The RMS (root mean square) value of AC is the effective value of an alternating voltage or current, i.e., the equivalent DC value that would produce the same heating (power) in a resistor as the AC does over time.

For a sinusoidal AC waveform with peak (maximum) value I0I_0I0​ or V0V_0V0​:

  • RMS current: Irms=I02≈0.707 I0I_{\text{rms}}=\dfrac{I_0}{\sqrt{2}}\approx 0.707,I_0Irms​=2​I0​​≈0.707I0​
  • RMS voltage: Vrms=V02≈0.707 V0V_{\text{rms}}=\dfrac{V_0}{\sqrt{2}}\approx 0.707,V_0Vrms​=2​V0​​≈0.707V0​

In words: the RMS value is found by squaring the instantaneous values over a full cycle, taking the mean of those squares, and then taking the square root, which is why it is called “root–mean–square.”