Calculate power factor (PF), kVA, kVAR and phase angle (φ) for single-phase and three-phase systems, from kW, voltage and current, from kW and kVA, or convert kW to kVAR from a known power factor.
In three-phase formulas, V is the line-to-line voltage and A is the line current. In single-phase formulas, V is line-to-neutral.
kW, kVAR and kVA form a right-angled triangle. Real power (kW) is the base, reactive power (kVAR) is the height, and apparent power (kVA) is the hypotenuse. The angle between kW and kVA is φ, and cos φ is the power factor.
A single-phase load draws 2.2 kW at 230 V and 12 A:
A three-phase panel reads 50 kW at 415 V with a measured line current of 87 A:
Enter the same numbers above to see these steps generated automatically.
If you already know the power factor, choose "kW and power factor" above, or use these formulas:
Example: 100 kW at PF 0.85 → kVA = 100 / 0.85 = 117.6 kVA, kVAR = 100 × 0.620 = 62.0 kVAR. On a 415 V three-phase supply that is a line current of 163.7 A.
To raise the power factor, size the capacitor bank in kVAR with the Power Factor Correction Calculator, and convert between kW and kVA with the kW to kVA Calculator.
For the same 10 kW load on 415 V three-phase, the line current rises sharply as PF drops. This is why utilities penalise low PF and why cables, breakers and transformers must be oversized:
| Power Factor | Line Current | vs PF 1.0 |
|---|---|---|
| 1.00 | 13.9 A | — |
| 0.90 | 15.5 A | +11% |
| 0.80 | 17.4 A | +25% |
| 0.70 | 19.9 A | +43% |
| 0.60 | 23.2 A | +67% |
| Load Type | Typical PF |
|---|---|
| Resistive heating / incandescent lighting | 1.00 |
| Induction motor (full load) | 0.80 – 0.85 |
| Induction motor (light load) | 0.50 – 0.70 |
| LED drivers (quality) | 0.90 – 0.95 |
| Fluorescent (magnetic ballast, uncorrected) | 0.50 – 0.60 |
| Welding machines | 0.50 – 0.60 |
Measured panel PF matters for feeder sizing. Build the full schedule with the Electrical Panel Load Calculator.
PF = kW / kVA = cos φ. For single phase, kVA = V × I / 1000, so PF = P / (V × I). For three phase, kVA = √3 × V × I / 1000, so PF = P / (√3 × V × I), with P in watts, V line-to-line and I the line current.
Measure kW, line-to-line voltage and line current. Calculate kVA = 1.732 × V × I / 1000, then PF = kW / kVA. Example: 50 kW at 415 V and 87 A gives kVA = 62.54 and PF = 0.80.
kVAR = kW × tan(arccos PF). Example: 100 kW at PF 0.85 gives kVAR = 100 × 0.620 = 62.0 kVAR, and kVA = 100 / 0.85 = 117.6 kVA.
Power factor is the ratio of real power (kW) doing useful work to apparent power (kVA) drawn from the supply. A PF of 1.0 means all current does useful work; at PF 0.7 a load draws about 43% more current than at PF 1.0.
0.95 or higher is a common design target. Many utilities apply penalty charges when average PF falls below about 0.90 (0.85 in some tariffs). Typical uncorrected values: induction motors 0.80–0.85 at full load, welders 0.5–0.6, resistive heating 1.0.
Lagging: current lags voltage, typical for inductive loads (motors, transformers, reactors). Leading: current leads voltage, caused by capacitive loads or over-compensated capacitor banks. kW, V and I readings alone cannot show which one you have; a power analyser is needed.
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