RMS Voltage Calculator

Convert peak (V_pk) or peak-to-peak (V_pp) voltage to RMS voltage for sine, square, and triangle waveforms. Results update instantly as you type.

Waveform Type

Input Voltage Type

Voltage V_pk Enter a positive voltage value

Decimal places

Formula in Use

V_rms = V_pk / √2

Show working steps

RMS Voltage (V_rms) —

Peak Voltage (V_pk) —

Peak-to-Peak Voltage (V_pp) —

How to Use This Calculator

1. Select a waveform type — choose Sine, Square, or Triangle depending on your signal.

2. Choose your input type — select whether your known voltage is peak (V_pk) or peak-to-peak (V_pp).

3. Enter the voltage value in volts. Results appear instantly. The calculator also returns the equivalent V_pk and V_pp for your reference.

4. Optional: tick Show working steps to see the step-by-step derivation, and adjust decimal places to suit your required precision.

Formula

Sine wave

V_rms = V_pk / √2 ≈ V_pk × 0.7071

V_rms = V_pp / (2√2) ≈ V_pp × 0.3536

Square wave

V_rms = V_pk

V_rms = V_pp / 2

Triangle wave

V_rms = V_pk / √3 ≈ V_pk × 0.5774

V_rms = V_pp / (2√3) ≈ V_pp × 0.2887

Where: V_rms = root mean square voltage, V_pk = peak voltage, V_pp = peak-to-peak voltage, √2 ≈ 1.4142, √3 ≈ 1.7321.

Example

Given: Sine wave, V_pp = 10 V

Step 1 — Convert V_pp to V_pk:
V_pk = V_pp / 2 = 10 / 2 = 5 V

Step 2 — Apply sine RMS formula:
V_rms = V_pk / √2 = 5 / 1.4142 ≈ 3.54 V

V_rms ≈ 3.54 V

Frequently Asked Questions

What is RMS voltage and why does it matter?
RMS (Root Mean Square) voltage is the equivalent DC voltage that would deliver the same power to a resistive load. It's the standard measure used for AC mains supplies — for example, 230 V AC in the UK refers to the RMS value, not the peak.

Why does waveform shape affect the RMS value?
The RMS conversion factor depends on how the voltage is distributed over time. A square wave holds its peak value for the entire cycle, so V_rms = V_pk. A sine wave dips to zero each half-cycle, so its RMS is lower (V_pk / √2). A triangle wave has an even gentler distribution, giving a factor of 1/√3.

What's the difference between V_pk and V_pp?
V_pk is the voltage from zero to the maximum positive (or negative) point of the waveform. V_pp is the full swing from the most negative to the most positive point, so V_pp = 2 × V_pk for symmetric waveforms.

Does this calculator work for asymmetric or non-standard waveforms?
No — the formulas used here assume ideal, symmetric waveforms. For arbitrary waveforms, RMS must be calculated by integrating the square of the voltage over a full period and taking the square root.

Is UK mains voltage 230 V peak or RMS?
RMS. The 230 V figure is the RMS value. The actual peak voltage is approximately 230 × √2 ≈ 325 V, and peak-to-peak is around 650 V.