RMS Voltage Calculator

RMS Voltage: Practical Definition

Root-mean-square (RMS) voltage is the DC-equivalent value that would deliver the same average power to a resistive load. For a waveform v(t), Vrms = √( (1/T) ∫₀ᵀ v²(t) dt ). This calculator lets you compute Vrms from peak values, peak-to-peak values, power and resistance, or direct sample data.

Why Engineers Use RMS

Power dissipation follows P = Vrms²/R. That is why equipment ratings—mains supplies, transformers, heaters, and many sensors—are stated in RMS. For example, 230 V (RMS) across 46 Ω produces about 1150 W, while 120 V (RMS) across 12 Ω produces about 1200 W.

Sinusoidal Relationship

For an ideal sine wave, Vrms = Vpeak/√2 ≈ 0.707·Vpeak and Vrms = Vpp/(2√2). A 10 Vpeak sine therefore has Vrms ≈ 7.07 V. If you also know the waveform is three-phase line-to-line, you may encounter √3 factors when converting between phase and line voltages.

Non‑Sinusoidal Waveforms

Many modern sources are not pure sine: PWM inverters, rectifiers, and switching supplies create harmonics. In those cases, Vrms must be computed from the squared waveform, not from a simple peak factor. Crest factor (Vpeak/Vrms) is 1.414 for a sine, 1.0 for a square, and can exceed 3 for narrow pulses.

From Peak‑to‑Peak Measurements

Oscilloscopes often show Vpp because it is easy to read. If the waveform is confirmed sinusoidal, converting is straightforward. For example, 20 Vpp sine corresponds to Vrms ≈ 20/(2√2) = 7.07 V. If the waveform is clipped or offset, use sample mode for best accuracy.

From Power and Resistance

When you know load power and resistance, Vrms = √(P·R). This is common in audio and heating design. A 100 W resistor load of 8 Ω requires Vrms = √(100·8) ≈ 28.28 V. The matching current is Irms = Vrms/R ≈ 3.54 A.

Sampling Method and Data Quality

In sample mode, Vrms = √( (1/N) Σ vᵢ² ). Accuracy improves with more points covering full cycles. Avoid mixing units in the same list. If your signal has a DC offset, include it in the samples—RMS naturally accounts for both AC ripple and DC level.

Typical RMS Ranges in Practice

Household outlets are commonly 120 V or 230 V RMS, while low-voltage electronics may use 1–24 V RMS. Many lab generators specify up to 10 Vrms into 50 Ω. Industrial variable-frequency drives can output hundreds of volts RMS but with high harmonic content.

Frequently Asked Questions

1) Is RMS the same as average voltage?

No. Average voltage is the mean of v(t), often near zero for AC. RMS is based on v²(t) and relates directly to heating and power in resistive loads.

2) Why is a sine wave RMS equal to 0.707 times the peak?

For a sine, the mean of sin² over one cycle is 1/2. Taking the square root gives √(1/2) = 1/√2 ≈ 0.707, so Vrms = Vpeak/√2.

3) What if my signal has a DC offset?

RMS naturally includes DC and AC together. If you enter samples that include the offset, the result reflects total effective voltage. If you only want AC RMS, subtract the mean first.

4) How many samples should I enter for good accuracy?

Use enough points to cover at least one full period, preferably several. More samples reduce error for complex waveforms. Even 20–50 points can work well for smooth signals.

5) Does this match a “true RMS” multimeter?

Yes when the meter is truly RMS and your inputs represent the real waveform. Average-responding meters assume a sine wave and can be wrong for PWM, rectified, or clipped signals.

6) Can I use this for non-periodic waveforms?

Yes in sample mode, but the result applies only to the sampled interval. Choose a window that represents typical operation, especially for bursts or changing duty cycles.

7) How do I get RMS current from RMS voltage?

For a resistive load, Irms = Vrms/R. If the load is reactive, use impedance magnitude |Z| instead of R, and note that phase angle affects real power.