Power Factor Calculator
Reactive power, angle, and the kVAR correction needed to reach a target power factor.
What it does
Motors, transformers, and every coil in a facility pull current that does real work and current that just sloshes back and forth. Power factor measures the split: the ratio of working kilowatts to total kilovolt-amperes. A factor of 0.75 means three-quarters of the current is earning its keep.
The tool above turns a load's real power and current power factor into the full picture: apparent power, reactive power, the phase angle in degrees, and the capacitor kVAR needed to lift the factor to your target. Raise the target and the correction shrinks; the underlying load has not changed.
The defaults run a 45 kW load at 0.75 aiming for 0.95: apparent power 60 kVA, reactive power 39.69 kVAR, angle 41.41 deg, and 24.9 kVAR of correction that lowers apparent power to 47.37 kVA. The Department of Energy's fact sheet walks through the same geometry on a 100 kW load at 0.70, where correction cuts apparent power from 142 to about 105 kVA and trims line current by roughly a quarter.
The definitions and the power triangle follow the DOE's Reducing Power Factor Cost fact sheet, HyperPhysics, and the AC power chapter of OpenStax University Physics. Capacitor sizing beyond this arithmetic is electrical design work.
How to use
- Enter the load's real power in kilowatts from a meter or nameplate.
- Enter the current power factor as a decimal from 0 to 1.
- Set the target factor; 0.95 is the common utility threshold.
- Read the angle and reactive power to understand the load.
- Take the correction kVAR to a qualified designer before ordering capacitors.
Formula
- P
- Real power in kW, the part doing useful work.
- S
- Apparent power in kVA, real plus reactive combined.
- Q
- Reactive power in kVAR, the part cycling between source and load.
- correction
- The kVAR a capacitor bank should supply to reach the target factor.
The angle between the real and apparent power vectors is the inverse cosine of power factor, and reactive power is real power times the tangent of that angle. Because apparent power is the hypotenuse, line current scales with 1 / PF, and resistive losses scale with its square, which is why utility penalties bite: at 0.75 you carry a third more current than the same load at unity. Correction must land above the current factor or it adds reactive power rather than removing it. Capacitor banks also interact with harmonics from drives and need staged switching, so the kVAR figure here starts the conversation with an electrical designer rather than ending it.
Worked example
Example: 45 kW at 0.75, correcting to 0.95
Defaults: 45 kW real power, current factor 0.75, target 0.95.
- Apparent power: 45 / 0.75 = 60 kVA.
- Angle: acos(0.75) = 41.41 deg, and tan = 0.8819.
- Reactive power: 45 x 0.8819 = 39.69 kVAR.
- Target angle: acos(0.95) = 18.19 deg, tan = 0.3287.
- Correction: 45 x (0.8819 - 0.3287) = 24.9 kVAR.
- New apparent power: sqrt(45^2 + 14.79^2) = 47.37 kVA, down from 60.
Reference table
| Power factor | Angle | tan(angle) |
|---|---|---|
| 0.60 | 53.13 deg | 1.3333 |
| 0.70 | 45.57 deg | 1.0202 |
| 0.75 | 41.41 deg | 0.8819 |
| 0.80 | 36.87 deg | 0.7500 |
| 0.90 | 25.84 deg | 0.4843 |
| 0.95 | 18.19 deg | 0.3287 |
| 1.00 | 0 deg | 0 |
Limits
- Assumes capacitor-based correction on sinusoidal loads.
- Ignores harmonics, which need detuned banks or filters.
- Not an electrical design: protection, switching, and staging are not sized here.
- Sums a single load's numbers; facility totals need metered data.
Common mistakes
- Setting a target below the current factor, which adds reactive power.
- Sizing capacitors by apparent power saved instead of kVAR.
- Forgetting that losses fall with the square of the current.
- Ignoring harmonics from variable-frequency drives.
- Treating the correction as energy saved rather than current relieved.
Try it yourself
Quick checks. Answers sit tucked under each question.
45 kW at 0.75, but targeting 0.90?
17.89 kVAR of correction; apparent power falls from 60 to 50 kVA.
100 kW at 0.70 to 0.95?
69.15 kVAR: reactive power drops from 102.02 kVAR to about 32.9, and apparent power from 142.86 to 105.26 kVA.
What if the target equals the current factor?
Zero correction: 0 kVAR, with apparent power unchanged at 60 kVA.
Questions
What is power factor?
The ratio of real power to apparent power: how much of the current flowing does useful work versus cycling reactively.
Why do utilities charge for low power factor?
Their wires, transformers, and losses are sized by current. A low factor means more current for the same useful power, so they bill the difference.
What is a kVAR?
A kilovolt-ampere reactive: the unit of reactive power, the component that shuttles between inductive loads and the source without doing net work.
Can power factor exceed 1?
No. Real power can never exceed apparent power, so 1 is the ceiling and means the current is perfectly in phase with voltage.
Does correction work for three-phase systems?
Yes. The kVAR figure applies the same way on a per-phase basis; the three-phase power calculator handles the line and phase conversions.
Is correcting power factor the same as saving energy?
Mostly it relieves current and losses rather than the load's own energy use: wire losses drop, capacity frees up, and penalty charges disappear.
Sources
- US Department of Energy fact sheet: Reducing Power Factor Cost
- HyperPhysics: Power in AC circuits
- OpenStax University Physics Volume 2, 15.4 Power in an AC Circuit