Power Factor Calculator
Work out real power (kW), reactive power (kVAR), apparent power (kVA), power factor and phase angle from any two values or from voltage and current, then size the capacitor bank needed to correct the power factor.
Power factor correction
How to use the Power Factor Calculator
- Choose what you know, for example real power and power factor, or voltage, current and power factor.
- Enter the values. For a three-phase supply use the line-to-line voltage (such as 400 V or 480 V).
- Press Calculate (results also update as you type) to see kW, kVAR, kVA, the power factor, phase angle and the power triangle.
- Set a target power factor (0.95 is common), the capacitor connection, voltage and frequency.
- Read the capacitor bank size in kVAR and the capacitance per capacitor in µF, with the working shown.
The power triangle
In an AC circuit with motors, transformers or other inductive loads, the supply delivers more than the useful power. The three quantities form a right triangle:
- Real power P (kW) does the work: P = S × PF
- Reactive power Q (kVAR) builds magnetic fields: Q = √(S² − P²) = P × tan φ
- Apparent power S (kVA) is what cables and transformers must carry: S = √(P² + Q²)
- Power factor PF = P ÷ S = cos φ
From voltage and current: single-phase S = V × I; three-phase S = √3 × VLL × I.
Worked example: correcting 100 kW from 0.75 to 0.95
At PF 0.75 the load draws S = 100 ÷ 0.75 = 133.3 kVA and Q = 88.2 kVAR. tan φ₁ = tan(arccos 0.75) = 0.8819 and tan φ₂ = tan(arccos 0.95) = 0.3287, so the capacitor bank needs
Qc = 100 × (0.8819 − 0.3287) = 55.3 kVAR
Apparent power falls to 100 ÷ 0.95 = 105.3 kVA, about 21% less current. For a 400 V, 50 Hz three-phase delta bank, each of the three capacitors supplies 18.44 kVAR: C = 18,441 ÷ (2π × 50 × 400²) ≈ 367 µF. In star, each capacitor sees 231 V and needs about 1,101 µF.
kVAR multiplier table
Multiply the load in kW by the factor below to get the kVAR needed (tan φ₁ − tan φ₂).
| Current PF | To 0.90 | To 0.95 | To 0.98 | To 1.00 |
|---|---|---|---|---|
| 0.70 | 0.536 | 0.692 | 0.817 | 1.020 |
| 0.75 | 0.398 | 0.553 | 0.679 | 0.882 |
| 0.80 | 0.266 | 0.421 | 0.547 | 0.750 |
| 0.85 | 0.135 | 0.291 | 0.417 | 0.620 |
| 0.90 | – | 0.156 | 0.281 | 0.484 |
Practical tips
- Aim for 0.95 rather than 1.00: the last few percent need a lot of extra kVAR, and over-correcting makes the load leading.
- Many utilities bill a penalty below a power factor of 0.9 or 0.95, which is the usual payback for a capacitor bank.
- Pick capacitors rated for the system voltage with headroom, and consider detuned (reactor) banks where variable-speed drives create harmonics.
Frequently asked questions
How do I convert kVA to kW?
Multiply kVA by the power factor: kW = kVA × PF. For example, 125 kVA at a power factor of 0.8 gives 125 × 0.8 = 100 kW.
What is power factor?
Power factor is the ratio of real power (kW), which does useful work, to apparent power (kVA), which the supply must deliver: PF = kW ÷ kVA. It ranges from 0 to 1, and it equals the cosine of the phase angle between voltage and current for sinusoidal loads.
How do I calculate kVAR?
Reactive power is Q = √(kVA² − kW²), or Q = kW × tan φ where φ = arccos(PF). A 100 kW load at PF 0.75 draws 100 × 0.8819 = 88.2 kVAR.
How do I size a power factor correction capacitor?
Use Qc = P × (tan φ1 − tan φ2), where φ1 is the current phase angle and φ2 the target. Correcting 100 kW from PF 0.75 to 0.95 needs 100 × (0.8819 − 0.3287) = 55.3 kVAR.
How do I convert kVAR to microfarads?
For a single capacitor C = Q ÷ (2π f V²) with Q in VAR. In a three-phase delta bank each of the three capacitors supplies Q/3 at the line voltage. In a star bank each sees the line voltage ÷ √3, so each needs three times the capacitance of the delta case.
What is the formula for three-phase apparent power?
S = √3 × V(line-to-line) × I. For example 400 V and 100 A gives √3 × 400 × 100 = 69.3 kVA. Real power is that times the power factor.