Formula
Power factor is kilowatts divided by kilovolt-amperes, which is the cosine of the phase angle. The three sides close: kVA squared equals kW squared plus kVAR squared. Three-phase apparent power uses √3 and the line-to-line voltage.
PF = kW / kVA = cos φ
kVAR = kW × (tan φ1 − tan φ2)
C = kVAR × 1,000 / (n × 2 × π × f × V²)
Inductive loads, motors, transformers, and magnetic ballasts, draw lagging current. Capacitors draw leading current and can cancel the lagging kilovars. Harmonics can resonate with those capacitors. That is an engineer’s problem. The capacitance here is per leg of a delta bank when the load is three-phase, and the single capacitor when it is single-phase. n is 3 or 1. Displayed kilovars are rounded. The capacitance uses the full figure.
Worked examples
75 kW and 100 kVA. Power factor 0.75, angle 41.41 degrees, 66.14 kVAR.
480 V, 120 A, 80 kW, three-phase. 99.77 kVA, power factor 0.8019, 59.61 kVAR.
100 kW from 0.80 to 0.95 at 480 V, 60 Hz. 42.13 kVAR. Current falls from 150.35 A to 126.61 A. About 162 microfarads per phase of a delta bank.
5 kW from 0.70 to 0.95 at 240 V, single-phase. 3.46 kVAR and about 159 microfarads.
Reference
A power factor of 1.0 has no reactive power. A target below the existing power factor is rejected. 0.5 is the lowest existing power factor this correction tab accepts.
Questions
How do you calculate power factor?
Divide real power in kilowatts by apparent power in kilovolt-amperes. That ratio is the cosine of the phase angle. 75 kW and 100 kVA is a power factor of 0.75.
What is a good power factor?
1.0 is a resistor. Utilities that bill commercial accounts for a low power factor often want something near 0.95. What counts as low is the rate schedule, not this page.
How do I convert kW to kVA?
Divide kilowatts by the power factor. 50 kW at 0.85 is 58.82 kVA. Three-phase kVA from the line is √3 times volts times amps, divided by 1,000.
How many kVAR do I need to correct power factor?
Multiply the kilowatts by the difference of the tangents of the two angles. 100 kW from 0.80 to 0.95 is 42.13 kVAR. A power factor of 1 needs no correction.
What is the formula for a power factor correction capacitor?
The kilovars come from the tangent difference. Capacitance of one leg is those vars divided by 2 π f V². A three-phase delta bank divides by 3 and uses the line-to-line voltage. This page does not select protection for that bank.
What is leading versus lagging power factor?
Lagging means the current lags the voltage, which is what motors and transformers do. Leading means the current leads, which is what capacitors do. Correcting a lagging load adds capacitors.
Does improving power factor lower my electric bill?
Only if the rate charges for reactive power or for a low power factor. A residential bill that is only kilowatt-hours does not change because the power factor changed. Read the tariff.
Sources
- Power factor is kW divided by kVA, by definition of those two powers. kVA squared equals kW squared plus kVAR squared. Three-phase kVA is √3 times line-to-line volts times amps, divided by 1,000.
- Correction kilovars are real power times the change in the tangent of the power-factor angle. Capacitance follows Q = 2 π f C V² on each leg. A delta bank uses three legs at the line-to-line voltage.
- NEC 2023 Article 460 covers capacitors and Article 430 covers motors. Both are cited so the installation has a home in the code. Neither is used to compute a number on this page.