Power Factor Calculator

How the power factor maths works

AC power has three faces. Real power P (kW) does work; reactive power Q (kVAr) sustains magnetic fields in motors, transformers and wiring; apparent power S (kVA) is the vector sum — what the wires and the utility bill demand charges actually carry:

S = P ÷ PF   ·   Q = P × tan(acos PF)

Capacitors supply reactive power locally, cancelling the magnetising current so the source no longer carries it. The classic correction formula sizes the bank:

Q_c = P × [tan(acos PF₁) − tan(acos PF₂)]

where PF₁ is the current and PF₂ the target power factor. The result is in kilovars (kVAr) — the nameplate rating you order.

Worked example

A 50 kW motor load running at PF 0.75 draws S = 50 ÷ 0.75 ≈ 66.7 kVA with Q ≈ 44.1 kVAr. Correcting to 0.95 needs Q_c = 50 × (0.8819 − 0.3287) ≈ 27.7 kVAr of capacitance. Apparent power falls to 52.6 kVA — 21% of cable and transformer capacity released, lower line losses (I²R falls with the square of current), and usually the end of any utility power-factor penalty.

Why utilities care

Utilities size everything — transformers, conductors, generator capacity — on kVA, not kW. A customer at PF 0.7 forces them to deliver 1.43 kVA per kW delivered, so most commercial tariffs bill a PF penalty or a kVA demand charge below roughly 0.90–0.95. Correction to 0.95 is the economic sweet spot; pushing to unity wastes money on the last few kVAr because the required capacitance grows nonlinearly near 1.0.

Frequently asked questions

1. What is power factor?

The ratio of real power (kW) to apparent power (kVA). PF 1.0 means all current does useful work; PF 0.75 means 25% more current flows than the useful work alone requires.

2. How do I calculate the capacitor size to correct power factor?

Qc = P × [tan(acos PF₁) − tan(acos PF₂)] — real power in kW times the difference of the tangent angles of the current and target power factors. The result in kVAr is the standard capacitor nameplate rating.

3. Why correct to 0.95 instead of 1.0?

The kVAr needed grows nonlinearly as PF approaches unity, so the last few points cost the most equipment. 0.95 already eliminates most utility penalties and frees ~20% capacity at typical starting PFs.

4. Does a low power factor increase my energy bill?

It usually increases the demand portion of a commercial bill — kVA demand charges or an explicit PF penalty. Residential tariffs are typically kW-based, so PF rarely matters at home.