AC Voltage Converter: Peak-to-Peak to RMS

On an oscilloscope the most direct measurement is peak-to-peak voltage: the vertical distance between the top and the bottom of the trace, no ground reference required. This page converts that Vpp into an RMS value for sine waves: Vrms = Vpp / (2√2), which means dividing by 2.8284. The default input of 622 V peak-to-peak returns 219.91 V RMS — that is 220 V mains as seen on a scope, swinging 311 V up and 311 V down. On a 120 V system, the same wave measures about 340 Vpp.

The formula chains two steps. For a symmetric sine, Vpp = 2 Vp, so Vp = Vpp/2; and the RMS of a sine is Vp/√2. Combined: Vrms = Vpp/(2√2) ≈ 0.3536 Vpp. Both assumptions matter. If the waveform is not a sine, the factor changes — a square wave gives Vrms = Vpp/2 and a triangle Vpp/(2√3) ≈ 0.2887 Vpp. And if the signal rides on a DC offset, Vpp stays the same while the true RMS grows, because the DC component adds in quadrature: Vrms² = Vdc² + Vac_rms². A single number cannot carry any of that information, and the tool has no way to guess it.

A practical workflow: measure Vpp on the scope with AC coupling engaged (to strip any offset), confirm the shape is sinusoidal, then convert here. A sanity check in the other direction helps too — a 10 Vpp sine should read 3.536 V RMS on a true-RMS meter; a large disagreement means the waveform is not a sine or an offset slipped in. The page converts one way only, whatever the double arrow in the title suggests; to go from RMS back to peak-to-peak, multiply by 2.8284. It performs no input validation either — negative numbers pass through silently and yield a negative RMS with no physical meaning.