Amps to kilowatts conversion formula (AC three phase)

Amps to kilowatts conversion formula (AC three phase)

The real power P in kilowatts is equal to square root of 3 times the power factor PF times the phase current I in amps, times the  line to line RMS voltage VL-L in volts divided by 1000:
P(kW) = √3 × PF × I(A) × VL-L(V) / 1000
So kilowatts are equal to square root of 3 times power factor PF times amps times volts divided by 1000:
kilowatt = √3 × PF × amp × volt / 1000
or
kW = √3 × PF × A × V / 1000

Example

What is power consumption in kW when the power factor is 0.8 and the phase current is 3A and the RMS voltage supply is 110V?
Answer: the power P is equal to square root of 3 times power factor of 0.8 times current of 3 amps times the voltage of 110 volts, divided by 1000.
P = √3 × 0.8 × 3A × 110V / 1000 = 0.457kW


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