Three-Phase Power Calculator
Enter line voltage, current and PF to get kW, kVA and kVAR for a balanced three-phase load — the full power triangle.
Open calculatorLast updated: 2026-09-15
How the calculation works
- Apparent power comes from √3 × V_LL × I (the standard balanced three-phase formula).
- Real power multiplies by PF; reactive power closes the triangle via Pythagoras.
Worked example
Interpreting the result
The gap between kVA and kW is reactive power — current sloshing between source and load that does no work but heats conductors. Utilities bill large customers for it. Q near zero (PF ≈ 1) means the supply is being used efficiently.
Assumptions
- Balanced three-phase system — unbalance changes the math substantially.
- Sinusoidal waveforms; harmonics distort the PF reading.
Limitations
- Does not handle unbalanced loads — measure each phase for those.
- True PF with harmonics (distortion PF) differs from displacement PF.
Three-phase apparent and real power by voltage and current
Line-to-line voltage, balanced load. Real power is shown at two typical power factors.
| Voltage | Current | Apparent (kVA) | Real at pf 0.80 (kW) | Real at pf 0.90 (kW) |
|---|---|---|---|---|
| 208 V | 10 A | 3.60 | 2.88 | 3.24 |
| 208 V | 20 A | 7.21 | 5.76 | 6.48 |
| 208 V | 50 A | 18.01 | 14.41 | 16.21 |
| 208 V | 100 A | 36.03 | 28.82 | 32.42 |
| 240 V | 10 A | 4.16 | 3.33 | 3.74 |
| 240 V | 20 A | 8.31 | 6.65 | 7.48 |
| 240 V | 50 A | 20.78 | 16.63 | 18.71 |
| 240 V | 100 A | 41.57 | 33.26 | 37.41 |
| 400 V | 10 A | 6.93 | 5.54 | 6.24 |
| 400 V | 20 A | 13.86 | 11.09 | 12.47 |
| 400 V | 50 A | 34.64 | 27.71 | 31.18 |
| 400 V | 100 A | 69.28 | 55.43 | 62.35 |
| 480 V | 10 A | 8.31 | 6.65 | 7.48 |
| 480 V | 20 A | 16.63 | 13.30 | 14.96 |
| 480 V | 50 A | 41.57 | 33.26 | 37.41 |
| 480 V | 100 A | 83.14 | 66.51 | 74.82 |
kW = √3 × V × I × pf ÷ 1000 and kVA = √3 × V × I ÷ 1000, with V the line-to-line voltage.
Why the formula has a √3
The three line voltages are 120° apart, so the voltage between any two lines is √3 (about 1.732) times the voltage across one winding. Power is the sum of three phases, which works out to √3 × line voltage × line current × power factor.
Multiplying by 3 instead of √3 is a common slip. It overstates the power by about 73 %, enough to oversize a feeder or undersize a generator the other way round.
Worked scenario: a 480 V motor drawing 30 A at power factor 0.85
The calculator gives 24.94 kVA of apparent power, 21.20 kW of real power and 13.14 kVAR of reactive power. The motor does 21.2 kW of useful work, but the supply must carry the full 24.9 kVA.
Mistakes to avoid
- Using phase voltage where the formula expects line-to-line voltage. Check which one your nameplate or meter reports.
- Ignoring power factor. Real power (kW) and apparent power (kVA) are different quantities, and equipment and cables are rated in amps, which follow kVA.
- Applying the result to an unbalanced load. The formula assumes the three currents are equal.
Frequently asked questions
Why the √3 factor?
In a balanced three-phase system, the vector sum of three 120°-shifted phase powers is √3 × V_LL × I — a result of the phase geometry, not an approximation.
What is kVAR?
Reactive power: the component of current that oscillates between source and inductive load without doing work. It fills magnetic fields in motors and transformers every cycle.