The three formulas
Power and current are linked by the voltage, and on AC also by the power factor:
- DC: I = P ÷ V
- Single phase AC: I = P ÷ (V × PF)
- Three phase AC: I = P ÷ (√3 × V × PF)
P is in watts, so multiply kilowatts by 1,000 first. On three phase, V is the line-to-line voltage, the 400 V or 480 V figure rather than the 230 V or 277 V from one line to neutral.
Worked examples
- A 5 kW heater on 230 V single phase, power factor 1: 5,000 ÷ 230 = 21.7 A.
- The same 5 kW as a motor at power factor 0.85: 5,000 ÷ (230 × 0.85) = 25.6 A, nearly 4 A more for the same work.
- A 15 kW motor on 400 V three phase at 0.85: 15,000 ÷ (1.732 × 400 × 0.85) = 25.5 A.
- A 2 kW load on a 48 V battery bank: 2,000 ÷ 48 = 41.7 A, which is why low voltage DC needs thick cable.
What power factor is
On AC, current and voltage do not always peak together. Power factor is the fraction of the current that is actually doing work, between 0 and 1.
- 1.0: resistive loads. Heaters, kettles, filament lamps.
- 0.8 to 0.9: motors, which is most industrial load.
- 0.95 to 0.99: modern switch-mode supplies with power factor correction.
The equipment's nameplate usually states it. A lower power factor means more current for the same kilowatts, so it changes the cable and breaker you need.
kW, kVA and motor nameplates
kW is real power, the part that does work. kVA is apparent power, what the wiring has to carry: kVA = kW ÷ PF. They are equal only at a power factor of 1. Since conductors and protection are chosen on current, size from kVA.
One trap on motors: the nameplate kW is the output at the shaft. The electrical input is higher by the efficiency, so a 15 kW motor at 92% efficiency draws 16.3 kW from the supply, and that is the figure to convert.
From amps back to kW
Rearrange the same formulas: P = V × I for DC, P = V × I × PF single phase, and P = √3 × V × I × PF for three phase. A clamp meter reading 25 A on 400 V three phase at 0.85 is 1.732 × 400 × 25 × 0.85 = 14.7 kW.
Tools
The kW to Amps Calculator converts both ways for DC, single and three phase, and gives the kVA. Ohm's Law Calculator covers voltage, current and resistance, while the Cable Size Calculator and Voltage Drop Calculator turn that current into a conductor size.