RMS Voltage Calculator — Peak, Peak-to-Peak, Average and RMS

Background.

A North American wall outlet is called 120 volts, yet the voltage at its terminals climbs to about 170 V, falls through zero to about −170 V and back, sixty times a second. The 120 is the root-mean-square value, and it earns its place on the label because it describes what the supply does: 120 V of AC heats a kettle element exactly as 120 V of DC would. That equivalence is the whole definition of RMS, and it is why mains supplies, amplifier ratings and multimeter readings all use it.

How peak and RMS relate depends entirely on the shape of the wave. For a sine wave the RMS is the peak divided by √2, about 0.7071 of it. For a square wave swinging between +V and −V it equals the peak, because the voltage spends the whole cycle at full height. A triangle or sawtooth is 0.5774 of the peak, a half-wave rectified sine exactly half. Apply the sine factor to a square wave and you understate it by 29%.

Two more quantities trip people up. Peak-to-peak is twice the peak only for a wave that swings equally either side of zero; after a rectifier the wave never goes negative, so its peak-to-peak span equals its peak. And "average" here means the average of the wave's magnitude — the arithmetic mean of a full sine cycle is zero. It is what an averaging meter responds to, and for a sine it is 2 ÷ π, or 0.6366, of the peak.

So you choose the shape, say which of the four values you have, and get the other three, plus two ratios that describe the shape — crest factor and form factor — and the power the waveform would deliver into a resistance you give. The shapes are ideal: symmetric, with no DC offset, no distortion and, for the square wave, a 50% duty cycle.

What is rms voltage calculator?

The root-mean-square value of a voltage is the square root of the average of its square over one cycle. Because the power a resistor converts to heat is proportional to the voltage squared, that average of the square is proportional to the average power, and its square root is the steady DC voltage that would produce the same heating. Peak is the height above zero, peak-to-peak the full span from lowest to highest point, and average the mean of the wave's absolute value. Crest factor is peak ÷ RMS; form factor is RMS ÷ average.

How to use this calculator.

1. 01Pick the waveform shape. Every conversion depends on it, so check the trace on an oscilloscope if you are not sure.
2. 02Say which value you have: an oscilloscope cursor usually gives peak or peak-to-peak; a true-RMS multimeter gives RMS; a basic averaging meter's display is scaled for sine waves, so treat its reading as RMS only when the signal really is a sine.
3. 03Enter the voltage, greater than zero, and a load resistance if you want the heating power.
4. 04Use the RMS figure for power, heating and specifications, and the peak for insulation, capacitor voltage ratings and amplifier or converter headroom.
5. 05Note that the square-wave option means a wave swinging between +V and −V. A logic signal switching between 0 and 5 V is a different shape, with an RMS of 3.5355 V at 50% duty.

The formula.

RMS is √(mean of v²) and the average is the mean of |v|, both over one cycle. Working them out for each ideal shape gives fixed fractions of the peak. A sine's v² averages to half its peak squared, so RMS = V_pk ÷ √2; its |v| averages to 2V_pk ÷ π. A square wave sits at ±V_pk throughout, so RMS and average both equal V_pk. A triangle's square averages to a third of the peak squared, giving V_pk ÷ √3, and its magnitude averages to V_pk ÷ 2. A half-wave rectified sine keeps one half of each cycle and is zero for the other, so its mean square halves again — RMS = V_pk ÷ 2 — and its average is V_pk ÷ π. Full-wave rectification flips the negative halves up, which leaves the sine's RMS and average unchanged but halves the peak-to-peak span. Whatever value you enter is first converted to the peak with the relevant fraction, and everything else follows. Crest factor is 1 ÷ (RMS fraction): 1 for a square, √2 for a sine, √3 for a triangle, 2 for a half-wave rectified sine. Form factor is the RMS fraction divided by the average fraction: 1 for a square, 1.1107 for a sine, 1.1547 for a triangle and 1.5708 for a half-wave rectified sine. Power into the resistance R is V_rms² ÷ R.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Tony R. Kuphaldt, 'Electric Circuits II — Alternating Current' (Lessons in Electric Circuits, Volume II), Workforce LibreTexts §1.3 'Measurements of AC Magnitude'. Primary source for the definitions and the published factor values. Peak is 'the height of an AC waveform as measured from the zero mark to the highest positive or lowest negative point on a graph'; peak-to-peak is 'the total height of an AC waveform as measured from maximum positive to maximum negative peaks on a graph'; RMS is 'a way of expressing an AC quantity of voltage or current in terms functionally equivalent to DC', being the value that would 'produce the same amount of heat dissipation across a resistor of given value', and is roughly 0.707 of peak for a sine wave, whose average is approximately 0.637 of peak. Crest factor is defined as peak divided by RMS and form factor as RMS divided by average, with the stated values: sine form factor 1.11, square wave both factors 1, triangle/sawtooth form factor 1.15. NOTE: the section's own conversion table is published as an image which could not be read, so the ratios implemented here are derived from the definitions and checked against these four stated decimal values, all of which they reproduce. Retrieved 2026-07-29.
2. [2]OpenStax (Rice University), University Physics Volume 2, §15.4 'Power in an AC Circuit'. Independent second authority for the sine-wave case and for the power relation. Equation 15.13 gives I_rms = I_0/√2 and V_rms = V_0/√2, and the average power in a resistor as P_ave = ½I_0V_0 = I_rms·V_rms = I_rms²R. The section also states that 'the 110 V from a household outlet is an rms value. The amplitude of this source is 110√2 V = 156 V', and that 'most ac meters are calibrated in terms of rms values'. Entering 110 V RMS on this page returns a peak of 155.563491861 V, which rounds to the source's 156 V. Retrieved 2026-07-29.
3. [3]OpenStax (Rice University), University Physics Volume 2, §15.2 'Simple AC Circuits'. Consulted for the surrounding treatment that establishes the sinusoidal source convention v(t) = V_0 sin(ωt) used to evaluate the mean-square integral behind the 1/√2 factor, and for the definition of the amplitude V_0 as the peak value. Used to confirm that the peak in these relations is the amplitude about zero rather than a peak-to-peak span. Retrieved 2026-07-29.