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Reactive Power (Power Triangle)

Q=S2−P2Q = \sqrt{S^{2} - P^{2}}
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Worked example: 10 kVA with 8 kW → 6 kvar. Press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.

Where Reactive Power (Power Triangle) fits

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See also

Power Factor from Real and Apparent Power: Both use apparent power and real power.Three-Phase Apparent Power: Both use apparent power.Transformer Full-Load Current: Both use apparent power.Transformer Percent-Impedance Voltage Drop: Both use apparent power.Transformer Efficiency from Core and Copper Losses: Both use apparent power.
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Reactive Power (Power Triangle) explained

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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)
In this toolkit

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.

Revised 16 October 2026
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formula.expert. (2026, October 16). Reactive Power (Power Triangle) Formula & Calculator. https://formula.expert/solvers/reactive-power-triangle

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