Circuit Analysis & Fundamentals

RMS, Peak & Crest Factor Calculator

Convert between peak amplitude and RMS for a sine, square, triangle or sawtooth, with rectified mean, crest factor and form factor from the exact closed forms.

About this calculator

Every alternating waveform has several different "sizes", and the trouble starts when two of them are confused. The peak is the largest instantaneous value. The RMS is the value that would deliver the same heating in a resistor as an equivalent DC level, which is why it is what an AC meter reports and what appears on a nameplate. The rectified mean is what you get by flipping the negative half up and averaging, and it is neither of the other two.

For an ideal waveform each of these follows from the amplitude in closed form, exactly. A sine has RMS = A/√2 and rectified mean 2A/π; a square wave has both equal to A; a symmetric triangle has RMS = A/√3 and mean A/2. Two dimensionless ratios summarise the shape: the crest factor, peak ÷ RMS, which tells you how much headroom an amplifier or converter needs above the RMS level, and the form factor, RMS ÷ rectified mean.

This calculator runs in both directions, because the question usually arrives from the meter end: 230 V RMS mains has a peak of 325 V, and that is the number a capacitor or a semiconductor has to survive. It also handles a DC offset correctly. A DC component does not change the AC RMS; it combines with it in quadrature, so the true RMS is √(RMS² + V_DC²), not the sum. Adding them arithmetically is a common and confident error.

One practical consequence gets its own result. An ordinary multimeter that is not marked "true RMS" rectifies, averages, and multiplies by the sine form factor of 1.1107 — so it is only correct on a sine. On a square wave it reads about 11 % high, and on a triangle about 4 % low. That is the whole reason true-RMS instruments exist, and the size of the error is shown here rather than merely asserted.

These are the exact closed forms for a mathematically ideal waveform. If you have a real or sampled signal — with noise, distortion or an arbitrary shape — the Signal Metrics calculator computes the same quantities numerically from its samples instead.

Design notes & common mistakes

The peak is what has to survive. A 230 V RMS supply reaches 325 V every half cycle, so a capacitor or semiconductor rated at 250 V because the nameplate said 230 fails — and this is one of the most common ways to specify a part wrongly.
A multimeter that is not marked true RMS rectifies, averages and scales by 1.1107, the sine form factor. It is right on a sine and wrong on everything else: about 11 % high on a square wave and about 4 % low on a triangle.
A DC offset combines with the AC in quadrature, √(RMS² + V_DC²), because the cross term averages to zero over a cycle. Adding the two directly always overstates the answer.
Crest factor is a headroom specification in disguise. A converter or amplifier sized on RMS alone will clip a waveform whose crest factor is higher than the sine's √2 — which is most real signals.
The triangle and the sawtooth share every quantity on this page. If two shapes need to be told apart, these statistics are the wrong instrument; the harmonic content is where the difference lives.

Assumptions

The waveform is mathematically ideal and perfectly periodic — a pure sine, a perfect square with zero rise time, or an exactly symmetric triangle or ramp.
The AC component has zero mean, so a DC offset and the AC part combine in quadrature.
Crest and form factors describe the AC shape alone and exclude any DC offset, which is a level rather than a shape.
Amplitude is the peak value measured from zero, not peak-to-peak.

When to use this calculator

Appropriate for

Converting between peak and RMS for a standard waveform in either direction
Finding the peak voltage a component must withstand from an RMS nameplate figure
Working out the headroom a crest factor demands of an amplifier or converter
Estimating the error an ordinary averaging multimeter makes on a non-sine waveform
Combining an AC signal with a DC offset correctly
Teaching or learning the difference between peak, RMS and rectified mean

Not suitable for

Analysing a real, measured or sampled signal — use the Signal Metrics calculator, which computes these quantities numerically from samples
Working with a distorted, clipped or arbitrary waveform, whose factors are not the ideal ones
Assessing harmonic content or distortion, which these amplitude statistics cannot see
Sizing insulation or selecting a component rating on its own, which is a full design activity with its own margins and standards

Engineering use

Intended use. Educational and analytical calculation of the exact closed-form amplitude statistics of an ideal periodic waveform.

Applicable for

Exact peak-to-RMS conversion in both directions for sine, square, triangle and sawtooth
Rectified mean, crest factor and form factor of those shapes
Combining a DC offset with an AC signal in quadrature
Quantifying the error of an averaging, non-true-RMS meter

Does not account for

Harmonic distortion, clipping and any departure from the ideal shape
Noise, ringing and finite rise time on a real waveform
Frequency, phase and harmonic content, which these statistics cannot distinguish
A specific instrument's bandwidth, crest-factor limit and accuracy specification
Transients and non-periodic behaviour

Verification required

Confirm the waveform really is the ideal shape assumed before applying its factors
Confirm whether a quoted amplitude is peak, peak-to-peak or RMS — the three differ by factors that are easy to transpose
Confirm whether an instrument is true-RMS before trusting a reading on a non-sine waveform

What this calculator does not cover

Describes an ideal shape, not a measured signal. A real waveform carries harmonics, noise, ringing and finite rise time, all of which move the RMS and move the crest factor considerably more.
A clipped or distorted sine is no longer a sine, and its factors are not the ones listed here — distortion changes the crest factor first and most visibly.
Says nothing about frequency, phase or harmonic content: the triangle and sawtooth share identical amplitude statistics precisely because these quantities cannot distinguish them.
The averaging-meter figure assumes the classic rectify-and-scale front end calibrated for a sine; a specific instrument may behave differently, and its bandwidth and crest-factor limits are separate specifications.
For a real or sampled signal these closed forms do not apply — the quantities have to be computed from the samples instead, which is a different calculation.
As with every calculator on this site: results are preliminary and educational, are not verified for any specific installation, and must be reviewed against the applicable code edition and stamped by a licensed Professional Engineer before real-world use.

Frequently asked questions

What is the peak voltage of 230 V RMS?

325.3 V. For a sine wave the peak is the RMS multiplied by √2, so 230 × 1.4142 = 325.27 V. That is about 41 % above the nameplate figure, and it is the voltage a capacitor, rectifier or insulation system actually has to withstand.

How do I convert peak to RMS?

Divide by the shape's own factor: √2 for a sine (RMS = 0.7071 × peak), 1 for a square wave (RMS = peak), and √3 for a triangle or sawtooth (RMS = 0.5774 × peak). The factor depends only on the shape, never on the amplitude or the frequency.

What is the difference between crest factor and form factor?

Crest factor is peak ÷ RMS and tells you how far above the RMS the signal actually reaches — the headroom an amplifier or converter must allow. Form factor is RMS ÷ rectified mean and describes the shape of the waveform relative to its average. For a sine they are √2 = 1.414 and π/(2√2) = 1.111 respectively.

Why does my multimeter read wrong on a square wave?

Because unless it says true RMS, it does not measure RMS at all. It rectifies the signal, averages it, and multiplies by 1.1107 — the form factor of a sine. On a square wave, whose rectified mean already equals its RMS, that scaling is pure error and the meter reads about 11 % high. On a triangle it reads about 4 % low.

How does a DC offset affect the RMS value?

It combines in quadrature, not by addition: the true RMS is √(RMS_AC² + V_DC²). A 10 V peak sine on a 5 V offset has an AC RMS of 7.07 V and a true RMS of √(50 + 25) = 8.66 V — not the 12.07 V that adding them would suggest. The offset does not change the AC RMS at all.

Should I use this or the Signal Metrics calculator?

Use this one when you have an ideal waveform and its amplitude: it evaluates the exact closed form, in either direction, and adds form factor and the averaging-meter error. Use Signal Metrics when you have an actual sampled signal, with whatever noise, offset and distortion it carries, and want those quantities computed numerically from the samples.

References

Standard closed forms for the amplitude statistics of ideal periodic waveforms: RMS = A/√2 for a sine, A for a square and A/√3 for a triangle, with rectified means 2A/π, A and A/2 respectively.
Charles K. Alexander and Matthew N. O. Sadiku, Fundamentals of Electric Circuits.
William H. Hayt, Jack E. Kemmerly and Steven M. Durbin, Engineering Circuit Analysis.

Related calculators

Signal Metrics Calculator

RMS, mean, average power, energy, peak, peak-to-peak, and crest factor of a signal — generated from a standard waveform or entered as samples.

AC Impedance & Phasor Calculator

Complex impedance of a series or parallel R-L-C combination at a chosen frequency — magnitude, phase, and both rectangular and polar forms, with the impedance-vs-frequency curve.

Ohm's Law Calculator & Power Wheel

Solve for voltage, current, resistance, or power from any two known values.

RLC Resonance Calculator

Resonant frequency, quality factor Q, bandwidth, and damping for a series or parallel RLC circuit — with the resonance curve and half-power points drawn.

Decibel & dBm Converter

Convert between linear ratios, dB, dBm, and watts, or cascade stage gains and losses to a running power level.

Get the ComputeVerse.ai quick reference

A free engineering quick-reference PDF, plus a note when new calculators launch across the library — one or two emails a month, nothing else.

No spam. Unsubscribe anytime. Your address is used to send the reference card and occasional new-calculator notes, and nothing else. Every email carries an unsubscribe link. Privacy policy