Educational explanation, not professional design advice. Last reviewed 24 October 2026. Disclaimer
In plain English
An AC machine such as a motor draws current for two jobs: doing useful work (turning the shaft) and building the magnetic field it needs to run. Only the first part does work, but the supply and the cables have to carry both. Power factor tells you what share of the current is doing useful work. A power factor of 1 means all of it; 0.7 means a lot of extra current is flowing without doing work.
Technical definition
Power factor is the ratio of active (real) power P to apparent power S: PF = P ÷ S. For sinusoidal voltage and current it equals cos φ, where φ is the phase angle between them. Active power is measured in watts (W), reactive power Q in volt-amperes reactive (var) and apparent power in volt-amperes (VA), with S² = P² + Q².
How it works and where it is used
Inductive loads such as induction motors, transformers and older fluorescent ballasts draw current that lags the voltage, giving a lagging power factor below 1. Lightly loaded motors have especially poor power factor. Because current is proportional to apparent power, a low power factor means higher current, larger voltage drop and higher cable losses for the same useful power. Utilities may charge industrial customers for reactive energy or low power factor, and capacitor banks are used to correct it.
Formula
PF = P ÷ S = cos φ S = √(P² + Q²)
Three-phase: P = √3 × VL × IL × PF Single-phase: P = V × I × PF
VL = line-to-line voltage, IL = line current. Applies to balanced three-phase loads; for distorted (non-sinusoidal) currents, power factor also includes harmonic effects and is no longer just cos φ.
Worked example
A three-phase motor on 400 V draws 10 A at a power factor of 0.8.
- S = √3 × 400 × 10 = 6.93 kVA
- P = 6.93 × 0.8 = 5.54 kW
- Q = √(6.93² − 5.54²) = 4.16 kvar
At a power factor of 0.95, the same 5.54 kW would need only 8.4 A.
In the workshop and in practice
Power factor matters when sizing cables, transformers and generators (rated in kVA, not kW), when checking voltage drop, and when reading industrial electricity bills. Motor nameplates state the power factor at full load.
Common mistakes and misconceptions
- Sizing a supply from kW alone. Generators and transformers are limited by kVA (current).
- Assuming power factor is fixed. It changes with motor load.
- Over-correcting. Too much capacitance gives a leading power factor and can cause over-voltage; correction should be designed.
Safety note
Power-factor correction capacitors can stay charged after isolation. Work on them only after proper isolation and discharge, by qualified persons.
Related calculators
- Single & Three-Phase AC Power Calculator — kW, kVA, kVAR and current for single-phase and three-phase loads.
- Voltage Drop Calculator — Estimated voltage drop, % drop and cable losses for DC, single-phase and three-phase circuits.
- Electricity Cost Calculator — Energy use (kWh) and running cost of any appliance or machine.
Related topics
- Voltage Drop — The voltage lost along a cable because of its resistance (and reactance) when current flows.
References
- IEC 60050-131: International Electrotechnical Vocabulary — Circuit theory (active, reactive and apparent power; power factor)
- Hughes Electrical and Electronic Technology (Hughes, revised by Hiley, Brown and Smith)
- IEEE Std 1459: Definitions for the measurement of electric power quantities under sinusoidal, nonsinusoidal, balanced or unbalanced conditions