The RMS voltage calculator above converts between the four ways a voltage waveform gets described: its root-mean-square value, its peak amplitude, its peak-to-peak swing and its rectified average. Each conversion depends on the shape of the wave, so the tool covers sine, square, triangle, sawtooth and both half-wave and full-wave rectified sine. It also reports the crest factor and the form factor, and works out the power the waveform would deliver into a resistive load.
Arb Digital builds free calculators that make the assumption visible rather than burying it. The factor 0.707 is so familiar that people apply it to everything, but it is a property of the sine wave alone. A triangle wave uses 0.577 and a square wave uses 1.000, and using the sine factor on either produces an error of twenty per cent or more in a quantity that directly determines heating. This page picks the right factor for the shape you tell it about, and explains where each one comes from.
What This RMS Voltage Calculator Does
It converts your one known quantity into the peak amplitude first, then derives the other three from that. The hero shows RMS, because that is the value almost every specification and rating is written in. The grid shows peak, peak-to-peak, rectified average and the crest factor, which is peak divided by RMS and describes how spiky the waveform is.
The subline gives the form factor, RMS divided by rectified average. That number matters more than it looks: it is the calibration constant built into cheap average-responding voltmeters, which measure the rectified average and then multiply by 1.1107 so that the display reads correctly for a sine wave. Feed such a meter a square or triangle wave and its answer is wrong by the ratio of the two form factors, which the note on this page works out explicitly.
Peak-to-peak is handled carefully because it is not always twice the peak. For a bipolar waveform that swings symmetrically about zero it is, but a rectified sine never goes negative, so its peak-to-peak swing equals its peak. The tool applies the correct relationship for each shape rather than doubling blindly.
How to Use It
- Select the waveform first. Nothing else on the page is meaningful until the shape is right, because every factor depends on it.
- Choose which quantity you already know. An oscilloscope usually gives you peak-to-peak, a multimeter gives RMS, and a data sheet often gives peak.
- Enter the value in volts. Any consistent unit works arithmetically, but the power figure assumes volts and ohms.
- Add a load resistance if you want power. Power is RMS squared divided by resistance, and using peak volts here would overstate a sine result by exactly a factor of two.
- Read the crest factor when sizing components. A high crest factor means the peak is far above the RMS, which is what stresses insulation and saturates amplifiers.
The Formula: How RMS Voltage Is Calculated
RMS means exactly what the name says: square the waveform, take the mean of the squares over a whole cycle, then take the square root. It is defined that way because power in a resistor goes as voltage squared, so the mean of the squares is the quantity that predicts heating. Section 15.2 of OpenStax University Physics Volume 2, Simple AC Circuits, defines Vrms = V0 ÷ √2 for a sinusoid and notes that appliances are rated in RMS rather than peak values for precisely this reason.
Doing the integral for each shape gives the factors this tool uses. For a sine, the mean of sin² over a cycle is one half, so RMS is peak divided by √2, about 0.70711. For a square wave the magnitude is constant, so the mean of the squares equals the square of the peak and RMS equals peak. For a triangle or a sawtooth the mean of the squares works out at one third, so RMS is peak divided by √3, about 0.57735. A half-wave rectified sine keeps only half the cycle, halving the mean square, so its RMS is exactly half the peak.
The rectified average is a different integral: the mean of the absolute value. For a sine it is 2 ÷ π times the peak, about 0.63662; for a square wave it equals the peak; for a triangle or sawtooth it is exactly half the peak. Note that the plain average of a symmetric AC waveform over a full cycle is zero, which is why the rectified mean is the quantity anyone actually uses.
Work the default. A sine wave with a peak of 10 V gives an RMS of 10 ÷ √2 = 7.071 V, a peak-to-peak of 20 V, and a rectified average of 10 × 2 ÷ π = 6.366 V. The crest factor is 10 ÷ 7.071 = 1.414 and the form factor is 7.071 ÷ 6.366 = 1.1107. Into an 8 Ω load the power is 7.071² ÷ 8 = 6.25 W.
Why Cheap Meters Get Non-Sinusoidal Waveforms Wrong
An average-responding voltmeter does not measure RMS at all. It rectifies the input, measures the average, and multiplies by the sine form factor of 1.1107 so the display happens to show the correct RMS for a sine wave. On any other shape that scaling is wrong, and the size of the error is fully predictable.
On a square wave, whose true form factor is 1.000, such a meter reads about eleven per cent high. On a triangle wave, form factor 1.1547, it reads about four per cent low. On the badly distorted current waveforms drawn by switch-mode power supplies, errors of thirty or forty per cent are routine. A true-RMS meter avoids all of this by computing the mean of the squares directly, which is why the label exists and why it costs more.
This tool reports what an average-responding meter would show alongside the true value, so you can see the discrepancy for the shape you selected. It is a useful sanity check whenever a measured voltage disagrees with a calculation by an oddly consistent percentage. If the ratio between your reading and the expected value matches one of these form-factor ratios, the meter is the problem, not the circuit.
Crest Factor and Why It Stresses Hardware
Crest factor is peak divided by RMS, and it describes how much headroom a waveform demands relative to the work it does. A square wave has a crest factor of 1.0, a sine 1.414, a triangle 1.732 and a half-wave rectified sine 2.0. Speech and music can exceed 10 on short transients.
Two consequences follow. First, insulation, semiconductor breakdown ratings and clearance distances must survive the peak, not the RMS, so a high-crest-factor waveform needs components rated well above its heating value. Second, an amplifier or a supply must deliver the peak without clipping even though its thermal design is set by the RMS, which is exactly why audio amplifiers quote both a continuous power rating and a much larger peak rating.
The same logic runs the other way for measurement instruments. Every true-RMS meter has a maximum crest factor it can handle, often around three at full scale, because a very spiky signal drives its front end into limiting even though the RMS reading looks modest. Exceeding it produces a reading that is too low with no warning indication at all.
Duty Cycle Changes Everything for Pulses
The square-wave factors on this page assume a symmetric fifty per cent duty cycle. Change the duty cycle and the RMS moves, because the mean of the squares is now weighted by how long the waveform spends high. A unipolar pulse train of amplitude V with duty cycle D has an RMS of V√D, so a ten per cent duty pulse of 10 V has an RMS of only 3.16 V while its peak is unchanged.
This matters wherever pulse-width modulation is used, which is most modern motor drives, lighting dimmers and switch-mode supplies. The heating in a load driven by PWM tracks the RMS, so halving the duty cycle does not halve the RMS voltage — it divides it by √2. Our duty cycle calculator handles the timing side of that relationship, and the power dissipation calculator converts the resulting RMS into heat in a component.
The same caution applies to any waveform with a DC offset. RMS of a combined signal is the square root of the sum of the squares of the DC and AC RMS components, not their sum. A 5 V DC offset with a 5 V RMS ripple gives 7.07 V RMS overall, not 10 V. This calculator treats the waveforms as offset-free, so subtract any DC component before entering values and recombine afterwards.
How This Differs From the Site's Other Voltage Tools
The boundary in one sentence: this page converts a single waveform between four descriptions of its amplitude, while the Ohm's law calculator relates voltage, current, resistance and power for a steady DC value and does not care what shape anything is.
The voltage divider calculator works out what a resistor pair does to a voltage, and the voltage drop calculator handles losses along a cable run. Neither converts between amplitude conventions, and both expect you to have already settled on RMS. The RLC impedance calculator takes an RMS voltage and returns the current an AC network draws, which is the natural next step after this page, and the frequency and period calculator covers the time axis that none of these amplitude conversions depend on. Anything mains-connected belongs with the breaker size calculator and a licensed electrician. The volt itself is defined within the SI, whose current definitions are published in the BIPM SI Brochure.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using 0.707 on every waveform — that factor belongs to the sine wave alone. A triangle uses 0.577 and a square uses 1.000.
- Reading peak-to-peak off a scope and calling it RMS — for a sine the two differ by a factor of about 2.83, which is a power error of eight times.
- Trusting a non-true-RMS meter on distorted waveforms — an average-responding instrument reads about eleven per cent high on a square wave and much worse on switch-mode current.
- Assuming peak-to-peak is always twice peak — it is not for unipolar waveforms such as a rectified sine, which never crosses zero.
- Adding a DC offset to an AC RMS value — the two combine in quadrature, so 5 V DC plus 5 V RMS of ripple gives 7.07 V RMS, not 10 V.
Related Free Tools From Arb Digital
Feed the RMS result into the RLC impedance calculator to get the current an AC network draws, or into the power dissipation calculator for heat in a component. The duty cycle calculator covers pulse timing, the frequency and period calculator the time axis, and the Ohm's law calculator the DC relations. Use the voltage divider calculator and the voltage drop calculator for circuit and cable work, and the breaker size calculator as the starting point for anything on mains. The full free online tools hub lists everything.
Frequently Asked Questions
Because power in a resistor depends on the square of the voltage, and the root mean square is the value that produces the same heating as an equal steady DC voltage. Peak tells you about stress and clearance, RMS tells you about energy.
No, that ratio applies only to a sine wave. A square wave has RMS equal to its peak, a triangle or sawtooth divides the peak by the square root of three, and a half-wave rectified sine gives exactly half the peak.
Average is the mean of the rectified waveform and RMS is the square root of the mean of the squares. For a sine they differ by the form factor of 1.1107, and only the RMS value predicts heating in a resistive load.
Most likely because it is average-responding rather than true RMS. Such meters are calibrated so their answer is correct for a sine wave and are predictably wrong on any other shape, typically eleven per cent high on a square wave.
How far the peak sits above the RMS. A high crest factor means components must withstand a much larger voltage than the heating figure suggests, and it also limits which measuring instruments can read the signal accurately.
For a unipolar pulse train the RMS is the amplitude multiplied by the square root of the duty cycle. A ten per cent duty pulse of ten volts has an RMS of about 3.16 volts, so halving duty divides RMS by the square root of two, not by two.
Only for waveforms that swing symmetrically about zero. A rectified sine never goes negative, so its peak-to-peak swing equals its peak, and this calculator applies the correct relationship for each shape.
This tool is provided for educational and study use. It assumes ideal, offset-free waveforms of the stated shape and a purely resistive load, so treat its output as an idealised result rather than a measurement. Any work on mains-voltage equipment must be carried out and signed off by a qualified electrician working to the applicable wiring rules.
