AC RMS / Peak Conversion
V_rms = V_peak / √2
Quick answer
This calculator solves V_rms = V_peak / √2 for RMS Voltage. With Peak Voltage 26.4 V, the result is 18.67 V. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The RMS (root mean square) voltage of a pure sine wave is the peak voltage divided by the square root of 2, approximately 0.707 times the peak. RMS is the standard way to express AC voltage because it represents the equivalent DC voltage that would deliver the same average power to a resistive load. When someone says "120V mains" or "230V mains," they mean the RMS voltage; the actual peak voltage is 170V or 325V respectively. This is the most fundamental AC relationship and is essential for power calculations, component voltage ratings, and safety analysis.
Variables
- V_rms — Root mean square voltage (V)
- V_peak — Peak (maximum) voltage (V)
Practical Notes
This formula applies only to pure sine waves. For other waveforms, the relationship changes: a square wave has V_rms = V_peak, and a triangle wave has V_rms = V_peak/√3. Mains voltage tolerance is typically ±10%, so 230V mains can peak at 253V × √2 = 358V. Always rate components for the worst-case peak voltage including tolerance.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Vrms | RMS Voltage | V | pV, nV, µV, mV, V, kV |
| Vpeak | Peak Voltage | V | pV, nV, µV, mV, V, kV |
Step by step
- 1. What you know: Peak Voltage 26.4 V
- 2. The relation: V_rms = V_peak / √2
- 3. Substitute: Vpeak = 26.4 V
- 4. Result: RMS Voltage = 18.67 V
Worked examples
Minimum range
Given: Peak Voltage 0.726 V
Result: RMS Voltage = 0.5134 V
Low range
Given: Peak Voltage 7.26 V
Result: RMS Voltage = 5.134 V
Typical
Given: Peak Voltage 26.4 V
Result: RMS Voltage = 18.67 V
High range
Given: Peak Voltage 0.506 kV
Result: RMS Voltage = 0.3578 kV
Maximum range
Given: Peak Voltage 5.06 kV
Result: RMS Voltage = 3.578 kV
Solving for each variable
Solve for RMS Voltage
Peak Voltage 0.726 V → 0.5134 V
Solve for Peak Voltage
RMS Voltage 0.33 V → 0.4667 V
How RMS Voltage changes with Peak Voltage
| Peak Voltage (input) | RMS Voltage (result) |
|---|---|
| 5.81 V | 4.108 V |
| 14.53 V | 10.27 V |
| 29.05 V | 20.54 V |
| 43.58 V | 30.81 V |
| 58.1 V | 41.08 V |
| 87.15 V | 61.62 V |
| 116.2 V | 82.17 V |
| 0.2324 kV | 0.1643 kV |
| 0.4067 kV | 0.2876 kV |
| 0.581 kV | 0.4108 kV |
The same result in other units
| Unit | Value |
|---|---|
| mV | 18670 |
| V | 18.67 |
| kV | 0.01867 |
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<p><a href="https://vbatpower.com/formulas/ac-rms-peak/">AC RMS / Peak Conversion</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate AC RMS / Peak Conversion?
Use V_rms = V_peak / √2. With Peak Voltage 26.4 V, RMS Voltage works out to 18.67 V.
How do you calculate conversion from rms power to peak power in ac?
Rearrange for RMS Voltage: with Peak Voltage 7.26 V, RMS Voltage is 5.134 V.
What is the formula for AC RMS / Peak Conversion?
The formula is V_rms = V_peak / √2. The RMS (root mean square) voltage of a pure sine wave is the peak voltage divided by the square root of 2, approximately 0.707 times the peak.
How do you find Peak Voltage when you know the other values?
Rearrange for Peak Voltage: with RMS Voltage 0.33 V, Peak Voltage is 0.4667 V.
What units does AC RMS / Peak Conversion use?
RMS Voltage is shown in mV, V, kV. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
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