What is the conversion for rms voltage to peak to peak voltage?

Answer 1

For sine waves:

To calculate the RMS value of a sine wave, multiply the peak value by 0.707. The peak value is, of course, one half the peak-to-peak value. To go the other way, reverse the order of operations. That is, if you're starting with an RMS value, divide by 0.707 and then multiply by two to get the p-p value. Another way to convert from RMS to p-p is to multiply the RMS value by two square roots of two: RMS x 2 x SQR(2).

Or more simply, to convert from RMS to peak to peak voltage:

(RMS x 1.414) x 2=P-P

For example:

120vac x 1.414= 170vac

169.68vac x 2 = 339.36vac P-P

Where there is a significant reactive component in the characteristic of the cabling or load, we must also consider the effects of the X/R ratio. The real vs imaginary components of the impedance:

V(peak) = V(rms) * sqrt(2) * (1+ e(exp -pi/(X/R)))

where "exp" is the exponent to which the value of e is raised.

Reading the power of e above in English:

"e to the power of (minus pi divided by the X/R ratio)".

Take careful note of the top line of the first answer "For sine waves". More specifically the formula applies only to a signal which is a pure sine wave (a single frequency, no harmonics or other frequencies). As soon as you combine two or more sine wave signals of different frequencies, the ratio of peak voltage to RMS voltage depends strongly on the phases of the component signals. Too complicated to answer here, in full explanation.

Vrms = (Vp-p / 2 )/ sq.root (2) = Vp-p / 2.828 for sinusoidal waves..

*Note: If the signal or the waveform is not sinusoidal you'll have to derive from basic steps with a sound knowledge about integrations.

RMS = root mean square = square root (mean(square values of voltages))