
  2. Next, use the formula Veff = Vpeak / โˆš2 to calculate the effective voltage.
  3. Finally, verify your calculation using the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Peak Voltage (Vpeak) = 10 V

Effective Voltage (Veff) = 10 / โˆš2 โ‰ˆ 7.07 V