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RMS, Average and Form Factor Calculator

The RMS value is the DC voltage that would produce the same heating, which is why meters and ratings use it. Peak and average matter too — peak for insulation and component ratings, average for rectifier output.

RMS, Average, Form & Peak Factor

RMS (heating) value, average value, form factor and peak (crest) factor for a chosen waveform of peak V_m. The dashed lines on the plot mark where each value sits on the wave.

RMS value
Average value
Form factor (RMS/avg)
Peak factor (V_m/RMS)
Sinusoidal waveform
RMSavg
  1. 1.Given: Sinusoidal wave, peak V_m = 100 V
  2. 2.FormulaRMS = V_m × (waveform RMS ratio)SubstituteRMS = 100 × 0.7071ResultV_rms = 70.7107 V
  3. 3.FormulaAverage = V_m × (waveform average ratio)Substituteavg = 100 × 0.6366ResultV_avg = 63.662 V
  4. 4.FormulaForm factor = RMS ÷ averageSubstituteFF = 70.7107 ÷ 63.662ResultFF = 1.1107
  5. 5.FormulaPeak factor = V_m ÷ RMSSubstitutePF = 100 ÷ 70.7107ResultPF = 1.4142
Common trap: "230 V" mains is the RMSvalue — the peak is 230 × √2 ≈ 325 V. RMS is the DC- equivalent heating value, which is why meters and ratings quote it. Average (over a full symmetrical cycle) is actually zero; the "average" here is of the rectified wave.

The formula

Sine wave: V_rms = V_peak / √2 ; V_avg = 0.637 × V_peak ; form factor = V_rms / V_avg

V_peak
maximum instantaneous value (volts)
V_rms
root-mean-square (effective) value (volts)
V_avg
average over a half cycle (volts)

Worked example

A 230 V RMS mains sine wave.

  1. V_peak = 230 × √2 = 325.3 V
  2. V_avg = 0.637 × 325.3 = 207.2 V
  3. Form factor = 230 / 207.2 = 1.11
  4. Crest factor = 325.3 / 230 = 1.414

325 V peak — which is why capacitors on a 230 V rail must be rated at 400 V, not 250 V.

Where you'll use it

Component voltage ratings, rectifier and meter calculations, and the standard derivation question on form factor for sine, square and triangular waves. A square wave has a form factor of 1; a triangular wave, 1.155.

The laws behind it

Parts this applies to

Resistor (fixed)Capacitor (aluminium electrolytic)Capacitor (tantalum)LED (light-emitting diode)MOSFETRectifier DiodeSchottky DiodeZener Diode

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