Peak / RMS Voltage Converter
Convert between peak voltage, RMS voltage, and peak-to-peak voltage for AC signals.
Calculate power, crest factor, and waveform parameters for sine waves, square waves, and more.
What Is RMS Voltage? RMS stands for Root Mean Square — the effective DC equivalent of an AC voltage. RMS is the voltage value that produces the same power dissipation in a resistor as an equivalent DC voltage. When you measure 230V from a wall outlet in Europe, that is the RMS voltage. The actual peak voltage is about 325V.
The Sine Wave Relationships For a pure sine wave: V_peak = V_rms × √2 ≈ V_rms × 1.4142 V_rms = V_peak / √2 ≈ V_peak × 0.7071 V_peak-to-peak = 2 × V_peak = 2√2 × V_rms Average (half-wave) = V_peak × 2/π ≈ V_peak × 0.6366
Why RMS Matters Power in AC circuits: P = V_rms² / R = I_rms² × R (same as DC formulas). Using peak voltage in power calculations overestimates by a factor of 2. Voltmeters measure RMS voltage for sinusoidal AC (unless they are “true-RMS” meters). Non-sinusoidal waveforms require true-RMS meters — standard average-responding meters give errors for distorted waveforms.
Common AC Voltages (RMS) United States / Canada: 120V RMS, 60 Hz → V_peak = 170V, V_pp = 339V. Europe / Australia / UK: 230V RMS, 50 Hz → V_peak = 325V, V_pp = 650V. 3-phase industrial (US): 208V (line-to-line RMS between phases in a 120V/208V system). High voltage transmission: 115 kV, 230 kV, 345 kV, 500 kV, 765 kV (all RMS values).
Crest Factor Crest factor = V_peak / V_rms — the ratio of peak to RMS value. Sine wave: crest factor = √2 ≈ 1.414. Square wave: crest factor = 1.0 (peak = RMS, since the square wave is constant at one of two values). Triangle wave: crest factor = √3 ≈ 1.732. White noise (Gaussian): crest factor ≈ 3–4 (statistically). Power electronics (SMPS): often have high crest factors (3–5) due to peaked current waveforms.
Form Factor Form factor = V_rms / V_avg (half-wave average). For a sine wave: form factor = π/(2√2) ≈ 1.1107. Non-1.0 form factors are why “average-responding” meters reading an RMS scale only work for pure sine waves. True-RMS meters compute √(average of v²) — accurate for any waveform.
Oscilloscope Measurements Oscilloscopes display peak-to-peak voltage directly on screen. To convert scope reading to RMS: V_rms = V_pp / (2√2) = V_pp × 0.3536 (for sine waves only). For digital oscilloscopes with math functions, a true-RMS measurement can be computed directly.
Audio and Signal Processing In audio, 0 dBV corresponds to 1 V RMS. 0 dBu corresponds to 0.7746 V RMS (the 600-ohm standard). Professional line level audio: +4 dBu ≈ 1.228 V RMS. Consumer audio line level: −10 dBV = 0.316 V RMS. Speaker voice coils see both positive and negative voltage swings — peak-to-peak voltage matters for insulation rating.