RMS Voltage Calculator

This calculator calculates the RMS Voltage value from either the peak voltage, the peak-to-peak voltage, or the average voltage.

Overview

The RMS voltage calculator calculates the RMS voltage value from the peak voltage, the peak-to-peak voltage, or the average voltage. It calculates the RMS voltage based on the above formulas for each.

Equations

$$V_{rms} = \frac{1}{\sqrt{2}}*V_{P} = 0.707*V_{P}$$ 

$$V_{rms} = \frac{1}{2\sqrt{2}}*V_{P-P} = 0.353*V_{P-P}$$

$$V_{rms} = \frac{\pi}{2\sqrt{2}}*V_{avg} = 1.111*V_{avg}$$

$$V_{P}$$: The maximum instantaneous value of a function as measured from the zero-volt level. For the waveform shown above, the peak amplitude and peak value are the same, since the average value of the function is zero volts.

$$V_{P-P}$$: The full voltage between positive and negative peaks of the waveform; that is, the sum of the magnitude of the positive and negative peaks.

$$V_{rms}$$: The root-mean-square or effective value of a waveform.

$$V_{avg}$$: The level of a waveform defined by the condition that the area enclosed by the curve above this level is exactly equal to the area enclosed by the curve below this level.

Further Reading

Textbook - Basic AC Theory

Worksheet - Peak, Average and RMS Measurements

Video - Sine Wave Characteristics