# V_{RMS}

##
What is a V_{RMS}?

### Definition

**V _{RMS}** stands for root-mean-square voltage.

### Why is RMS used?

Unlike DC voltages which are constant over time, AC (alternating current) voltages are time varying and sinusoidal in shape. The RMS value of an AC signal is equivalent to the DC voltage that would be required to produce the same heating effect (power). The RMS of mains electricity in the U.S. is 110V_{RMS} and in Europe it is 220V_{RMS}.

### How is RMS voltage different to the average voltage?

A sinusoidal signal (Figure 1) alternates between a peak positive and peak negative value once every cycle. Therefore, the average value of the signal is zero, so the average value of the signal is not a useful quantity. The power of an AC signal is used on both the positive and negative cycles. RMS is calculated using the square of signal voltage values at specific points in time. Since squaring eliminates negative numbers, it incorporates the contribution of the negative values. In this way, it is similar to calculating the standard deviation of a set of numbers which have a mean of zero.

### What is the relationship between RMS and peak voltage?

The formula that relates V_{RMS} and V_{pk} is:

**V _{pk}=√2 V_{RMS}**