AC RMS / Peak Conversion

Formula

Description

The RMS (root mean square) voltage of a pure sine wave is the peak voltage divided by the square root of 2, approximately 0.707 times the peak. RMS is the standard way to express AC voltage because it represents the equivalent DC voltage that would deliver the same average power to a resistive load. When someone says "120V mains" or "230V mains," they mean the RMS voltage; the actual peak voltage is 170V or 325V respectively. This is the most fundamental AC relationship and is essential for power calculations, component voltage ratings, and safety analysis.

Variables

• V_rms — Root mean square voltage (V)
• V_peak — Peak (maximum) voltage (V)

Practical Notes

This formula applies only to pure sine waves. For other waveforms, the relationship changes: a square wave has V_rms = V_peak, and a triangle wave has V_rms = V_peak/√3. Mains voltage tolerance is typically ±10%, so 230V mains can peak at 253V × √2 = 358V. Always rate components for the worst-case peak voltage including tolerance.