RMS Voltage Calculator — Peak to RMS & Peak-to-Peak
Convert peak voltage, peak-to-peak voltage or RMS voltage of a sine wave to all three forms. Also calculates the half-wave-rectified average, form factor and crest factor — essential for oscilloscope readings and AC circuit design.
Input type
V
Equivalent DC voltage delivering the same power to a resistive load
- 1
Peak voltage (input)
V_peak = 170 V = 170 - 2
RMS voltage = V_peak ÷ √2
170 ÷ √2 = 120.2082For a pure sine wave, V_rms = V_peak / √2.
How does this calculator work?
For a pure sine wave, V_rms = V_peak / √2 ≈ 0.7071 × V_peak. Peak-to-peak V_pp = 2 × V_peak. Half-wave-rectified average V_avg = (2/π) × V_peak ≈ 0.6366 × V_peak. Crest factor = √2 ≈ 1.414; form factor ≈ 1.111. Mains voltage ratings (120 V, 230 V) are always RMS.
Formula
How this is calculated
For a pure sine wave v(t) = V_peak × sin(ωt), three voltage measures are in common use. The peak voltage V_peak is the maximum excursion from zero — what an oscilloscope cursor shows directly. The peak-to-peak voltage V_pp = 2 × V_peak spans from negative to positive peak. The RMS (root-mean-square) voltage V_rms = V_peak / √2 ≈ 0.7071 × V_peak is defined so that it delivers the same power to a resistive load as the same DC voltage: P = V_rms² / R. Mains supply ratings (230 V UK/EU, 120 V US) are always RMS.
The half-wave-rectified average V_avg = (2/π) × V_peak ≈ 0.6366 × V_peak is the mean of the positive half-cycle only. Basic (non-true-RMS) AC meters measure this and multiply by a fixed factor of π/(2√2) ≈ 1.1107 to read approximate RMS — but this only works for pure sine waves. The form factor (V_rms / V_avg ≈ 1.1107 for a sine) and crest factor (V_peak / V_rms = √2 ≈ 1.4142 for a sine) characterise the waveform shape.
All relationships here are valid only for a pure, undistorted sine wave. Distorted waveforms (clipped audio, PWM outputs, non-linear loads) have different form and crest factors and require a true-RMS meter or the actual waveform data to compute V_rms correctly.
Frequently asked questions
The rated mains voltage is an RMS value. Applying V_peak = V_rms × √2 gives 230 × 1.414 ≈ 325 V. Transformers, capacitors and insulation must be rated for this peak, which is why high-voltage components are rated above the nominal mains voltage.
Divide by 2 to get V_peak, then divide by √2 to get V_rms: V_rms = V_pp / (2√2) ≈ V_pp × 0.3536. For example, a 340 V_pp mains sine gives 340 / (2 × 1.414) ≈ 120 V_rms.
No. For a square wave, V_rms = V_peak (form factor = 1, crest factor = 1). For a triangle wave, V_rms = V_peak / √3. This calculator is for sine waves only. A true-RMS meter or numerical integration of the waveform is needed for arbitrary shapes.
Also known as
TG we-Calculate Editorial Team. (2026). RMS Voltage Calculator — Peak to RMS & Peak-to-Peak [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/rms-voltage-calculator
TG we-Calculate Editorial Team. "RMS Voltage Calculator — Peak to RMS & Peak-to-Peak." TG we-Calculate. 2026. https://we-calculate.com/calculator/rms-voltage-calculator.
TG we-Calculate Editorial Team, "RMS Voltage Calculator — Peak to RMS & Peak-to-Peak," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/rms-voltage-calculator
@misc{wecalculate_rms_voltage_calculator, title = {RMS Voltage Calculator — Peak to RMS & Peak-to-Peak}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/rms-voltage-calculator}}, year = {2026}, note = {TG we-Calculate} }
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