Three-Phase Power and Power Factor Calculator

Line current, kW, kVA and kvar of a balanced three-phase load from power, voltage and power factor, with the capacitor needed to correct the power factor.

How it works

In a balanced three-phase circuit the active power (the useful power that does work) is P = √3 × VLL × IL × PF. The apparent power S = √3 V I is what the supply and the cables must carry, and the power factor PF = P ÷ S = cos φ says how much of it does work. The rest is reactive power Q = √(S² − P²), which swings back and forth between the load and the supply (it is needed by motors and transformers to make magnetic fields).

P = √3 V I cos φ, S = √3 V I, Q = √3 V I sin φ, Qc = P (tan φ₁ − tan φ₂)

A low power factor means a larger current for the same power: more cable, larger transformers and more losses (I²R), and utilities may charge for the reactive power. Motor sizes and drives are in Motion Control and Actuators, and wire sizes in the Wire Ampacity and Voltage Drop Calculator.

Worked example

A 22 kW induction motor (shaft power) with an efficiency of 90 % and a power factor of 0.82 runs from a 400 V, 50 Hz supply. Correct the power factor to 0.95.

  • Input power P = 22 000 ÷ 0.90 = 24.44 kW. Apparent power S = 24 444 ÷ 0.82 = 29.81 kVA.
  • Line current I = 29 810 ÷ (√3 × 400) = 43.03 A. Reactive power Q = √(29.81² − 24.44²) = 17.06 kvar; φ = 34.9°.
  • To correct to 0.95: Qc = 24.44 × (tan 34.9° − tan 18.2°) = 24.44 × (0.6980 − 0.3287) = 9.03 kvar (use a 10 kvar standard bank).
  • In delta, C = 9 028 ÷ (3 × 400² × 2π × 50) = 60 µF per phase.
  • The line current falls to 24 444 ÷ (√3 × 400 × 0.95) = 37.1 A, a reduction of 14 %.

Things to know

This is for balanced, sinusoidal loads. Unbalanced loads and non-sinusoidal (harmonic-rich) currents from drives and rectifiers need an analysis of each phase and of the total harmonic distortion.

Fixed capacitors correct a constant load; for a varying load use an automatic bank with steps, and avoid over-correction (a leading power factor), which can cause overvoltage and resonance with the supply inductance.

With variable-speed drives and electronic loads the displacement power factor (cos φ) may differ from the true power factor, which includes distortion: correct the cause (filters, active front ends) and not just add capacitors.

Capacitor banks on a network with harmonics need detuning reactors: a plain capacitor can resonate with the supply and fail.

Utility tariffs often define the power factor limit (commonly 0.9 or 0.95): check the penalty rules before sizing the correction.

Common questions

What is power factor?

The ratio of active power to apparent power (cos φ for sinusoidal currents). A power factor of 1 means all the current does useful work; below 1 some of it only magnetizes the load.

Why is there a √3 in three-phase formulas?

Because the line-to-line voltage of a balanced three-phase system is √3 times the voltage of each phase to neutral, so the total power of the three phases is 3 Vph I cos φ = √3 VLL I cos φ.

How do I find the current of a 3-phase motor?

I = P ÷ (√3 × V × PF × η), with P the shaft power. For a 22 kW motor at 400 V, PF 0.82 and η 0.9 this is about 43 A. Use the nameplate current for real design.

Sources

  • IEC 60038 (standard voltages); IEC 60831 and IEC 60871 (capacitors for power factor correction); IEEE Std 1459 (definitions of power).
  • Wildi, T., Electrical Machines, Drives and Power Systems, Pearson; Chapman, S. J., Electric Machinery Fundamentals, McGraw-Hill.

Last reviewed: November 2, 2026