kW, kVAR, kVA: The Power Triangle

9 min · difficulty 4/10

You have to pick a transformer for a motor load. The motor draws 80 kW of real power and 60 kVAR of reactive power. A 80 kVA transformer is sitting on the shelf. Is it big enough? It is tempting to say yes, the load is 80 kW and the transformer is 80 kVA, done. Hold that thought before you order it.

The catch is that an AC load does not pull just one kind of power. Real power (kW) does the useful work: heat, torque, light. Reactive power (kVAR) does no net work, but it is what magnetizes the field inside motors and transformers so they can run. Both flow through the same wires, and the wire feels the combination, not just the part that does work.

Add them and you do not get 140. They sit at a right angle to each other, so you combine them like the legs of a right triangle. The apparent power (kVA) is the hypotenuse, and it is the total the conductor and transformer actually carry.

The power triangle: real, reactive, and apparent power A right triangle drawn to scale. The horizontal leg is real power 80 kW. The vertical leg is reactive power 60 kVAR. The hypotenuse is apparent power 100 kVA. A right-angle marker sits between the real and reactive legs, and the angle theta sits at the origin between the real leg and the hypotenuse. The relationship kVA squared equals kW squared plus kVAR squared holds: 100 squared equals 80 squared plus 60 squared. A transformer is rated in kVA, the hypotenuse, because it carries the total current. The power triangle why a transformer is rated in kVA, not kW θ Real power 80 kW Reactive 60 kVAR Apparent power 100 kVA The relationship kVA² = kW² + kVAR² 100² = 80² + 60² cos θ = kW ÷ kVA The transformer carries the total current, set by the apparent power (kVA).
Real, reactive, and apparent power form a right triangle: 80 kW and 60 kVAR give 100 kVA. A transformer is rated in kVA, the hypotenuse, because it carries the total current the load draws.

Run the numbers for our motor: square root of (80 squared plus 60 squared) is square root of 10,000, which is 100 kVA. That 80-60-100 is the old 3-4-5 right triangle. So the 80 kVA unit is too small. You need 100 kVA, because the transformer has to carry the apparent power, not the real power.

That is the whole reason a nameplate says kVA and not kW. The hardware is sized by the total current it carries, and that current is set by apparent power, kVAR included. The kW tells you what work gets done; the kVA tells you what the iron and copper have to survive.

Power factor penalties, reactive charges, and %Z mismatches show up as real line items on a utility bill or a bid rejection. DistroForge Insider applies these fundamentals to pricing and equipment-selection intelligence.

Question 1 of 4

A motor load draws 80 kW of real power and 60 kVAR of reactive power. What is the apparent power the transformer must carry? (apparent = square root of kW squared plus kVAR squared)

Educational material only. This is not engineering, safety, or procurement advice. Confirm any value against manufacturer documentation and a licensed professional before specifying equipment.