RMS Voltage Calculator
Convert between peak and RMS voltage for any common waveform type. Instantly shows Vpp, average voltage, crest factor, and form factor.
⚡ What is RMS Voltage?
RMS voltage (Root Mean Square voltage) is the effective value of an alternating voltage waveform. It represents the equivalent DC voltage that would produce the same power dissipation in a resistive load. When your electricity supplier rates mains voltage at 230 V (or 120 V in North America), that figure is the RMS value, not the peak.
RMS values are critical in three common engineering scenarios. First, in power calculations: P = V_rms squared / R applies directly, just as it does for DC. Second, in component stress rating: capacitors, MOSFETs, and diodes must withstand the peak voltage, which for a 230 V RMS sine wave is about 325 V. Third, in signal processing: audio amplifiers and RF systems specify signal levels in V_rms so that power comparisons are meaningful across different waveform shapes.
A common misconception is that RMS voltage is simply an average. The average of a symmetric AC waveform over a full cycle is zero, which would be useless for power calculations. RMS avoids this by squaring the instantaneous values (making them all positive), averaging them, then taking the square root. The result is always a positive number that represents true heating power.
The conversion factor between peak and RMS depends entirely on the waveform shape. A sine wave uses a factor of 1/sqrt(2) = 0.7071. A square wave has an RMS equal to its peak because it is always at maximum amplitude. A triangle or sawtooth wave uses 1/sqrt(3) = 0.5774. This calculator handles all four common waveform types and also outputs the peak-to-peak voltage, average voltage, crest factor, and form factor so you have everything needed for design decisions.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 - European 230 V Mains Supply
What is the peak voltage of a standard 230 V European mains supply?
Example 2 - Oscilloscope Shows 100 V Peak Sine Wave
Convert a 100 V peak sine wave to RMS for power calculations
Example 3 - Square Wave PWM Signal at 12 V Peak
Find the RMS and average voltage of a symmetric 12 V square wave (50% duty cycle)
Example 4 - Triangle Wave Signal Generator Output 50 V Peak
Convert a 50 V peak triangle wave to RMS
❓ Frequently Asked Questions
🔗 Related Calculators
What is RMS voltage and why does it matter?
RMS (Root Mean Square) voltage is the equivalent DC voltage that delivers the same power to a resistive load as the AC waveform. A 230 V RMS mains supply delivers the same heating power as 230 V DC. It is the standard way to express AC voltage because it directly relates to power dissipation.
How do you convert peak voltage to RMS for a sine wave?
Divide the peak voltage by the square root of 2 (approximately 1.4142). So for a 325 V peak sine wave: V_rms = 325 / 1.4142 = 229.8 V, which rounds to 230 V mains. This formula applies only to pure sine waves.
What is the crest factor of a waveform?
Crest factor is the ratio of peak voltage to RMS voltage. A pure sine wave has a crest factor of 1.4142 (root 2). A square wave has a crest factor of 1. A triangle wave has a crest factor of 1.7321 (root 3). Higher crest factor means higher peak stress on components.
What is the form factor of a waveform?
Form factor is the ratio of RMS voltage to average voltage (full-wave rectified). For a sine wave it is 1.1107, for a square wave it is 1, and for a triangle wave it is 1.1547. It is used in rectifier and power supply design.
What is the RMS voltage of a 230 V mains supply?
The 230 V rating IS the RMS voltage. The peak voltage is 230 x 1.4142 = 325.3 V and the peak-to-peak voltage is 650.5 V. Components must be rated for at least the peak voltage with a safety margin.
How do I find the peak-to-peak voltage from RMS?
For a sine wave: V_pp = 2 x V_peak = 2 x V_rms x sqrt(2) = 2.8284 x V_rms. Enter your RMS value in the RMS to Peak mode and the calculator shows V_pp directly.
Is the RMS voltage formula different for square waves?
Yes. For a symmetric square wave the RMS voltage equals the peak voltage because the wave is always at either +V_peak or -V_peak. The crest factor is 1 and the form factor is 1.
What is the average voltage of a sine wave?
The average of a full-wave rectified sine wave is (2/pi) x V_peak, approximately 0.6366 x V_peak. For a 325 V peak sine wave the average is about 206.9 V. Note the average over a full cycle (unrectified) is zero.
Why does a triangle wave have a higher crest factor than a sine wave?
A triangle wave spends more time near zero and less time near its peak than a sine wave. This lower average value relative to the peak means you need a higher peak to deliver the same RMS power, giving a crest factor of sqrt(3) = 1.7321 versus sqrt(2) = 1.4142 for a sine wave.
How do I measure RMS voltage on an oscilloscope?
Most digital oscilloscopes have a built-in RMS measurement. Select the channel and press Measure, then choose Vrms. Analog oscilloscopes show peak values by default, so you must divide by sqrt(2) manually for sine waves. Oscilloscopes measure true RMS for sine waves; for non-sine waveforms only true-RMS meters and oscilloscopes give correct readings.
What is the difference between peak voltage and peak-to-peak voltage?
Peak voltage (V_peak) is the maximum voltage measured from the zero baseline to the highest point of the waveform. Peak-to-peak (V_pp) is the total swing from the most negative to the most positive point, which for symmetric waveforms is exactly 2 x V_peak.
Can I use the RMS formula for non-sinusoidal mains waveforms?
The formulas in this calculator assume ideal waveforms. Real mains power often contains harmonics that make the waveform slightly non-sinusoidal. For accurate power measurement in distorted waveform environments, use a true-RMS power meter rather than applying the sine wave formula.