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Power Factor from Real and Apparent Power

Also known as PF · kW over kVA

PF=PS\text{PF} = \frac{P}{S}
sig figs

Worked example: 8 kW out of 10 kVA → PF 0.8. Press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.

Where Power Factor from Real and Apparent Power fits

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Three-Phase Real PowerSingle-Phase Real Power with Power FactorPhase Angle from Power FactorThree-Phase Motor Full-Load Current
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See also

Reactive Power (Power Triangle): Both use real power and apparent power.Transformer Efficiency from Core and Copper Losses: Both use power factor and apparent power.Power-Factor Correction kvar: Both use power factor and real power.Single-Phase Real Power with Power Factor: Both use power factor and real power.Three-Phase Real Power: Both use power factor and real power.Three-Phase Apparent Power: Both use apparent power.
4 more relatedTransformer Full-Load Current: Both use apparent power.Transformer Percent-Impedance Voltage Drop: Both use apparent power.Phase Angle from Power Factor: Both use power factor.Three-Phase Motor Full-Load Current: Both use power factor.
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Power Factor from Real and Apparent Power explained

PFPS

Power factor is an efficiency of delivery, not of conversion: it says how much of the capacity you rented from the utility is producing work. A load reading 8 kW on the wattmeter but 10 kVA on the volt-amp meter runs at PF = 0.8, meaning a fifth of the supplied capacity is sloshing back and forth building magnetic fields instead of turning shafts. Both fields here are watt fields; enter kVA in the kW box, since VA and W are the same dimension.

Utilities care because that reactive current still heats their conductors and transformers, so large customers face a power-factor penalty: often triggered below 0.9 or 0.95. Lightly loaded induction motors are the usual culprit, drifting to 0.3–0.5 PF at no load; the standard cures are capacitor banks and, better, not oversizing motors in the first place.

Power Factor from Real and Apparent Power formula

PF=PS\text{PF} = \frac{P}{S}
Where
  • PF\text{PF}= Power factor
  • PP= Real power (W)
  • SS= Apparent power (VA) (W)
In this toolkit

Three-phase power and power factor

8 formulasReal, reactive and apparent power, power factor, phase angle and correction kvar — the power triangle as an electrician uses it.

Revised 16 October 2026
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formula.expert. (2026, October 16). Power Factor from Real and Apparent Power Calculator. https://formula.expert/solvers/power-factor-real-apparent

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