Three-Phase Power Formulas & Current Tables
Formulas for kW, kVA and line current, with lookup tables for 400 V and 415 V systems and a worked example.
Three-Phase Power Formulas and Current Tables
These formulas apply to a balanced three-phase load, such as a motor, a heater bank or a transformer, where the three line currents are equal. VL is the voltage between two phases (line-to-line). In Sri Lanka and many other 50 Hz countries the low-voltage supply is 400 V between phases and 230 V from phase to neutral, so VL = 400 V is used in the tables below.
√3 = 1.732
Formula table
| Quantity | Formula (balanced load) |
|---|---|
| Apparent power S (kVA) | S = √3 × VL × IL ÷ 1000 |
| Active power P (kW) | P = √3 × VL × IL × PF ÷ 1000 |
| Reactive power Q (kVAr) | Q = √(S² − P²) = S × sin φ |
| Line current from kW | IL = P × 1000 ÷ (√3 × VL × PF) |
| Line current from kVA | IL = S × 1000 ÷ (√3 × VL) |
| Motor input current | IL = Pshaft × 1000 ÷ (√3 × VL × PF × η) |
| Power factor | PF = P ÷ S = cos φ |
| Star (wye) connection | VL = √3 × Vphase; IL = Iphase |
| Delta connection | VL = Vphase; IL = √3 × Iphase |
Table 1: Line current for a given kVA (balanced load)
Use it for transformers, generators and UPS ratings. Current at 400 V is 1.443 A per kVA, and at 415 V it is 1.391 A per kVA.
| Rating | Current at 400 V (A) | Current at 415 V (A) |
|---|---|---|
| 1 kVA | 1.4 | 1.4 |
| 5 kVA | 7.2 | 7.0 |
| 10 kVA | 14.4 | 13.9 |
| 15 kVA | 21.7 | 20.9 |
| 20 kVA | 28.9 | 27.8 |
| 25 kVA | 36.1 | 34.8 |
| 30 kVA | 43.3 | 41.7 |
| 40 kVA | 57.7 | 55.6 |
| 50 kVA | 72.2 | 69.6 |
| 63 kVA | 90.9 | 87.6 |
| 75 kVA | 108.3 | 104.3 |
| 100 kVA | 144.3 | 139.1 |
| 125 kVA | 180.4 | 173.9 |
| 160 kVA | 230.9 | 222.6 |
| 200 kVA | 288.7 | 278.2 |
| 250 kVA | 360.8 | 347.8 |
| 315 kVA | 454.7 | 438.2 |
| 400 kVA | 577.4 | 556.5 |
| 500 kVA | 721.7 | 695.6 |
| 630 kVA | 909.3 | 876.5 |
| 800 kVA | 1154.7 | 1113.0 |
| 1000 kVA | 1443.4 | 1391.2 |
Table 2: Line current at 400 V for a given kW and power factor
The kW here is the electrical input power of the load. For a motor given by its shaft output, also divide by efficiency (see the motor formula above).
| Load | PF 1.0 (A) | PF 0.9 (A) | PF 0.85 (A) | PF 0.8 (A) |
|---|---|---|---|---|
| 1 kW | 1.4 | 1.6 | 1.7 | 1.8 |
| 2.2 kW | 3.2 | 3.5 | 3.7 | 4.0 |
| 3 kW | 4.3 | 4.8 | 5.1 | 5.4 |
| 4 kW | 5.8 | 6.4 | 6.8 | 7.2 |
| 5.5 kW | 7.9 | 8.8 | 9.3 | 9.9 |
| 7.5 kW | 10.8 | 12.0 | 12.7 | 13.5 |
| 11 kW | 15.9 | 17.6 | 18.7 | 19.8 |
| 15 kW | 21.7 | 24.1 | 25.5 | 27.1 |
| 18.5 kW | 26.7 | 29.7 | 31.4 | 33.4 |
| 22 kW | 31.8 | 35.3 | 37.4 | 39.7 |
| 30 kW | 43.3 | 48.1 | 50.9 | 54.1 |
| 37 kW | 53.4 | 59.3 | 62.8 | 66.8 |
| 45 kW | 65.0 | 72.2 | 76.4 | 81.2 |
| 55 kW | 79.4 | 88.2 | 93.4 | 99.2 |
| 75 kW | 108.3 | 120.3 | 127.4 | 135.3 |
| 90 kW | 129.9 | 144.3 | 152.8 | 162.4 |
2. Apparent power: S = 30 ÷ 0.85 = 35.3 kVA.
3. Reactive power: Q = √(35.3² − 30²) = 18.6 kVAr.
4. If the power factor is raised to 0.95, the current falls to 45.6 A, which is why a utility or a generator rating cares about PF. See the power factor correction calculator.
- Using phase voltage in the formula. With the √3 formula you must use the line-to-line voltage (400 V), not 230 V.
- Confusing kW and kVA. Breakers, cables and generators carry the current set by kVA, while the energy bill follows kW.
- Ignoring efficiency on motors. A 7.5 kW motor rating is shaft output, so its input current is higher than 7,500 ÷ (1.732 × 400).
- Assuming the load is balanced. If the three phases carry different currents, calculate each phase separately or use the neutral current calculator.
Frequently asked questions
What is the three-phase power formula? P = √3 × VL × IL × power factor, with the line-to-line voltage VL and the line current IL.
How do I convert kW to amps on three-phase? Divide the power in watts by √3 × line voltage × power factor. For example, 10 kW at 400 V and PF 0.9 draws about 16 A.
What is the difference between star and delta? In star the line voltage is √3 times the phase voltage and line current equals phase current. In delta the line current is √3 times the phase current and line voltage equals phase voltage.
Safety note. These figures are reference values and not a substitute for your local electrical code or a qualified electrician.