Power Factor Calculator
Enter any two values from the power triangle (real power, apparent power, reactive power, or power factor) to calculate the rest. Works for single-phase and three-phase AC circuits.
Enter any two of the four values below (leave the others blank).
Real Power P
—
kW
Apparent Power S
—
kVA
Reactive Power Q
—
kVAR
Power Factor
—
PF angle: —
The Power Triangle
In AC circuits with reactive loads, power has three components forming a right triangle:
$$S^2 = P^2 + Q^2$$
- P — Real power (kW): actual work performed; what you pay for on your electricity bill
- S — Apparent power (kVA): the total power drawn from the supply; V × I
- Q — Reactive power (kVAR): power stored and released by inductors and capacitors; does no useful work but stresses wiring and transformers
$$PF = \cos(\theta) = \frac{P}{S} = \frac{kW}{kVA}$$
Apparent Power Formulas
| Circuit type | Formula |
|---|---|
| Single-phase AC | $S = V \times I$ |
| Three-phase AC | $S = \sqrt{3} \times V_{line} \times I_{line} = 1.732 \times V \times I$ |
Why Power Factor Matters
A low power factor means more current is drawn for the same real power output. This causes:
- Higher wiring and transformer losses (I²R losses increase)
- Need for larger wire, switchgear, and transformers
- Utility penalties for commercial customers with PF below 0.95
| Power factor | Quality | Notes |
|---|---|---|
| 1.00 | Unity | Purely resistive load |
| 0.95–1.00 | Excellent | Typical well-corrected industrial facility |
| 0.85–0.95 | Good | Acceptable for most applications |
| 0.70–0.85 | Fair | Utility penalties may apply in commercial settings |
| < 0.70 | Poor | Significant reactive power; correction recommended |
Power Factor Correction
Inductive loads (motors, transformers, fluorescent ballasts) have lagging power factor — they draw reactive current. Power factor correction adds capacitor banks to supply the reactive current locally, reducing the reactive current on utility lines.
$$Q_{correction} = P \times (\tan\theta_1 - \tan\theta_2)$$
Where θ₁ is the current power factor angle and θ₂ is the target power factor angle.
Frequently Asked Questions
What is the difference between kW and kVA? kW (kilowatts) is real power — the actual energy consumed per second to do useful work. kVA (kilovolt-amperes) is apparent power — the product of RMS voltage and RMS current. They are equal only when power factor = 1.0 (purely resistive load). For most AC equipment, kVA > kW.
Why do generators and UPS systems use kVA ratings? Generators and UPS units are limited by the current they can supply, not just the real power. A load with poor power factor draws more current for the same kW. Rating in kVA accounts for this — a 10 kVA generator can supply 10 kW to a unity PF load, or only 8.5 kW to a 0.85 PF load.
What power factor do motors have? Induction motors have power factors ranging from about 0.4 (small motor at no load) to 0.85–0.90 (large motor at full load). A motor's nameplate kVA and power factor are listed at full-load conditions.
