Three Phase Power Calculator

For a balanced load, P = √3 × VL × IL × cos φ, where VL is the line-to-line voltage, IL the line current and cos φ the power factor. The apparent power is S = √3 × VL × IL and the reactive power Q = √3 × VL × IL × sin φ.

Not for the total power: the same line voltage and line current give the same kW whichever way the load is connected. What changes is each phase: in star each phase sees VL / √3 (230 V on a 400 V system) and carries the line current; in delta each phase sees the full line voltage and carries IL / √3.

That works only with the phase voltage and phase current: P = 3 × Vph × Iph × cos φ. Measured at the switchboard you usually have the line voltage and line current, and substituting Vph = VL / √3 turns the 3 into √3.

Calculate each phase on its own, P = Vph × I × cos φ with that phase's current and power factor, and add the three. The √3 formula with an average current is only an approximation when the currents differ.

At 400 V, 50 A per line is 34.6 kVA. At a power factor of 0.85 that is about 29.4 kW and 18.2 kVAr; for a resistive load it is the full 34.6 kW.

The angle φ between the voltage and the current, whose cosine is the power factor. A power factor of 0.85 is an angle of about 31.8°; a lagging (inductive) load has the current behind the voltage.