Effective voltage is the RMS (root mean square) voltage of an AC signal, and for a standard sine wave, you find it by dividing the peak voltage by the square root of 2. That works out to multiplying the peak voltage by 0.707. So if your AC signal peaks at 170 volts, the effective voltage is 170 × 0.707, which equals about 120 volts.
This number matters because it tells you the equivalent DC voltage that would deliver the same amount of power. When someone says a wall outlet is “120 volts,” they’re quoting the effective voltage, not the actual peak of the wave.
What “Effective” Actually Means
Alternating current constantly changes direction and magnitude. At some moments the voltage is at its maximum, at others it passes through zero. So what single number accurately represents this constantly fluctuating signal? The answer is the voltage that would heat a resistor by the same amount as a steady DC source. That heating equivalence is exactly what RMS voltage captures.
The math confirms this nicely. Power delivered by a DC source equals voltage squared divided by resistance. For an AC source, the average power turns out to be the peak voltage squared divided by twice the resistance. When you substitute the RMS voltage (peak divided by the square root of 2) into the standard DC power formula, the factor of two disappears, and the AC power equation looks identical to the DC one. This is why RMS voltage is called the “effective” voltage: it’s the DC voltage that does the same work.
The Core Formula for Sine Waves
For any sinusoidal AC signal, the relationship is straightforward:
- Effective (RMS) voltage = Peak voltage × 0.707
- Peak voltage = RMS voltage ÷ 0.707 (or RMS × 1.414)
If you’re starting from a peak-to-peak measurement (the full distance from the lowest point of the wave to the highest), first cut that number in half to get the peak voltage, then multiply by 0.707. For example, an oscilloscope reading of 340 volts peak-to-peak gives you a peak of 170 volts and an effective voltage of about 120 volts.
If all you have is the average voltage of a sine wave, you can recover the peak by multiplying the average by 1.57 (which is π ÷ 2), then apply the 0.707 factor to get RMS.
Real-World Grid Voltages
The numbers on your wall outlet are effective voltages. In the United States, the standard is 120 V RMS, which means the actual peak voltage hitting your wiring is about 170 V. Larger appliances like electric dryers and cooktops run on 240 V RMS circuits, peaking near 340 V. In Europe and much of the rest of the world, the standard is 230 V RMS at 50 Hz, with a peak around 325 V.
When a manufacturer lists a wattage rating on an appliance, that rating assumes the standard RMS voltage of the outlet it’s designed for. If the wattage isn’t listed, you can estimate it by multiplying the current draw in amps by the outlet’s effective voltage (120 V or 240 V in the US).
Non-Sinusoidal Waveforms
The 0.707 shortcut only works for pure sine waves. Other waveform shapes have different relationships between peak and effective voltage.
- Square wave: The RMS voltage equals the peak voltage. Because the signal spends all its time at maximum magnitude (positive or negative), there’s no reduction from peak to effective.
- Triangle or sawtooth wave: The RMS voltage equals the peak voltage divided by the square root of 3, or about 0.577 times the peak.
For any periodic waveform that doesn’t fit a neat category, you can calculate RMS from scratch using the general definition: square the voltage at every instant over one complete cycle, average those squared values across the full period, then take the square root of that average. In calculus terms, that’s the square root of the integral of the squared waveform divided by the period. This is the universal method that works regardless of wave shape.
Measuring Effective Voltage With a Multimeter
Most basic multimeters are “average responding,” meaning they measure the average of the signal and then apply a correction factor that assumes a perfect sine wave. For household power and other clean sinusoidal signals, this works fine. But if you’re measuring anything with a distorted or non-sinusoidal waveform (variable-speed motor drives, dimmer switches, pulse-width modulated signals), an average-responding meter will give you the wrong number, sometimes significantly so.
A “True RMS” multimeter solves this problem. It directly computes the heating value of whatever waveform it sees, regardless of shape. The reading is accurate for sine waves, square waves, and everything in between. If your work involves anything beyond simple resistive loads on clean AC power, a True RMS meter is the tool you need.
One detail worth knowing: most AC multimeters use a DC-blocking capacitor, so they only measure the AC component of a signal. For symmetrical waveforms like sine, triangle, and square waves, this doesn’t matter because there’s no DC offset. But for asymmetrical waveforms like pulse trains, the meter will reject the DC portion and underreport the total effective voltage. Some meters offer an “AC+DC” mode that captures both components.
Quick Reference for Common Conversions
- Peak to RMS (sine wave): multiply peak by 0.707
- RMS to peak (sine wave): multiply RMS by 1.414
- Peak-to-peak to RMS (sine wave): multiply peak-to-peak by 0.3535
- Average to peak (sine wave): multiply average by 1.57
- US wall outlet: 120 V RMS = 170 V peak
- European wall outlet: 230 V RMS = 325 V peak