Table of Contents
What Is RMS Voltage?
RMS (root-mean-square) voltage is the equivalent DC voltage that would deliver the same power to a resistive load as the AC voltage. For a sinusoidal waveform, the RMS value is the peak voltage divided by the square root of 2 (approximately 1.414). When you measure household voltage as 120V or 230V, that is the RMS value, not the peak.
The concept of RMS is essential in electrical engineering because it allows direct comparison between AC and DC power delivery. A 120V RMS AC source delivers exactly the same heating power to a resistor as a 120V DC source would. This makes RMS the most practical way to specify AC voltages and currents.
RMS Voltage Formulas
Common AC Voltages Worldwide
| Region | RMS (V) | Peak (V) | Vpp (V) |
|---|---|---|---|
| USA / Canada | 120 | 169.7 | 339.4 |
| Europe / UK | 230 | 325.3 | 650.5 |
| Japan (East) | 100 | 141.4 | 282.8 |
| Australia | 230 | 325.3 | 650.5 |
Different Waveforms
| Waveform | RMS / Peak Ratio |
|---|---|
| Sine wave | 0.7071 (1/√2) |
| Square wave | 1.000 |
| Triangle wave | 0.5774 (1/√3) |
| Sawtooth wave | 0.5774 (1/√3) |
Frequently Asked Questions
Why is RMS used instead of peak voltage?
RMS voltage directly corresponds to power delivery. Two different waveforms with the same RMS value deliver the same average power to a resistive load. Peak voltage alone does not tell you how much power will be dissipated.
What is the relationship between Vrms and power?
Power in a resistive load is P = V_rms^2 / R = I_rms^2 × R. This is identical to the DC power formula, which is exactly why RMS values are so useful in AC circuit analysis.
Does this calculator work for non-sinusoidal waveforms?
This calculator assumes a pure sinusoidal waveform. For square waves, triangle waves, or distorted signals, the ratio between peak and RMS is different. Use the waveform table above for the correct conversion factor.