Define RMS and average value

Average value is the mean of all instantaneous values of an alternating quantity over one complete cycle:

$$I_{av}=\frac{1}{T}\int_0^T i\,dt$$

For a symmetrical wave, such as a sine wave, this full-cycle mean is zero, so the average value is taken over a half cycle:

$$I_{av}=\frac{2}{T}\int_0^{T/2} i\,dt$$

For a sine wave: $I_{av}=\frac{2}{\pi}I_m = 0.637\,I_m$.

RMS (effective) value is the value of direct current that produces the same heating effect in a resistor as the alternating current does in the same time. It is the square root of the mean of the squares of the instantaneous values over one cycle.

$$I_{rms}=\sqrt{\frac{1}{T}\int_0^T i^2\,dt}$$

For a sine wave: $I_{rms}=\frac{I_m}{\sqrt2}=0.707\,I_m$.

The ratio $I_{rms}/I_{av}=1.11$ is called the form factor of a sine wave. Ammeters and voltmeters on AC supply read RMS values (for example, a 230 V supply has a peak of $230\sqrt2 = 325$ V).