Three-Phase Power: kW, kVA, and Why Power Factor Sits Between Them

Three-phase power confuses people for one simple reason: there are two kinds of "power" in the circuit, and the meter only shows you one of them at a time.

The two numbers

Apparent power (kVA) is what the conductors and transformers actually carry: voltage times current, with the √3 factor that three-phase geometry adds.

S (kVA) = √3 × V (line-to-line) × I ÷ 1000

Real power (kW) is the part that does work — turns motors, makes heat, lights lamps. The two are related by power factor:

P (kW) = S (kVA) × PF

The rest is reactive power (kvar), which sloshes back and forth magnetising motors and transformers. It does no work, but it still occupies conductor and transformer capacity — which is why utilities care about power factor and why a heavily loaded feeder can be carrying far more current than the kW alone would suggest.

A worked example

A 480 V three-phase feeder carries 100 A at a power factor of 0.85.

• Apparent power: √3 × 480 × 100 ÷ 1000 = 83.1 kVA
• Real power: 83.1 × 0.85 = 70.7 kW
• Reactive power: √(83.1² − 70.7²) = 43.7 kvar

Same feeder, same current — but only 70.7 kW of it is billable work. Improve the power factor to 0.95 and the same 70.7 kW needs only about 89 A instead of 100 A. That is the whole economic argument for power factor correction, in one line of arithmetic.

The mistakes to avoid

1. Dropping the √3. Single-phase habits understate three-phase apparent power by 73%.
2. Mixing line and phase voltage. The formula above uses line-to-line voltage; on a wye system the phase voltage is the line voltage divided by √3.
3. Treating kVA and kW as interchangeable on a nameplate. A transformer is rated in kVA because it does not know your power factor; a load is usually specified in kW because that is the work it does. The conversion between them is the power factor, every time.

Check your own numbers

If you want to run the same calculation with your own feeder values, the free Three-Phase Power Calculator from GridCircuits works kW, kVA, kvar, current and power factor in either direction, shows the formula it uses, and runs entirely in your browser — nothing is uploaded and there is no sign-up.

Before your next load study, pick one feeder and do this conversion by hand once. It takes two minutes, and after that the √3 will never surprise you again.