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Reactive Power (Power Triangle)

Q=S2−P2Q = \sqrt{S^{2} - P^{2}}

Worked example: 10 kVA with 8 kW → 6 kvar — press Try an example to run it live, then adjust anything.

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Reactive Power (Power Triangle) explained

QPS

Real power P and reactive power Q are 90° apart, so they add like the legs of a right triangle with apparent power S as the hypotenuse: S² = P² + Q². A load pulling 10 kVA while doing 8 kW of work is carrying 102−82=6\sqrt{10^2 - 8^2} = 6 kvar of reactive burden — the classic 3-4-5 triangle in electrical dress. Vars are watts dimensionally, so enter kvar and kVA in the kW fields here.

Reactive power does no net work over a cycle; it is energy borrowed to build a magnetic field and returned half a cycle later. The borrowing is not free — the round trip flows as real current through your conductors and the utility's transformers. That is why the fix is local: put capacitors near the motor and the vars shuttle between motor and capacitor instead of travelling back to the substation.

Reactive Power (Power Triangle) formula

Q=S2−P2Q = \sqrt{S^{2} - P^{2}}
Where
  • QQ= Reactive power (var) (W)
  • SS= Apparent power (VA) (W)
  • PP= Real power (W)

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Part of this formula set

Three-phase power and power factor

8 formulasReal, reactive and apparent power, power factor, phase angle and correction kvar — the power triangle as an electrician uses it.