Power Factor

Formula

Description

Power factor is the ratio of real power (watts) doing useful work to apparent power (volt-amperes) flowing in the circuit. It equals the cosine of the phase angle between voltage and current waveforms. A power factor of 1.0 (unity) means voltage and current are perfectly in phase and all power delivered is consumed as useful work. Reactive loads like motors, transformers, and fluorescent lighting have power factors below 1.0 because they draw current that is out of phase with voltage, creating reactive power that shuttles back and forth without doing useful work.

Variables

• PF — Power factor (0 to 1, dimensionless)
• P — Real (true) power in watts (W)
• S — Apparent power in volt-amperes (VA)
• φ — Phase angle between voltage and current (degrees)

Practical Notes

Industrial facilities with power factors below 0.85-0.90 typically incur penalty charges from utilities because the reactive current increases transmission losses. Power factor correction capacitors or synchronous condensers are added to bring the PF closer to unity. Modern switch-mode power supplies include active PFC circuits to achieve PF > 0.95.