Peak to Peak Voltage Calculator

Peak to Peak Voltage Calculator finds the full swing of a sine, square or triangle wave from an RMS, peak or average voltage, with crest factor, half-wave values and its dBV level.

Peak to Peak Voltage Calculator Formula for Each Input

Peak-to-peak voltage is the full height of an AC wave, measured from its most positive point to its most negative point. Tony Kuphaldt's Lessons in Electric Circuits defines peak as the height from the zero line to the highest point, so peak-to-peak is twice the peak on a symmetric wave.

The Peak to Peak Voltage Calculator takes one known voltage and a wave shape. The Known Voltage menu offers RMS, peak or average, and each has its own peak-to-peak voltage formula for a sine wave. The first starts from the peak, written Vp, with Vp-p for the result.

$$V_{P-P}=2\times V_P$$

The second starts from RMS, the figure a multimeter or a nameplate gives. Two times the square root of two is 2.828, so 120 V RMS becomes 339.4 V peak-to-peak.

$$V_{P-P}=2\sqrt{2}\times V_{RMS}$$

The third starts from the average of the rectified wave. Pi times 108 V average gives the same 339.3 V, because the average of a sine wave is 0.637 of its peak.

$$V_{P-P}=\pi \times V_{AVG}$$

The main result of the Peak to Peak Voltage Calculator reads 339.4 V Full Swing for the 120 V default. The Formulas With Your Numbers panel shows each step, with 120 V × 1.414 giving a 169.7 V peak and 169.7 V × 0.6366 giving a 108 V average. Entries can be in millivolts, volts or kilovolts.

Peak-to-Peak Voltage to RMS

Converting peak-to-peak voltage to RMS runs the second formula backward. Divide the swing by 2.828 for a sine wave, which is the same as multiplying by 0.3536. One volt peak-to-peak is therefore 0.3536 V RMS.

$$V_{RMS}=\frac{V_{P-P}}{2\sqrt{2}}$$

To use the Peak to Peak Voltage Calculator as a peak-to-peak-to-RMS calculator, halve the swing and enter it as Peak Voltage. A 10 V peak-to-peak sine wave goes in as 5 V, and the first card returns 3.536 V RMS with a 3.183 V average.

The RMS to peak voltage formula is the other half of the same relation. Peak equals RMS times 1.414, and RMS equals peak times 0.707. The first card shows that gap as Peak Above RMS, which is 41.42% for every sine wave.

$$V_P=\sqrt{2}\times V_{RMS}$$

RMS and peak-to-peak measure different things. Peak-to-peak is a size on a screen, and it sets how much voltage a part must withstand. RMS is the DC-equivalent heating value, so it sets power. The RMS Voltage Calculator is the companion tool when RMS is the value wanted.

Peak Voltage of 120V, 230V and 240V RMS

Outlet, nameplate and multimeter voltages are RMS values, so 120 volts, 220 volts, 230 volts and 240 volts are all RMS and not peak. AC voltage is not stated peak-to-peak. The RMS value of 220 V AC electricity is simply 220 V, and its peak is 311.1 V.

The Common RMS Voltages Chart in the Peak to Peak Voltage Calculator lists ten supply voltages with the entered value highlighted. The peak to peak voltage of 230V RMS is 650.5 V, and a 480 V RMS system peaks at 678.8 V.

The peak matters when choosing parts. A capacitor on a rectified 120 V line charges toward the 169.7 V peak, not 120 V. The 208 V and 480 V rows are line voltages on three-phase supplies, and the Three-Phase Power Calculator takes those same RMS figures.

Sine, Square and Triangle Waves

The 2.828 factor belongs to sine waves only. The Wave Shape panel in the Peak to Peak Voltage Calculator switches the math to a square wave or a triangle and sawtooth wave. The second card names the two ratios that change, crest factor and form factor.

Crest factor is peak divided by RMS, and form factor is RMS divided by average. Kuphaldt's textbook lists the same 1.414, 1 and 1.732 crest factors. A 120 V RMS triangle wave swings 415.7 V peak-to-peak, while a 120 V RMS square wave swings only 240 V.

Going the other way, 1 V peak-to-peak is 0.3536 V RMS as a sine, 0.5 V as a square wave and 0.2887 V as a triangle. For a square wave the first card reads All Three Values Match, because peak, RMS and average are equal.

The shape also decides whether a meter can be trusted. Fluke's guide to true-RMS meters says an averaging meter can read up to 40% low or 10% high on distorted waves. Such a meter multiplies the average by the sine form factor of 1.111.

On a 120 V RMS square wave that meter would show 133.3 V, which is 11% high. On a 120 V RMS triangle it would show 115.4 V. The note under the Peak to Peak Voltage Calculator results switches to a meter warning whenever a non-sine shape is selected.

Finding Peak-to-Peak Voltage on an Oscilloscope

An oscilloscope shows the swing directly. Keysight's note on vertical divisions gives the method. Count the divisions from the lowest point of the trace to the highest and multiply by the volts per division setting.

A trace that spans 6 divisions at 2 V per division is 12 V peak-to-peak. Entered in the Peak to Peak Voltage Calculator as a 6 V peak, it returns 4.243 V RMS and a 3.82 V average. A multimeter on the same sine wave should read close to that 4.243 V.

Digital scopes do the count themselves. David Herres describes the cursors and automatic measurements on a Tektronix MDO3000 in Test and Measurement Tips, with a sine wave shown as 500 mV peak-to-peak. That reading is 176.8 mV RMS.

The halving step assumes a wave centered on zero volts. A signal riding on a DC offset has unequal positive and negative peaks, so the swing is still correct but the peak and RMS figures are not.

Half-Wave Rectifier Values

The third card of the Peak to Peak Voltage Calculator covers a wave with one half of each cycle removed, as a single diode leaves it. Its average is half the full-wave average, and its RMS is the full RMS divided by 1.414.

For 120 V RMS the half-wave average is 54.02 V and the half-wave RMS is 84.85 V. The average is 31.83% of the peak, which is one over pi. These figures treat the diode as ideal. Kuphaldt's chapter on rectifier circuits puts the loss in a silicon bridge at two diode drops, or 1.4 V.

A resistive load on the half-wave output runs at half power, because power follows RMS voltage squared. A 120 V heater element behind one diode sees 84.85 V RMS, and (84.85 ÷ 120)² is 0.5.

dBV, dBu and dBm Levels

Audio and RF work quote signal size in decibels. The fourth card of the Peak to Peak Voltage Calculator converts the RMS value three ways. Sound On Sound's decibel glossary sets 0 dBV at 1.0 V RMS and 0 dBu at 0.775 V RMS.

$$dBV=20{\log }_{10}(V_{RMS})$$

A 1 V RMS sine wave is 2.828 V peak-to-peak and reads 0 dBV, 2.22 dBu and 13.01 dBm. The dBm row is power into the 50 Ω load the calculator assumes, where 0 dBm is 1 mW. The 120 V default reads 41.58 dBV.

These levels always come from RMS. Dennis Bohn of Rane makes the point in the note No Such Thing as Peak Volts dBu, since the 0.775 V reference is an RMS level by definition. A scope reading has to be converted to RMS before it is quoted in dBu.

RMS Volts Against RMS Watts

What is 800 RMS in watts?

RMS volts do not convert to watts without a load resistance. Power is RMS voltage squared divided by resistance. An amplifier rated 800 W into 4 Ω delivers 56.57 V RMS, which is an 80 V peak and 160 V peak-to-peak.

$$P=\frac{V_{RMS}^2}{R}$$

Into 8 Ω the same 800 W needs 80 V RMS and 226.3 V peak-to-peak. The Ohm's Law Calculator solves the voltage from power and resistance, and the result goes into the Peak to Peak Voltage Calculator as RMS.

How much RMS is 1200 watts?

It depends on the load in the same way. A 1,200 W amplifier into 4 Ω puts out 69.28 V RMS and 196 V peak-to-peak. A 1,200 W heater on a 120 V RMS outlet draws 10 A RMS through 12 Ω, and the current peaks at 14.14 A.

For a sine wave the instantaneous power at the voltage peak is twice the average, since the peak voltage squared is twice the RMS squared. The Electrical Power Calculator works out that average power from volts and amps.

How do you calculate RMS and peak value in AC?

For a sine wave, multiply the peak by 0.707 to get RMS, and multiply RMS by 1.414 to get the peak. The Peak to Peak Voltage Calculator shows a 120 V RMS system peaking at 169.7 V and a 240 V system at 339.4 V. For any other shape, divide the peak by that shape's crest factor.

The general method squares the voltage at every instant, averages the squares over a cycle and takes the square root. A true-RMS meter reports that same heating value by thermal or electronic means, which is why its reading holds for any wave shape.