📊 RMS Value Calculator

The RMS (root mean square) value represents the equivalent DC value that would produce the same heating effect in a resistor as an AC waveform. When a wall outlet in the US says "120 V," that is the RMS value—the peak voltage of the sine wave is actually about 170 V. The RMS value is what matters for power calculations: a 120 V RMS sine wave delivers the same power to a heater as a 120 V DC source.

For a sinusoidal waveform, the RMS value equals V_RMS = V_peak / √2 ≈ 0.707 × V_peak. The crest factor (ratio of peak to RMS) is √2 ≈ 1.414 for sine waves. Different waveforms have different RMS relationships: square waves have RMS = peak (factor 1.0), triangle waves have RMS = peak / √3 ≈ 0.577 × peak, and sawtooth waves share the same √3 factor as triangles.

The RMS value is computed by squaring all instantaneous values of the waveform, taking the mean of those squares, and then taking the square root. Mathematically, V_RMS = √(1/T × ∫ v²(t) dt) over one period T. For standard waveforms, this integral yields the familiar constants:

This calculator also provides the peak-to-peak value (V_pp = 2 × V_peak) and the average (mean) value, which for a sine wave full-cycle is zero and for a half-cycle is 0.637 × V_peak.

1. Select the waveform type: sine, square, triangle, or sawtooth.
2. Enter either the peak voltage/current or the peak-to-peak value.
3. The calculator will compute the RMS value automatically.
4. Review the derived values: RMS, average, form factor, and crest factor.
5. Use the RMS value for power calculations: P = V_rms × I_rms × power factor.

Why is 120 V wall outlet actually 170 V at its peak?

The 120 V specification is the RMS value. The sine wave reaches a peak of 120 × √2 ≈ 169.7 V and swings from +170 V to -170 V (340 V peak-to-peak). The RMS value is what determines the power delivered to a load, not the peak.

What is the difference between RMS and average value?

RMS is the square root of the mean of squared values; it represents the equivalent DC heating effect. Average is the arithmetic mean of the absolute values over a half-cycle. For a sine wave, RMS = 1.11 × average (the form factor). They are only equal for DC.

Does RMS apply to current as well as voltage?

Yes. The same RMS principle applies: 1 A RMS through a resistor produces the same heating as 1 A DC. Both voltage and current have RMS values, and power in AC is calculated as P = V_rms × I_rms × cos(φ) for resistive-inductive loads.

What is crest factor and why does it matter?

Crest factor is the ratio of peak value to RMS value (V_peak / V_rms). For a sine wave, it is √2 ≈ 1.414. High crest factors (spiky waveforms) can cause measurement errors and stress components. Multimeters specify a maximum crest factor they can measure accurately.

How do I calculate RMS for a non-standard waveform?

For arbitrary waveforms, V_rms = √(1/T × ∫ v²(t) dt). If you have discrete samples, compute V_rms = √(sum of squares / number of samples). This is what "true RMS" digital multimeters do internally with fast sampling.

What is the form factor for a half-wave rectified sine?

The RMS of a half-wave rectified sine wave is V_peak / 2, and the average is V_peak / π. The form factor (RMS / average) is π / 2 ≈ 1.57, higher than the 1.11 of a full-wave. The crest factor is 2.0.

True RMS multimeters measure the actual heating equivalent of any waveform, while cheaper "average-responding" meters only give correct readings for pure sine waves. A non-sinusoidal waveform measured with an average-responding meter can be off by 10-40%. For household AC, the mains voltage is always specified in RMS: 120 V in the US/Canada, 230 V in the EU/UK, 100 V in Japan. When sizing fuses and breakers, use RMS current—the heating effect that trips a thermal breaker depends on the RMS value, not the peak. For PWM (pulse-width-modulated) signals, the RMS value depends on the duty cycle: V_RMS = V_peak × √(duty cycle).