Three-Phase Power Calculator

The √3 is geometry, not a safety margin.

The √3 is geometry, not a safety margin. Three-phase power or current, with apparent and reactive power alongside.

Written and maintained by Mohit PatelLast checked August 4, 2026How we build these

I want to find

Line-to-line voltage

Line current

Power factor

Real power

5.889 kW

6.928 kVA apparent · power factor 0.85

Real power5,889 W (5.889 kW)

Apparent power6,928.2 VA (6.928 kVA)

Reactive power3,649.7 VAR

Line current10 A

Line-to-line voltage400 V

Phase voltage (star)230.94 V

Power factor0.85

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

Where to go next

The Three-Phase Power question rarely arrives on its own. These are the ones that usually come with it:

Circuit Breaker Size Calculator — The breaker protects the wire, not the appliance.
Motor Amperage Calculator — Sized to the surge, not the running current.
Impedance Calculator — Magnitude and phase — they do not simply add.
Speed Distance Time Calculator — Any one of the three from the other two, in four units.

Sources

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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