# RMS Voltage Calculator

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

Volts (V)

Volts (V)

### 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.

Textbook - Basic AC Theory

Worksheet - Peak, Average and RMS Measurements

Video - Sine Wave Characteristics

Basic AC Circuits - RMS Voltage

1 Comment • P
Pedant Engineer August 07, 2021

If this is meant as a method of measuring the rms value of a mains voltage then the accuracy of the result is really not great. This method relies on the quantity being sinusoidal and mains is typically quite distorted and if measured on the secondary of the average small power transformer it can have far worse distortion.
If there is a uC in the system a simple software routine taking samples squaring them and adding them up and periodically taking the average and square root (integer not floating point numbers) is quick and essay and makes no assumptions about harmonic content or distortion. Some care required with mains connections though of course but can be done and safe if done right.

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