RMS, Peak & Average Voltage Calculator

Understanding the RMS, peak and average voltage calculator — concept and principle

This calculator converts an AC voltage between its RMS, peak and peak-to-peak values and also gives the rectified average and the crest factor, for sine, square and triangle waveforms. It is useful when you read a mains rating, size a rectifier or capacitor's voltage rating, interpret an oscilloscope trace, or understand why a meter reading differs from the waveform's peak.

The wave reaches 325 V for an instant, but heats like a steady 230 V.

How it is calculated

First the calculator finds the peak value V_pk from your input (RMS ÷ factor, peak as entered, or peak-to-peak ÷ 2). Then:

RMS: sine V_pk/√2, square V_pk, triangle V_pk/√3.
Peak-to-peak: 2 · V_pk (for symmetric waveforms).
Average (rectified): sine 2V_pk/π ≈ 0.637 V_pk, square V_pk, triangle V_pk/2.
Crest factor: V_pk / V_rms, which is √2 for sine, 1 for square and √3 for triangle.

The principle

RMS (root mean square) is the square root of the average of the squared voltage over a cycle. It is defined that way because power in a resistor is V²/R, so the RMS value is the DC voltage that would heat the same resistor equally. For a sine wave, the average of sin² over a cycle is exactly ½, so V_rms = V_pk·√½ = V_pk/√2. A square wave spends all its time at ±V_pk, so its RMS equals its peak. A triangle wave's average of the squared ramp is ⅓, giving V_pk/√3. The plain average of a symmetric AC wave is zero, so the "average" quoted here is that of the rectified (absolute) wave.

Worked example

Inputs: 230 V, input is RMS, sine wave.
Peak: 230 × √2 = 325.27 V.
Peak-to-peak: 2 × 325.27 = 650.54 V.
Rectified average: 325.27 × 2/π = 207.07 V.
Crest factor: 325.27 ÷ 230 = 1.4142 (√2), and RMS stays 230 V.

Each point is the calculator re-run with only “Value (V)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Value (V)	RMS (V)
57.5	57.5
115	115
172	172.5
230	230
288	287.5
345	345
460	460

How to read the result

Mains voltages such as 230 V or 120 V are RMS values, so components connected directly to them must withstand the peak (about 325 V or 170 V) plus a margin for tolerance and transients. A full-wave rectifier with a smoothing capacitor charges to nearly the peak, not the RMS. A higher crest factor means sharper peaks relative to the heating value.

Common mistakes

Treating the mains rating as the peak voltage.
Using the sine factor √2 for non-sinusoidal waves, which gives wrong values for square, triangle or distorted waveforms.
Trusting an average-responding meter on non-sine waves; only a true-RMS meter reads them correctly.

Keep in mind: The formulas assume ideal, symmetric waveforms with no DC offset. Real mains is slightly distorted and varies within tolerance. Mains voltage is dangerous; measurements should follow electrical safety rules.

Frequently asked questions

Why is RMS used instead of peak?

RMS directly relates to power and heating, so a 230 V RMS supply delivers the same power to a heater as 230 V DC.

What is the form factor?

It is RMS divided by rectified average, about 1.11 for a sine wave. Average-responding meters use it to display an RMS value.

Does a DC offset change the RMS?

Yes. With a DC component, V_rms = √(V_dc² + V_ac,rms²), which this calculator does not include.

Sources: IEC 60050-103, International Electrotechnical Vocabulary: Mathematics, functions (root-mean-square value, peak factor) · C. K. Alexander and M. N. O. Sadiku, Fundamentals of Electric Circuits, McGraw-Hill, section on effective or RMS value

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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