AC Voltage Converter: RMS, Peak, Peak-to-Peak and Average for Sine, Square and Triangle Waves
Convert any AC voltage between RMS, peak, peak-to-peak and average for sine, square and triangle or sawtooth waves, with crest factor, DC offset and load power.
How it works
Sine: Vrms = Vp ÷ √2 ≈ 0.7071 Vp · Vavg = 2Vp ÷ π ≈ 0.6366 Vp · Square: Vrms = Vavg = Vp · Triangle or sawtooth: Vrms = Vp ÷ √3 ≈ 0.5774 Vp · Vavg = Vp ÷ 2 · All: Vpp = 2 × Vp · crest factor = Vp ÷ Vrms · form factor = Vrms ÷ Vavg · with DC offset: Vrms,total = √(DC² + Vrms²)
An AC voltage can be described four ways. The peak (Vp) is the highest value the wave reaches above zero; peak-to-peak (Vpp) is the full swing from the lowest to the highest point, twice the peak for a symmetric wave and what you read off an oscilloscope screen. The RMS (root mean square) value is the DC voltage that would heat a resistor the same amount, so it is what mains ratings and true-RMS multimeters give: 120 V mains in the US is 120 V RMS and swings between about +170 V and −170 V. The average is taken over the rectified wave or one half-cycle, because over a full cycle a symmetric wave averages to zero. The ratios between them depend on the shape. A sine wave has Vrms = 0.7071 Vp and Vavg = 0.6366 Vp; a square wave spends all its time at the peak, so its RMS and average equal the peak; a triangle or sawtooth wave has Vrms = Vp ÷ √3 and Vavg = Vp ÷ 2. The calculator converts from whichever value you know, compares all three shapes, and under More options adds a DC offset (total RMS = √(DC² + AC RMS²)), the period and the power in a resistive load. It differs from the RMS-of-a-list calculator, which finds the root mean square of a set of numbers rather than converting a waveform.
Worked example
US mains is 120 V RMS. As a sine wave its peak is 120 × √2 = 169.71 V, so it swings 2 × 169.71 = 339.41 V peak-to-peak. The rectified average is 2 × 169.71 ÷ π = 108.04 V. The crest factor is 169.71 ÷ 120 = 1.414 and the form factor 120 ÷ 108.04 = 1.111. At 60 Hz one cycle lasts 16.667 ms. If the same 120 V RMS were a square wave, its peak would be just 120 V; as a triangle wave, 120 × √3 = 207.85 V.
Sources: Electronics Tutorials: RMS voltage (Vrms = 0.7071 × Vpk, 20 V peak = 14.14 V RMS) · Electronics Tutorials: Average voltage (0.637 × Vpk, form factor 1.11) · Inch Calculator: Peak voltage calculator (240 Vpp → 120 V, 85 V RMS → 120.208 V) · Electronics For You: RMS voltage calculator (10 V peak → 7.07 V RMS)
Frequently asked questions
How do you convert RMS to peak voltage?
For a sine wave multiply the RMS value by √2 (1.414). For example, 230 V RMS mains peaks at 230 × √2 ≈ 325.27 V. For a square wave the peak equals the RMS; for a triangle wave multiply by √3 (1.732).
How do you convert peak-to-peak voltage to RMS?
Halve it to get the peak, then divide by √2 for a sine wave: Vrms = Vpp ÷ (2√2) = Vpp × 0.3536. A 10 Vpp sine wave on an oscilloscope is 3.536 V RMS.
Why is RMS used instead of the average?
Because RMS tells you the heating effect: a 120 V RMS supply delivers the same power to a heater as 120 V DC. The plain average of a symmetric AC wave is zero, so it says nothing about power.
What is the crest factor?
The ratio of the peak to the RMS value: 1.414 for a sine wave, 1 for a square wave and 1.732 for a triangle wave. Audio signals and the current drawn by electronic power supplies can have crest factors of 3 or more, which matters when sizing amplifiers, meters and UPS units.
Does a normal multimeter read RMS correctly?
Only for sine waves, unless it is a true-RMS meter. Average-responding meters measure the rectified average and multiply it by 1.111, the sine-wave form factor, so on a square or distorted wave the reading can be off by 10% or more.
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This calculator is for educational purposes. Double-check important results before acting on them.