RMS voltage is the “effective” voltage of an AC signal — the amount that would deliver the same power to a resistor as an equivalent DC voltage. For a pure sine wave, Vrms=Vpeak2V_{\text{rms}}=\frac{V_{\text{peak}}}{\sqrt{2}}Vrms​=2​Vpeak​​, so RMS is about 70.7% of the peak value.

Quick Scoop

  • RMS stands for root mean square. It’s used because AC voltage constantly changes, so RMS gives one useful number for power calculations.
  • Example: if a sine wave has a peak of 170 V, its RMS value is about 120 V. That’s why household outlets are usually labeled by RMS voltage, not peak voltage.
  • In plain terms, RMS tells you how much “useful push” the voltage provides over time.

Formula

For a sinusoidal waveform:

Vrms=Vpeak2≈0.707 VpeakV_{\text{rms}}=\frac{V_{\text{peak}}}{\sqrt{2}}\approx 0.707,V_{\text{peak}}Vrms​=2​Vpeak​​≈0.707Vpeak​

This relationship is commonly used for AC power and heating calculations.

Why It Matters

RMS voltage is the standard way to compare AC to DC because it reflects the same heating or power effect in a load. That makes it the value you usually want when reading mains voltage, sizing circuits, or estimating power.

TL;DR: RMS voltage is the AC voltage equivalent that does the same work as a DC voltage. For a sine wave, divide peak voltage by 2\sqrt{2}2​.