How the RMS Voltage Calculator Works
The root-mean-square (RMS) voltage of a periodic AC waveform is the equivalent constant DC voltage that would dissipate the same average power in a resistive load. Formally, Vrms = √( (1/T) ∫₀ᵀ v(t)² dt ), where v(t) is the instantaneous voltage and T is one period. This calculator applies that definition to three common waveform shapes — sine, square, and triangle/sawtooth — and converts between whichever value you already know (peak, peak-to-peak, or RMS) and the other three.
RMS formulas for sine, square, and triangle waves
For a pure sine wave v(t) = Vpeak·sin(ωt), squaring and averaging over a full cycle gives Vrms = Vpeak/√2 ≈ 0.7071 × Vpeak. This is the value behind standard mains ratings: 120V and 230V mains are RMS values with peak voltages of roughly 170V and 325V. For an ideal square wave that switches instantly between +Vpeak and −Vpeak, the instantaneous voltage is always at full amplitude, so v(t)² is constant at Vpeak² for the entire period, giving Vrms = Vpeak exactly. For a symmetric triangle or sawtooth wave that ramps linearly between −Vpeak and +Vpeak, integrating the squared ramp gives Vrms = Vpeak/√3 ≈ 0.5774 × Vpeak.
Peak, peak-to-peak, and average voltage
Peak-to-peak voltage (Vpp) is simply twice the peak voltage for any waveform shape: Vpp = 2 × Vpeak. Average (rectified) voltage is the mean of the full-wave-rectified waveform over one cycle — for a sine wave this is Vavg = 2Vpeak/π ≈ 0.6366 × Vpeak, for a square wave Vavg = Vpeak, and for a triangle wave Vavg = Vpeak/2. Oscilloscopes typically read peak or peak-to-peak voltage directly off the waveform, while most AC multimeters display RMS voltage — but only "true-RMS" meters compute it correctly for non-sinusoidal signals; cheaper "average-responding" meters assume a sine wave and can read incorrectly on square or triangle waves.