# RMS Voltage Calculator

This RMS voltage calculator can be used to determine the root mean square (RMS) voltage values of the most frequently employed periodic waveforms; for example, sine wave, triangle wave, square wave, and others.

You can use this calculator to compute the RMS voltage value in three simple steps:

1. Input the peak voltage
2. Select the waveform
3. Click on the "Calculate RMS" button.
RMS Calculator

Volts (V)

## Reference

The value of a given AC voltage continually changes from zero to the positive peak, through zero to the negative peak, and then back to zero. The majority of the time, the AC voltage value is below peak voltage; as such, this does not present an effective measure of its actual effect.

As an alternative, we can employ the root mean square voltage (VRMS); for example, the VRMS for sine waves is approximately 0.7071 (1/√2) of the peak voltage (Vpk):

VRMS = Vpk / √2

and

Vpk = √2 × VRMS

These equations can also be applied to current.

The formulas for alternative waveforms are provided in the table below.

Waveform RMS Voltage
Sine Wave Vpk / √2
Square Wave Vpk
Triangle Wave Vpk / √3
Sawtooth Wave Vpk / √3
Half-Wave Rectified Sine Vpk / 2
Full-Wave Rectified Sine Vpk / √2

The RMS voltage value is the actual value that results from varying voltage or current. It is the equivalent steady DC value, which has the same effect.

Let's look at an example. A lamp that is connected to a 12V RMS AC supply will be illuminated with the same level of brightness as it does when it is connected to a steady 12V DC supply. However, if the lamp is connected to a 12V peak AC supply, it will be dimmer because the RMS value of this supply is only 8.5V (comparable to a steady 8.5V DC).

The RMS value of a current or voltage is displayed on AC voltmeters and ammeters.

A 12V AC supply is the equivalent of 12V RMS with a peak voltage (Vpk) of 17V. The mains in the UK is supplied at 230V AC. This is the equivalent to 230V RMS; as such, the mains peak voltage is approximately 320V.

## Example of an RMS Voltage Calculation

Let's say a sinusoidal voltage has a maximum value of 200V and we want to determine its RMS value.

We can do so as follows:

VRMS = Vpk / √2

VRMS = 0.7071 × 200V = 141.42V

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