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

Background.

RMS voltage is the number that tells you what an AC waveform actually does. A 170 V peak sine wave is 120 V RMS, and the 120 V is the useful figure because it is exactly the DC voltage that would heat the same resistor at the same rate — 144.5 W into 100 Ω either way. That equivalence is the entire definition, and it is why mains supplies, amplifier ratings and multimeter readings are all quoted in RMS.

The conversion depends completely on the shape of the waveform, and this is where the arithmetic goes wrong. A sine wave's RMS is 0.707 of its peak. A square wave's RMS is its peak, exactly. A triangle or sawtooth is 0.577 of peak, and a half-wave rectified sine is 0.5. Feed a square wave into the sine-wave factor and you understate it by 29 %. This page therefore asks for the shape first and applies the right factor, in either direction: give it any one of peak, peak-to-peak, average or RMS, and it returns the other three.

Two details deserve attention because they cause most of the errors on this subject. First, peak-to-peak is not always twice the peak. It is for anything that swings symmetrically about zero, but a rectified waveform never goes below zero, so its peak-to-peak span equals its peak. Second, average does not mean the arithmetic mean. The arithmetic mean of a full sine cycle is zero. What is meant — and what an averaging meter responds to — is the mean of the absolute value, which for a sine wave is 0.637 of peak. Both are stated beside the result.

Alongside the four voltages the page reports the two shape numbers that matter in design. The crest factor, peak divided by RMS, tells you how much headroom the peaks need: 1 for a square wave, √2 for a sine, 2 for a half-wave rectified sine. Insulation, capacitor ratings and amplifier clipping are all set by the peak, so a high crest factor means the RMS reading is understating the stress. The form factor, RMS divided by average, is exactly 1 only for a square wave, and any other value is the reason an averaging multimeter calibrated for sine waves misreads a triangle or a chopped waveform.

Everything here assumes an ideal, symmetric, DC-free waveform with no distortion, no harmonics and a 50 % duty cycle where that applies. Real signals are not, and a true-RMS meter measures what is actually present rather than assuming a shape. The five shapes offered are the ones whose factors follow directly from the definitions and can be checked against a published source; nothing has been extrapolated to shapes that could not be.

What is rms voltage calculator?

The root-mean-square value of a waveform is the square root of the mean of its square over one period. That definition sounds abstract until you connect it to power: since power in a resistor goes as the square of voltage, the mean of the square is proportional to the mean power, and its square root is the DC voltage that would produce the same mean power. RMS is therefore the equivalent-heating voltage, and it is why AC quantities can be substituted directly into DC power formulas. Evaluating that integral over one cycle gives a fixed ratio to the peak for any given shape: 1/√2 for a sine, 1 for a square, 1/√3 for a triangle or sawtooth, 1/2 for a half-wave rectified sine, and 1/√2 again for a full-wave rectified sine. The average value, by contrast, is the mean of the absolute value, and it has a different ratio for each shape — 2/π for a sine, 1 for a square, 1/2 for a triangle. The two ratios are independent quantities, which is why the form factor between them varies from shape to shape, and why a meter that measures one and reports the other must know what shape it is looking at.

How to use this calculator.

1. 01Pick the waveform shape. Every conversion factor on the page depends on it, and choosing the wrong one is the main source of error.
2. 02Say which quantity your measurement is — peak, peak-to-peak, RMS or average. A scope cursor is usually peak or peak-to-peak; a multimeter is RMS.
3. 03Enter the value, then a load resistance if you want the heating power.
4. 04Read the RMS figure for anything to do with power, heating or specification, and the peak figure for anything to do with insulation, capacitor ratings or amplifier headroom.
5. 05Check the peak-to-peak result on a rectified waveform: it equals the peak, not twice it.
6. 06Use the crest factor to size headroom, and the form factor to judge whether an averaging meter can be trusted on this shape.

The formula.

Take the worked example: a sine wave with a 170 V peak, driving 100 Ω. The RMS value is 170 ÷ √2 = 120.2081528017 V. Squaring that and dividing by the resistance gives 144.5 W — and the same 144.5 W is what 120.2081528017 V of DC would deliver into the same resistor. That equality is not a coincidence or an approximation; it is what RMS is defined to produce.

The peak-to-peak span is 340 V, twice the peak, because a sine wave swings symmetrically about zero. The average is 2 × 170 ÷ π = 108.2253613025 V — the mean of the absolute value over a cycle, which is 0.637 of the peak, matching the figure the source text states. The arithmetic mean of that same waveform is exactly zero, which is why the absolute value is used and why the page says so beside the number.

The two shape factors follow. The crest factor is peak ÷ RMS = 170 ÷ 120.2081528017 = 1.4142135624, which is √2 — the value every sine-calibrated meter and every rule of thumb quietly assumes. The form factor is RMS ÷ average = 120.2081528017 ÷ 108.2253613025 = 1.1107207345, which the source rounds to 1.11.

Change the shape and every number moves except the peak. The same 170 V peak as a square wave is 170 V RMS — 289 W into the same load, exactly double the sine's power — with both factors equal to 1. As a triangle it is 98.1495457622 V RMS and 85 V average, with a crest factor of √3 and a form factor of 1.1547, which the source rounds to 1.15. As a half-wave rectified sine it is 85 V RMS, with a crest factor of 2, and its peak-to-peak span is 170 V rather than 340 V.

All of these come from evaluating the definitions rather than from a lookup table, because the conversion table in the source is published as an image that could not be read reliably. The mean of sin² over a period is ½, giving 1/√2; the mean of |sin| is 2/π; a triangle's mean square is ⅓ and its mean absolute value ½; a half-wave rectified sine keeps half of the sine's mean square, giving ¼ and hence ½ for the RMS ratio. Every one of the four decimal values the source does state in text — 0.707, 0.637, form factor 1.11 for a sine and 1.15 for a triangle, both factors 1 for a square — is reproduced by these derivations, and tests assert each of them.

Rounding happens once, at the return boundary, to ten decimal places. Both classification bands read the unrounded shape factors, and because those factors are properties of the waveform rather than of your measurement, they are identical whatever voltage you enter — a fact a test pins by doubling the input and checking that the factors do not move while the power quadruples.

What is not modelled: distortion, harmonics, DC offset, duty cycles other than 50 %, and any real waveform that is not one of these five shapes. For those, a true-RMS instrument is the answer, because it measures the waveform in front of it instead of assuming one.

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 — a test asserts it. 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.