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RMS Voltage for a Sine Wave — result sheet
Convert sinusoidal peak voltage to RMS, peak-to-peak, average-rectified voltage, and resistive-load power.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Vᵣₘₛ = Vₚₑₐₖ/√2; Vₚₚ = 2Vₚₑₐₖ; average(|v|) = 2Vₚₑₐₖ/π; P = Vᵣₘₛ²/R.
For a pure sine wave, RMS voltage is the DC-equivalent heating voltage and equals the peak divided by √2. The calculator also shows peak-to-peak and average-rectified values, then estimates power only for the entered ideal resistive load so waveform assumptions remain visible.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Peak voltage — V peak; minimum 1.0E-6; maximum 1000000000
- Resistive load — Ω; minimum 1.0E-6; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Peak voltage | 170 |
| Resistive load | 10 |
A 170 V peak sine wave is about 120.208 V RMS, 340 V peak-to-peak, and 1,444.997 W in a 10 Ω resistor.
Assumptions and limits
- The waveform is a centered, steady sinusoid with no DC offset, clipping, distortion, or asymmetry.
- The power result assumes a purely resistive load whose resistance does not vary with temperature or voltage.
- RMS voltage alone is not a complete description of non-sinusoidal or reactive AC systems.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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