Power calculator
Power is volts times amps for a DC or purely resistive load. On AC with a power factor, real power is V × I × pf for single phase and √3 × V × I × pf for three phase. A 400 V three-phase load at 16 A and 0.9 power factor draws 9.98 kW real from 11.09 kVA apparent.
How to calculate electrical power
The gap between watts and volt-amps is the single most misunderstood thing in electrical sizing. Watts is the power actually doing work; volt-amps is the product of the voltage and the current the supply has to deliver. For a resistive load they are equal. For a motor, current lags voltage and the two diverge by the power factor, so a 10 kW motor at 0.8 might pull 12.5 kVA. Cables, breakers and generators all have to be sized for the apparent power, because the current is real whether it is doing useful work or not.
Questions
P = V × I for DC. For AC, P = V × I × power factor single phase, and P = √3 × V × I × power factor three phase.
kW is real power doing work; kVA is apparent power the supply must deliver. They are equal only when the power factor is 1.
Use 1 for heating, incandescent lighting and resistive loads. Motors are typically 0.8 to 0.9; check the nameplate.
Divide by 745.7 for mechanical horsepower. A 3 kW motor is about 4 hp of output, before efficiency losses.
Because line-to-line voltage and phase current are not in phase with each other. The √3 falls out of the vector sum of three balanced phases.