Three-Phase Power Calculator
The √3 is geometry, not a safety margin.
Work out Three-Phase Power. The √3 is geometry, not a safety margin. Answers in the units the job actually uses.
Real power
5.889 kW
6.928 kVA apparent · power factor 0.85
Three-phase power is √3 × line voltage × line current × power factor. The √3 is not a fudge or a safety margin — it appears because the three phases are 120° apart rather than in step, and it falls straight out of the vector sum. Phase voltage in a star connection is the line voltage divided by √3, which is why a 400 V three-phase supply gives 230 V between any phase and neutral. The same √3, seen from the other side. Real, apparent and reactive power form a right triangle: apparent is the hypotenuse and the power factor is the cosine of the angle. Everything here assumes a balanced load — an unbalanced one needs each phase worked separately, with the neutral carrying the difference.
How the Three-Phase Power Calculator works
Three-phase power or current, with apparent and reactive power alongside. The √3 appears because the phases are 120° apart rather than in step — it falls out of the vector sum rather than being a correction factor.
Also known as: kva to amps three phase · why root 3 in three phase · 3 phase current from kw · 400v to 230v phase voltage
Frequently asked questions
What is the three-phase power formula?
√3 × line voltage × line current × power factor. The √3 is roughly 1.732 and comes from the 120° phase separation, not from any safety allowance.
Why is a 400 V supply also 230 V?
Because 400 V is measured between two phases and 230 V between a phase and neutral. The ratio is exactly √3, which is the same factor seen from the other side.
What is the difference between kW and kVA?
Kilowatts are real power that does work; kilovolt-amps are apparent power, the product of voltage and current. The power factor is the ratio between them, and equipment is rated in kVA because that is what determines the current it must carry.
Why does a poor power factor matter?
Because the supply carries current that does no work. At 0.5 the cables and transformers handle twice the current for the same delivered power, which is why industrial users are charged for it.
What about unbalanced loads?
The formula assumes a balanced three-phase load. An unbalanced one needs each phase worked separately, and the neutral carries the difference — which is why neutral conductors matter more in modern installations full of single-phase electronics.
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