Root-Mean-Square Amplitude:

Frequently it is essential to express the effective amplitude of an ac wave. This is the current, voltage, or power which a dc source would generate to have the same common effect in a real circuit or system. Whenever you say a wall outlet has 117 V, you mean 117 efficient volts. The most general figure for effective ac levels is known as the root-mean-square, or rms, value.

The expression root mean square means that the waveform is mathematically "operated on" by taking the square root of the mean of the square of all its instantaneous values. The rms amplitude is not the similar thing as the average amplitude. For a perfect sine wave, the rms value be equivalent to 0.707 times the peak value, or 0.354 times the pk-pk value. In opposition, the peak value is 1.414 times the rms value, and pk-pk value is 2.828 times the rms value. The rms figures frequently are quoted for perfect sine-wave sources of voltage, like the utility voltage or the efficient voltage of a radio signal.

For a perfect square wave, the rms value is similar as the peak value, and the pk-pk value is two times the rms value and twice the peak value. For irregular and sawtooth waves, the relationship among the rms value and the peak value depends on the precise shape of the wave. The rms value is not at all more than the peak value for any wave shape.