Power Factor Calculator

Power factor: cos φ, real and apparent power

The power factor is the ratio of real power (P, in watts) to apparent power (S, in volt-amperes): PF = cos φ = P / S. Reactive power Q (in VAr) is the energy oscillating between source and load without doing useful work. The three relate through the power triangle: S² = P² + Q². Purely resistive loads (heaters) have PF = 1; inductive loads (motors, transformers) have PF < 1 with current lagging; capacitive loads (capacitor banks) have PF < 1 with current leading. In Brazil, ANEEL Resolution 414/2010 and PRODIST Module 8 charge industrial customers a reactive surcharge when PF falls below 0.92, corrected by parallel capacitor banks. Example: a 10 kW motor with PF=0.7 draws S=14.3 kVA; correcting to PF=0.95 drops S to 10.5 kVA, reducing current and cable losses.

Applications: industry, data centers and billing

Power factor matters for industrial plants (mandatory PF ≥ 0.92 in Brazil), data centers sizing UPS and generators, transformer dimensioning (rated in kVA, not kW), and energy bills — poor PF means higher current for the same useful power, more losses in cables, and reactive surcharges from the utility.

FAQ

Why does PF below 0.92 cost money? The utility must supply extra current (and bigger cables/transformers) to deliver the same real power. Brazilian regulation passes that cost to the consumer.

How do I correct power factor? Add capacitor banks in parallel to compensate inductive reactive power. Sizing: Q_cap = P · (tan φ_old − tan φ_new).

Does PF apply to homes? Residential bills usually charge only kWh, so PF isn't billed directly. It still affects appliance efficiency and wire heating.

What's a typical motor PF? Induction motors run around 0.7–0.85 at full load, dropping sharply at low load — one reason to size motors close to actual demand.