Root mean square

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RMS of a sine wave

Root Mean Square (RMS) in an AC current means the DC equivalent of the power in the AC wave into a resistive load. AC voltage is commonly named by it's RMS value. For example, the 120V coming out of a standard wall plug in the United States is actually 0-170V, but because would equal 120V DC if rectified/smoothed, we name it "120VAC" (the RMS value).

The RMS value is found by taking the peak of a sine wave (we'll use 169.68) and multiplying by .707.

169.68V * .707 = 119.96V (or approx. 120V)

A more accurate factor to use would be \frac{1}{\sqrt{2}}=\sin(45^\circ)\approx 0.7071067811865475244

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RMS of a series of arbitrary values

RMS is the square root of the mean of the squares of the values so the RMS for a collection of N values \{x_1,x_2,\dots,x_N\} is:

x_{\mathrm{rms}} = \sqrt {{1 \over N} \sum_{i=1}^{N} x_i^2} = \sqrt {{x_1^2 + x_2^2 + \cdots + x_N^2} \over N}
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