What does this calculator do?
In a balanced three-phase system, the total active power can be calculated from line quantities and the power factor, without measuring each phase separately.
P = √3 × VL × IL × PF
Enter the values in the units shown. The calculator converts units automatically and displays the result in practical units.
Worked example
400 V, 10 A and PF = 0.9 give about 6.24 kW.
Practical tips
- Make sure the voltage you enter is line-to-line (phase-to-phase).
- The formula assumes a balanced system: equal loads on all three phases.
- For motors, also account for efficiency when converting electrical power to shaft power.
Common mistake to avoid
Check whether your values are line or phase quantities: mixing them gives wrong results.
The three powers of a three-phase system
In a balanced three-phase system, using the line voltage VL (between phases) and the line current IL:
- Active power (W): P = √3 · VL · IL · cos φ
- Apparent power (VA): S = √3 · VL · IL
- Reactive power (var): Q = √3 · VL · IL · sin φ
- Line current: IL = P / (√3 · VL · cos φ)
These formulas hold for both star (wye) and delta connections, as long as you use line values. In star, VL = √3 · Vphase; in delta, IL = √3 · Iphase.
Worked examples
| Case | Data | Result |
|---|---|---|
| Power of a load | 400 V, 10 A, cos φ = 0.85 | P = 1.732 × 400 × 10 × 0.85 ≈ 5.89 kW · S ≈ 6.93 kVA |
| Motor current | 15 kW electrical, 400 V, cos φ = 0.85 | I = 15 000 / (1.732 × 400 × 0.85) ≈ 25.5 A |
| 208 V commercial supply | 10 kW, 208 V, cos φ = 0.9 | I = 10 000 / (1.732 × 208 × 0.9) ≈ 30.8 A |
| 480 V industrial plant | 50 kW, 480 V, cos φ = 0.85 | I = 50 000 / (1.732 × 480 × 0.85) ≈ 70.8 A |
For the same power, the lower the voltage, the higher the current. That is why 208 V systems need thicker cables than 400 V or 480 V systems for the same load.
Common mistakes
- Using the phase voltage with √3: if you enter the 230 V phase voltage of a 400 V system, the result comes out √3 times too small.
- Forgetting the power factor: without cos φ you get kVA, not kW.
- Misreading a motor nameplate: nameplate kW (or hp) is mechanical shaft power; the electrical input is that figure divided by the efficiency.
- Sizing cables on rated current alone: also consider starting current, ambient temperature and voltage drop, as required by your local electrical code.
Frequently asked questions
What is the difference between kW and kVA?
kW measures the power actually converted into work; kVA measures the total power flowing through the network. They are related by kW = kVA × cos φ. Transformers and generators are rated in kVA.
Why does √3 appear in the formula?
Because the three phases are 120° apart. When you add up their powers using line values, the factor √3 ≈ 1.732 appears.
How do I improve a low power factor?
Usually with capacitor banks that compensate the reactive power of motors and other inductive loads. You can estimate the effect with the power factor calculator.
Educational tool. Check tolerances, datasheets, standards and real operating conditions before using the results in critical applications.