RMS Value Calculator – Calculate Root Mean Square Voltage

Calculate RMS voltage for different waveforms. RMS is the effective DC-equivalent voltage for AC signals.

Waveform Type

Peak Voltage (V)

How to Use This RMS Value Calculator

Select waveform type

Choose the waveform shape: sine, square, triangle, or sawtooth. Each has a different RMS relationship to peak voltage.

Enter peak voltage

Input the peak (maximum) voltage value. This is the amplitude from zero to the waveform's highest point.

Calculate RMS

Click Calculate to see the RMS voltage, peak voltage, and peak-to-peak voltage for your waveform.

RMS Conversion Factors by Waveform

Waveform	RMS Formula	RMS Factor	Example (Vp=10V)
Sine Wave	Vp/√2	0.707	7.07V
Square Wave	Vp	1.000	10.00V
Triangle Wave	Vp/√3	0.577	5.77V
Sawtooth Wave	Vp/√3	0.577	5.77V
Pulse (50% duty)	Vp/√2	0.707	7.07V

Note: RMS factors assume symmetrical waveforms centered around zero. DC offset changes the calculation.

Understanding RMS Voltage

RMS (Root Mean Square) voltage is the DC-equivalent voltage that delivers the same power to a resistive load. If 10V RMS heats a resistor the same as 10V DC, that's the definition — equal heating effect.

For sine waves, RMS equals peak divided by √2 (about 0.707). This is why US household "120V AC" actually peaks at 170V — the RMS value is what matters for power calculations. European 230V RMS peaks at about 325V.

Different waveforms have different RMS relationships because power depends on voltage squared. A square wave spends all its time at peak voltage, so RMS equals peak. A triangle wave spends most time at lower voltages, so RMS is only 57.7% of peak.

Practical note: Most multimeters measure RMS assuming a sine wave. For non-sinusoidal waveforms (PWM, switching supplies), you need a "true RMS" meter or calculate it from the waveform shape.

Peak vs RMS vs Peak-to-Peak

Peak Voltage (Vp)

The maximum voltage from zero to the waveform's highest point. For a sine wave centered at zero, this is the amplitude. Peak voltage determines insulation requirements — components must withstand the peak, not just RMS.

Peak-to-Peak Voltage (Vpp)

The total voltage swing from most negative to most positive. For symmetrical waveforms, Vpp = 2 × Vp. Oscilloscopes typically display peak-to-peak values since they show the complete waveform.

RMS Voltage (Vrms)

The effective voltage for power calculations. Power = Vrms² / R. AC voltage ratings (wall outlets, transformers, motors) are almost always RMS values unless specified otherwise.

Average Voltage

For symmetrical AC waveforms, the average over a complete cycle is zero. Rectified average (absolute value) is different from RMS. For sine waves, average rectified = 0.637 × Vp, while RMS = 0.707 × Vp.

Frequently Asked Questions

Why is RMS used instead of average?

Average voltage of symmetrical AC is zero — not useful for power calculations. RMS accounts for the fact that power depends on voltage squared. Both positive and negative halves deliver power, so RMS gives the meaningful equivalent DC value.

Is 120V AC the peak or RMS?

120V is RMS. The peak is 120 × √2 = 170V. Peak-to-peak is 340V. This matters for component selection — a capacitor rated for 150V would fail on 120V AC because the peaks reach 170V.

What's the RMS of a DC signal?

For pure DC, RMS equals the DC value itself. There's no variation, so the "root mean square" is just the constant value. A 5V DC supply has 5V RMS.

How do I measure RMS without a true RMS meter?

For sine waves, measure peak with an oscilloscope and divide by √2. For other waveforms, you need to know the shape and apply the correct factor. True RMS meters sample and calculate Vrms = √(average of v²) directly.

Does frequency affect RMS?

No. RMS depends only on waveform shape and amplitude, not frequency. A 10V peak sine wave has 7.07V RMS whether it's 50Hz, 1kHz, or 1MHz. Frequency affects reactance in circuits, but not the RMS value itself.

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