Quick answer
Power factor = real power (kW) ÷ apparent power (kVA). With 80 kW and 100 kVA the power factor is 0.8, the phase angle is arccos(0.8) = 36.87° and the reactive power is √(100² − 80²) = 60 kvar.
Enter real and apparent power. The calculator returns power factor, phase angle and reactive power.
Related tools: Factor Calculator: List every factor of a positive whole number. Power of 2 Calculator: Compute 2 raised to an integer power exactly. Common Factor Calculator: All common factors of two numbers.
How to use the Power Factor Calculator
- Enter real power (kW) (above 0).
- Enter apparent power (kVA) (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Real power | A number, in kW | > 0 |
| Apparent power | A number, in kVA | > 0 |
Formula and method
Formula
pf = kW ÷ kVA; φ = arccos(pf); kvar = √(kVA² − kW²)
IEEE-754 double precision; shown to the decimals indicated.
Real power cannot exceed apparent power.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Real power = 80; Apparent power = 100.
| Result | Value |
|---|---|
| Power factor | 0.8 |
| Phase angle | 36.87° |
| Reactive power | 60 kvar |
Example 2
Inputs: Real power = 4.5; Apparent power = 5.
| Result | Value |
|---|---|
| Power factor | 0.9 |
| Phase angle | 25.842° |
| Reactive power | 2.1794 kvar |
Example 3
Inputs: Real power = 12; Apparent power = 12.
| Result | Value |
|---|---|
| Power factor | 1 |
| Phase angle | 0° |
| Reactive power | 0 kvar |
The first line is the headline result (power factor). Below it the power Factor Calculator lists phase angle and reactive power, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Why utilities care
A low power factor means more current for the same useful power, which loads wiring and transformers. Many utilities charge commercial customers for a power factor below about 0.9, and capacitors are added to correct it.
The power triangle
kW, kvar and kVA form a right triangle: kVA² = kW² + kvar². The angle between kW and kVA is the phase angle, and its cosine is the power factor.
How the result changes with apparent power
Holding every other input at the first worked example, this table changes only apparent power. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Apparent power | Power factor | Phase angle | Reactive power |
|---|---|---|---|
| 100 | 0.8 | 36.87° | 60 kvar |
| 200 | 0.4 | 66.422° | 183.303 kvar |
| 400 | 0.2 | 78.463° | 391.9184 kvar |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Real power: entering "0" shows "Real power must be greater than 0." beside that field and no result.
Choosing between the Power Factor Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Factor Calculator](/math/factor-calculator/) | number | Factors |
| [Power of 2 Calculator](/math/power-of-2/) | exponent n | 2^10 |
| [Common Factor Calculator](/math/common-factor-calculator/) | first number and second number | Common factors |
| [Power Converter](/converters/power-converter/) | value, from and to | Horsepower (mechanical) → Watt (W) |
| [Power Calculator](/science/power-calculator/) | use | Power |
Assumptions and limitations
- pf is between 0 and 1
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for real power to confirm this.
Frequently asked questions
What is a good power factor?
Above about 0.9 is considered good, and 1.0 means all power does useful work.
Can it exceed 1?
No. Real power can never exceed apparent power, so the factor is at most 1.
How do I correct it?
Add capacitors for inductive loads.
What does the Power Factor Calculator calculate?
Power factor, phase angle and reactive power from real and apparent power. It returns Power factor, Phase angle and Reactive power.
What formula does the Power Factor Calculator use?
pf = kW ÷ kVA; φ = arccos(pf); kvar = √(kVA² − kW²). Real power cannot exceed apparent power.
What do I need to enter in the power Factor Calculator?
You enter Real power (kW) and Apparent power (kVA).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. pf is between 0 and 1.
What is an example of a power Factor result?
With real power 80 and apparent power 100, the power factor is 0.8.
Related calculators
- Factor Calculator — List every factor of a positive whole number.
- Power of 2 Calculator — Compute 2 raised to an integer power exactly.
- Common Factor Calculator — All common factors of two numbers.
- Power Converter — Convert watts, kilowatts, horsepower and BTU per hour.
- Power Calculator — Mechanical power from work and time, or force and velocity.
Sources
- OpenStax, Algebra and Trigonometry 2e (Rice University): exponents, radicals, logarithms and inverse trigonometric functions
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.