What is RMS Voltage?

The Root Mean Square ($V_{rms}$) voltage is the effective value of an alternating current (AC) voltage. In simple terms, it represents the DC voltage level that would dissipate the same amount of power in a resistive load as the AC voltage.

This value is crucial because AC voltage is constantly changing—following a sinusoidal wave pattern—and an average value would be misleading (the average voltage of a full cycle is zero). RMS voltage provides a standardized, equivalent metric for power calculation.

Real-World Application: Household AC supply ratings (like 120 V in North America or 230 V in Europe) are always given as the RMS value. If your outlet is rated $120 \, V_{rms}$, the actual peak voltage ($V_{peak}$) hitting the appliances is much higher, approximately $170 \, V$.

The RMS voltage is calculated from the peak voltage using the formula $V_{rms} = V_{peak} / \sqrt{2}$, assuming a purely sinusoidal waveform.

How to Use the Calculator

1. Input Peak Voltage: Locate the input field labeled “1. Enter Peak Voltage ($\mathbf{V_{peak}}$):”.
2. Enter Value: Input the maximum (peak) voltage value of the AC signal in Volts (V). *Example: For a standard US wall outlet, this is typically around 170 V.*
3. Calculate: Click the “Calculate RMS Voltage” button.
4. Interpret Result: The “Result” section will display the full, substituted formula in LaTeX format along with the final $V_{rms}$ value, rounded to two decimal places.