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.
Last 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.
Formula
P = √3 × V × I × PF S = √3 × V × I Q = √(S² − P²)
| Symbol | Meaning | Unit |
|---|---|---|
P | Real power | kW |
S | Apparent power | kVA |
Q | Reactive power | kVAR |
PF | Power factor = P/S | — |
Worked example
400 V, 20 A, PF 0.85: S = 1.732 × 400 × 20 / 1000 = 13.9 kVA; P = 11.8 kW; Q = 7.3 kVAR. The 7.3 kVAR is what a PF-correction bank would target if you wanted PF 1.0.
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.
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.