Three Phase Power Calculator: kW, kVA and Power Factor
Three Phase Power Calculator: kW, kVA and Power Factor
Works in both directions: from line voltage, current and power factor to the full power triangle, or from a required kW load back to the line current, which is the generator and feeder sizing question.
The apparent power S in kVA is root 3 times line voltage times line current. Real power P is S times the power factor, and reactive power Q closes the right triangle, Q equals the root of S squared minus P squared. Generators and transformers are rated in kVA because they carry the full current regardless of how much of it does useful work, which is why a poor power factor costs machine capacity.
How to use this tool
Two directions, one triangle. Give it line voltage, line current and power factor, and it returns the full power triangle: kVA, kW, kVAR and the phase angle. Or give it a load in kW with the voltage and power factor, and it returns the line current the load will draw and the kVA of machine needed to serve it, which is the generator sizing question asked directly.
kW, kVA and the triangle between them
Apparent power S, in kVA, is root 3 times line voltage times line current: the product of what the conductors and windings actually carry. Real power P, in kW, is S times the power factor: the part doing work. Reactive power Q, in kVAR, closes the right triangle, the root of S squared minus P squared: current sloshing between source and load to feed magnetic fields, carried by the wires but delivering nothing.
Machines are rated in kVA because heating follows current, and current does not care what fraction of it is useful. A generator rated 70 kVA will serve 70 kW of unity power factor load, but only 56 kW of load at 0.8, because the same windings are full either way. Poor power factor is not inefficiency in the friction sense; it is capacity spent carrying current that does no work.
A worked check you can repeat on paper
A 400 V three phase feeder carrying 100 A at 0.8 power factor. S is root 3 times 400 times 100, which is 69.28 kVA. P is 0.8 of that, 55.43 kW, and Q is the root of 69.28 squared minus 55.43 squared, which is 41.57 kVAR. Check the triangle: 55.43 squared plus 41.57 squared recovers 69.28 squared, and the angle whose cosine is 0.8 is 36.87 degrees, the same angle that lives inside the 3-4-5 triangle.
Run it backwards as the sizing question: a 55.43 kW load at 400 V and 0.8 power factor draws 55430 over root 3 times 400 times 0.8, which is exactly 100 A, and needs 69.28 kVA of generator. Order the 60 kVA set because the kW number looked comfortable, and it will not carry the load.
Mistakes that catch people out
Sizing a generator in kW against a kVA rating. As above: divide the kW by the power factor first. Fix: the tool reports the kVA required in so many words.
Using phase voltage where line voltage belongs. On a 400 V wye system the phase voltage is 230 V, and mixing them scatters errors of root 3 everywhere. Fix: these formulas take line to line voltage and line current.
Assuming power factor is always 0.8. Modern loads range from near unity to well below 0.7 at partial load. Fix: use the nameplate or measured value; 0.8 is a convention, not a law.
Forgetting the formulas assume balance. Root 3 relationships hold for balanced three phase. Fix: a badly unbalanced system needs per phase treatment, not one number.
How this was checked
The 400 V, 100 A, 0.8 case was verified to full precision in both directions, including the identity that P squared plus Q squared returns S squared exactly and the phase angle of 36.87 degrees. The reverse mode was confirmed to round trip: the kW output of the forward calculation, fed back with the same voltage and power factor, returns exactly 100 A. Unity power factor was checked as the degenerate case, with Q exactly zero and kW equal to kVA.
Related Calculators and Reference
The current this tool produces is the input to the Cable Size and Ampacity Estimator and to the Voltage Drop Calculator, which together decide what conductor serves the load. The DC and resistive fundamentals live in the Ohm Law Calculator, and the 36.87 degree angle in the worked example connects back to the Triangle Solver, because the power triangle is a triangle like any other. For the current a load draws from its watts, kilowatts, kVA or horsepower at any voltage, DC or AC, single or three phase, with the breaker a continuous load needs, use the Watts to Amps Calculator. Also see the Power Factor Correction Calculator: the capacitor kVAR needed to raise a lagging power factor to a target, and the current it saves.