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Vpeak = Vrms × √2 ≈ Vrms × 1.414
For sinusoidal AC waveforms, the peak voltage is √2 times the RMS voltage.
| RMS (V) | Peak (V) | Application |
|---|---|---|
| 120 V | 169.7 V | US household |
| 230 V | 325.3 V | EU household |
| 240 V | 339.4 V | UK/AU household |
| 277 V | 391.7 V | US commercial |
| 480 V | 678.8 V | US industrial |
Peak voltage (Vpeak) is the maximum instantaneous voltage reached by an alternating current (AC) waveform during one complete cycle. For a sinusoidal waveform, the peak voltage occurs at the 90-degree and 270-degree points of each cycle. It is related to the RMS (root mean square) voltage by the factor √2, so Vpeak = Vrms × 1.4142. Understanding peak voltage is critical because it determines the maximum voltage stress on insulation, the breakdown voltage requirements of components, and the headroom needed in amplifier and power supply designs. While RMS voltage represents the effective heating value, peak voltage represents the actual maximum that the circuit experiences.
Determine the RMS voltage of your AC source. This is the value typically shown on multimeters and listed on equipment nameplates. For example, a standard US outlet provides 120 V RMS.
Multiply the RMS voltage by √2 (approximately 1.4142). This relationship holds true for pure sinusoidal waveforms, which are the standard for mains power and most AC generators.
Ensure your signal is sinusoidal. For square waves, Vpeak = Vrms, and for triangle waves, Vpeak = Vrms × √3. Different waveform shapes require different conversion factors.
The peak-to-peak voltage is twice the peak voltage for symmetrical waveforms: Vpp = 2 × Vpeak. This value represents the full swing of the waveform from its negative to positive maximum.
Capacitors, diodes, and transistors must be rated to withstand the peak voltage, not the RMS voltage. A 120 V RMS circuit actually reaches 170 V peak, so components must be rated above this value to prevent breakdown and failure.
Wire insulation, PCB trace spacing, and transformer insulation must all handle the peak voltage plus a safety margin. Dielectric breakdown occurs at peak voltages, making this the critical value for insulation coordination and safety standards.
The output of a full-wave rectifier (before filtering) equals the peak input voltage minus diode drops. DC power supply designers must know the peak voltage to calculate the unfiltered output and ripple voltage.
| Application | RMS (V) | Peak (V) | Peak-to-Peak (V) |
|---|---|---|---|
| US Residential (120 V) | 120 | 169.7 | 339.4 |
| EU Residential (230 V) | 230 | 325.3 | 650.5 |
| UK/AU Residential (240 V) | 240 | 339.4 | 678.8 |
| US Commercial (277 V) | 277 | 391.7 | 783.5 |
| US Industrial (480 V) | 480 | 678.8 | 1357.6 |
| Japan Residential (100 V) | 100 | 141.4 | 282.8 |
| Medium Voltage (4160 V) | 4,160 | 5,883 | 11,766 |
RMS voltage is a time-averaged value that represents the equivalent DC voltage for power delivery. Since a sine wave spends most of its time at values below the peak, the RMS value (which weights all instantaneous values equally) is lower than the peak. Specifically, Vrms = Vpeak / √2 ≈ 0.707 × Vpeak for sinusoidal waveforms.
No, this formula only applies to pure sinusoidal (sine wave) signals. For a square wave, Vpeak = Vrms. For a triangle wave, Vpeak = Vrms × √3. For arbitrary waveforms, the crest factor (ratio of peak to RMS) varies and must be determined for each specific waveform shape.
Most standard multimeters measure RMS voltage (or average-responding calibrated to RMS for sine waves). To find peak voltage, measure the RMS voltage and multiply by 1.414. For direct peak measurement, you need an oscilloscope or a peak-detecting voltmeter. Some true-RMS multimeters also have a peak-hold feature.
Capacitors experience the full peak voltage across their dielectric material. If a capacitor is rated at only the RMS voltage of the circuit, it will be exposed to voltages 41% higher than its rating at each cycle peak, leading to dielectric stress, premature aging, and potential catastrophic failure.
After a full-wave bridge rectifier, the DC output voltage (before filtering) equals Vpeak minus two diode forward voltage drops (approximately 1.2 V to 1.4 V for silicon diodes). For a 120 V RMS input, the peak output is approximately 169.7 − 1.4 = 168.3 V DC. A filter capacitor then smooths this to near-peak voltage.
Convert peak voltage to RMS voltage for AC power calculations and circuit analysis.
Calculate the full voltage swing from negative peak to positive peak of an AC waveform.
Calculate voltage using Ohm's law from current and resistance values in any circuit.