The formulas
- Real power: kW = V × I × PF × √3 ÷ 1000, where V is the line-to-line voltage and I the line current (DOE, Determining Electric Motor Load and Efficiency, Equation 1).
- Apparent power: kVA = V × I × √3 ÷ 1000, so PF = kW ÷ kVA.
- Reactive power: kVAR = √(kVA² − kW²), because reactive power acts at 90° to real power (DOE, Reducing Power Factor Cost).
- Current from power: I = kVA × 1000 ÷ (V × √3), and kVA = kW ÷ PF.
- Motor input at full load: kW = hp × 0.7457 ÷ efficiency (DOE Equation 2).
Worked examples
- Measured motor: DOE's fact sheet averages three readings to 469.7 V, 37 A and PF 0.763. 469.7 × 37 × 0.763 × 1.732 ÷ 1000 = 22.97 kW (the sheet rounds it to 22.9 kW).
- Power triangle: a 100 kW load with 100 kVAR of reactive power is √(100² + 100²) = 142 kVA, so PF = 100 ÷ 142 = 0.70, as in DOE's power factor fact sheet.
- Transformer current: 75 kVA at 208 V three-phase is 75,000 ÷ (208 × 1.732) = 208.2 A per line.
- Motor estimate: a 25 hp motor at 93% full-load efficiency draws 25 × 0.7457 ÷ 0.93 = 20.05 kW input.
All four are automated test cases for this calculator.
Good to know
- Use line-to-line volts (208, 240, 480, 600). If the voltages or currents differ between phases, average the three, as the DOE method does.
- Power factor changes with load. A lightly loaded motor has a much lower power factor than its nameplate value.
- This tool gives physics only. It doesn't size conductors, breakers or overloads; use the NEC, your local code and the nameplate for that. For wire runs, try the voltage drop calculator.
Common questions
How do I convert three-phase amps to kW?
Multiply line-to-line volts by line amps by power factor by the square root of 3 (1.732), then divide by 1,000. This is Equation 1 in the U.S. Department of Energy motor fact sheet.
What is the difference between kW, kVA and kVAR?
kW is real power that does work, kVAR is reactive power for magnetic fields, and kVA is the apparent power the system has to carry. Power factor is kW divided by kVA, and kVAR acts at 90 degrees to kW (the power triangle).
Can I use this to size wire or breakers?
No. It gives the physics only. Conductor, overcurrent and motor protection sizing come from the NEC, your local code and the equipment nameplate and instructions.
Sources
- U.S. Department of Energy: Determining Electric Motor Load and Efficiency (Equations 1 to 3)
- U.S. Department of Energy: Reducing Power Factor Cost (kW, kVA, kVAR and the power triangle)
Formulas checked against the sources above and our automated test cases on 2026-10-19. Planning aid, not engineering advice.