Power Factor Calculator
Find the power factor of an AC load. Enter the real power in kW and the apparent power in kVA to get the power factor (kW ÷ kVA, equal to cos φ), the phase angle, and the reactive power in kVAR.
Example: with Real power (kW) 8 · Apparent power (kVA) 10 → Power factor: 0.8 (80%).
- Phase angle & reactive power36.87° phase angle, 6 kVAR reactive
- AssessmentFair — some utilities surcharge below ~0.9
Computed by the calculator below using its default values. Change any input to see your own numbers.
Power factor = real power ÷ apparent power = kW ÷ kVA, which also equals cos φ. Reactive power kVAR = √(kVA² − kW²) is the current that does no useful work.
Real, apparent, and wasted power
In an AC circuit, apparent power (kVA) is the product of voltage and current, but not all of it does useful work. Real power (kW) is the part that actually turns a motor or heats an element. Their ratio is the power factor: kW ÷ kVA, which also equals the cosine of the phase angle between voltage and current. A power factor of 1 means every amp is doing work; a power factor of 0.8 means only 80% is.
The gap shows up as reactive power, kVAR = √(kVA² − kW²), which sloshes back and forth between the source and inductive loads like motors and transformers without doing work. Utilities still have to supply the current for it, so many charge industrial customers a penalty below about 0.9. Correcting power factor — usually with capacitors that offset inductive loads — cuts the current draw and those charges.
How it’s calculated
Power factor PF = real power (kW) / apparent power (kVA) = cos φ. The phase angle is φ = arccos(PF) in degrees. Reactive power kVAR = √(kVA² − kW²) from the power triangle, where kVA is the hypotenuse. PF is clamped to 1 for the angle when inputs give a ratio above 1.
A sinusoidal (linear) load, so power factor equals cos φ. Non-linear loads with harmonics have a lower true power factor than the displacement cos φ alone, which this does not model.
Power factor, phase angle and quality
| Power factor | Phase angle | Assessment |
|---|---|---|
| 1.00 | 0° | Unity — ideal |
| 0.95 | 18.2° | Excellent |
| 0.90 | 25.8° | Good — common utility target |
| 0.80 | 36.9° | Fair — typical of many motors |
| 0.70 | 45.6° | Poor |
| 0.50 | 60.0° | Very poor |
Phase angle computed as φ = arccos(PF).
Common mistakes
- Swapping kW and kVA — power factor is kW ÷ kVA, and it can never exceed 1.
- Confusing kVAR (reactive) with kVA (apparent); kVA is the hypotenuse of the power triangle.
- Assuming a good power factor means low energy use; it means less wasted current, not fewer kWh.
- Applying cos φ to a harmonic-rich load, where the true power factor is lower than the displacement angle suggests.
Frequently asked questions
What is the power factor formula?
Power factor = real power ÷ apparent power = kW ÷ kVA, which also equals cos φ, the cosine of the phase angle between voltage and current.
What is a good power factor?
1.0 is ideal. Utilities often want 0.9 or better; below that, many charge industrial customers a penalty because of the extra reactive current they must supply.
What is reactive power?
kVAR = √(kVA² − kW²). It is the power that oscillates between the source and inductive loads without doing useful work, yet still requires current from the grid.
How do you improve power factor?
Add power-factor correction, usually capacitors that offset inductive loads like motors. This lowers the reactive power and the total current, cutting utility penalties.