# RMS Voltage Calculator

Calculate the RMS voltage given the peak or the peak-to-peak voltage with the calculator below.

## Convert Peak Voltage to RMS Voltage

## Convert Peak-to-Peak Voltage to RMS Voltage

## RMS Voltage Results:

Do you want to calculate peak voltage or peak-to-peak voltage?

## How to Calculate RMS Voltage

Root mean square, or RMS voltage is the square root of the mean of the squares of the voltages in the AC waveform. For example, if there are 100 voltages sampled in waveform, the RMS would be equal to the square root of all of the voltages squared, added together, and divided by 100.

The following formula illustrates how to find RMS voltage given a sample of voltages.

V_{RMS} = √ V_{1}^{2} + V_{2}^{2} + … + V_{n}^{2}n

You can also find RMS voltage if you know the peak voltage or peak-to-peak voltage.

### Peak Voltage to RMS Voltage Formula

Given the peak voltage, the RMS voltage can be calculated using this formula where V_{P} is the peak voltage.

V_{RMS} = 1√2 × V_{P}

In other words, RMS voltage is equal to one divided by the square root of two times the peak voltage.

**For example,** find the RMS voltage using a peak voltage of 120 V.

V_{RMS} = 1√2 × 120 V

V_{RMS} = 0.7071 × 120 V

V_{RMS} = 84.8528 V

### Peak-to-Peak Voltage to RMS Voltage Formula

The RMS voltage can also be found if the peak-to-peak voltage is known using this formula where V_{P-P} is the peak-to-peak voltage.

V_{RMS} = 12 × √2 × V_{P-P}

Thus, RMS voltage is equal to one divided by two times the square root of two, times the peak voltage.

**For example,** let’s find the RMS voltage using a peak-to-peak voltage of 24 V.

V_{RMS} = 12 × √2 × 24 V

V_{RMS} = 0.3536 × 24 V

V_{RMS} = 8.4853 V