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For an alternating voltage, the simple mean over a cycle would be zero. 'RMS' means 'root mean square', and is defined as the square root of the mean value of the square of the voltage, taken over a cycle. Thus whether the voltage is + or - , as it is in alternate half cycles, the value of its square is always positive, giving a real number for the square root. In fact the RMS value of voltage produces an RMS current which dissipates power at the same rate as a DC current of the same value. To find the RMS value of a sine wave with no DC offset, divide the peak value of the sine wave by square root of 2.

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Since the r.m.s. value of a sine wave is 1.414Vpk, and the mean voltage of a sine wave is 1.57Vpk, then, starting with the r.m.s. value:

Vmean = (Vr.m.s. x 1.414) ÷ 1.57

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