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
Vrms = Vpeak × k
Vrms = Root Mean Square voltage (V)
Vpeak = Peak (amplitude) voltage (V)
k = waveform coefficient (see table below)
Sine wave: k = 1 ÷ √2 ≈ 0.7071
Square wave: k = 1 (Vrms = Vpeak)
Triangle / Sawtooth: k = 1 ÷ √3 ≈ 0.5774
Peak-to-peak: Vpp = 2 × Vpeak
Crest factor: CF = Vpeak ÷ Vrms = 1 ÷ k
Form factor: FF = Vrms ÷ Vavg
Average (sine, full-wave): Vavg = (2 ÷ π) × Vpeak ≈ 0.6366 × Vpeak
Average (triangle/sawtooth): Vavg = Vpeak ÷ 2 = 0.5 × Vpeak
Example: Vpeak = 325 V sine wave: Vrms = 325 ÷ √2 = 229.8 V (rounds to 230 V mains)
📖 How to Use This Calculator
Steps
1
Choose your calculation direction - Select Peak to RMS if you know the peak voltage and want the RMS value, or RMS to Peak if you have an RMS measurement and need the peak and peak-to-peak values.
2
Select the waveform type - Choose Sine, Square, Triangle, or Sawtooth from the dropdown. Each waveform has a different conversion coefficient that the calculator applies automatically.
3
Enter the voltage value - Type your peak voltage or RMS voltage in the input field, or drag the slider to set the value. The default is 170 V peak, which represents approximately 120 V RMS mains.
4
Read the results - The calculator instantly shows RMS voltage, peak voltage, peak-to-peak voltage, average voltage (full-wave rectified), crest factor, and form factor all at once.
💡 Example Calculations
Example 1 - European 230 V Mains Supply
What is the peak voltage of a standard 230 V European mains supply?
1
The 230 V rating is the RMS value of a sine wave. Switch to RMS to Peak mode and enter 230 in the RMS field.
2
Sine wave crest factor = sqrt(2) = 1.4142. So V_peak = 230 x 1.4142 = 325.3 V.
3
Peak-to-peak = 2 x 325.3 = 650.5 V. Components such as filter capacitors must be rated above this value.
Vpeak = 325.3 V | Vpp = 650.5 V
Try this example →Example 2 - Oscilloscope Shows 100 V Peak Sine Wave
Convert a 100 V peak sine wave to RMS for power calculations
1
Select Peak to RMS mode. Enter 100 V in the peak voltage field and choose Sine Wave.
2
V_rms = 100 / sqrt(2) = 100 / 1.4142 = 70.71 V.
3
Power in a 50 ohm load: P = V_rms squared / R = 70.71 squared / 50 = 5000 / 50 = 100 W.
Vrms = 70.71 V | Power in 50 Ω = 100 W
Try this example →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)
1
Select Peak to RMS mode. Enter 12 V as peak voltage and choose Square Wave.
2
For a square wave, V_rms = V_peak = 12 V. Crest factor = 1 and form factor = 1.
3
Peak-to-peak = 24 V. Average voltage (full-wave) = 12 V. A 12 V square wave heats a resistor identically to 12 V DC.
Vrms = 12.0 V | Vpp = 24.0 V | Crest factor = 1.0
Try this example →Example 4 - Triangle Wave Signal Generator Output 50 V Peak
Convert a 50 V peak triangle wave to RMS
1
Select Peak to RMS mode. Enter 50 V as peak voltage and choose Triangle Wave.
2
V_rms = 50 / sqrt(3) = 50 / 1.7321 = 28.87 V. Crest factor = sqrt(3) = 1.7321.
3
Average voltage = 50 / 2 = 25 V. Form factor = 28.87 / 25 = 1.1547.
Vrms = 28.87 V | Vpp = 100.0 V | Crest factor = 1.7321
Try this example →❓ Frequently Asked Questions
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 through the formula P = V_rms squared / R.
How do you convert peak voltage to RMS for a sine wave?
Divide the peak voltage by the square root of 2, which is 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. The reverse is: V_peak = V_rms x 1.4142. This formula applies only to pure sine waves; use this calculator for other waveform types.
What is the crest factor of a sine wave vs a square wave?
A pure sine wave has a crest factor of sqrt(2) = 1.4142. A square wave has a crest factor of 1 because its RMS equals its peak. A triangle or sawtooth wave has a crest factor of sqrt(3) = 1.7321. Crest factor matters for component stress ratings, UPS capacity, and power quality analysis.
What is the peak voltage of 120 V RMS (US mains)?
V_peak = 120 x sqrt(2) = 120 x 1.4142 = 169.7 V, approximately 170 V. The peak-to-peak voltage is 339.4 V. This is why US capacitors in power supplies are often rated at 200 V or 250 V to handle the peak with a safety margin.
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 pi/(2 x sqrt(2)) = 1.1107. For a square wave it is 1. For a triangle or sawtooth wave it is 2/sqrt(3) = 1.1547. Form factor appears in rectifier and power supply design when sizing filter capacitors and transformers.
Why does RMS voltage equal peak voltage for a square wave?
A symmetric square wave at 50% duty cycle is always at either +V_peak or -V_peak and never at any intermediate value. When you square those values, average them, and take the square root, you get exactly V_peak. There is no reduction factor. This is why square-wave signals stress power supply components more than sine waves of the same RMS value.
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. The average of an unrectified sine wave over a complete cycle is zero, which is why average is always defined over the rectified (absolute value) waveform in AC circuit analysis.
How do I measure RMS voltage on an oscilloscope?
Most digital oscilloscopes have a built-in RMS measurement. Select the channel, press Measure, then choose Vrms. Analog oscilloscopes show peak or peak-to-peak values, so divide the peak reading by sqrt(2) for sine waves. For non-sinusoidal waveforms only true-RMS meters and digital oscilloscopes give correct RMS readings; standard averaging meters read about 11% too low on triangle waves.
Does a triangle wave have a higher or lower RMS than a sine wave at the same peak?
Lower. A triangle wave spends more time near zero and less time at its peak than a sine wave. Its RMS coefficient is 1/sqrt(3) = 0.5774 versus 1/sqrt(2) = 0.7071 for a sine wave. So a 100 V peak triangle wave has an RMS of 57.74 V while a 100 V peak sine wave has an RMS of 70.71 V.
What is the difference between peak voltage and peak-to-peak voltage?
Peak voltage (V_peak) is the maximum amplitude 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. For symmetric waveforms V_pp = 2 x V_peak. Oscilloscopes usually display V_pp, so divide by 2 to get V_peak before converting to RMS.
Can I apply the sine wave RMS formula to distorted mains waveforms?
No. The formula V_rms = V_peak / sqrt(2) is exact only for pure sine waves. Real mains power often contains odd harmonics (3rd, 5th, 7th) from non-linear loads like switched-mode power supplies and variable-speed drives. The total harmonic distortion (THD) shifts the true RMS away from the ideal value. Use a true-RMS power meter for accurate measurements in distorted environments.
Why do engineers use RMS voltage instead of peak voltage?
Because power dissipation depends on V_rms squared, not V_peak squared. Specifying a 230 V RMS supply tells you immediately how much power it can deliver to a known load. Specifying 325 V peak does not: you would need to know the waveform shape before you could calculate power. RMS makes AC power calculations as straightforward as DC power calculations.