TAHA Engineering Toolsby TAHA Knowledge Lab

Electrical Engineering

Single & Three-Phase AC Power Calculator

kW, kVA, kVAR and current for single-phase and three-phase loads.

Inputs

Calculate from
Right-angled power triangle: real power P horizontal, reactive power Q vertical, apparent power S as the hypotenuse, angle phi between P and S.φP — real power (kW)Q — reactive(kVAR)S — apparent (kVA)cos φ = P ÷ S
Power triangle (drawn for power factor 0.8). Real power P does useful work; reactive power Q builds magnetic fields in motors; the supply must carry the apparent power S. Power factor cos φ = P ÷ S. Diagram not to scale.

Three-phase: line-to-line voltage (e.g. 400 V). Single-phase: supply voltage (e.g. 230 V).

Between 0 and 1. Resistive heaters ≈ 1. For motors, use the nameplate value.

Result

Real power
5.54256
Apparent power
6.9282kVA
Reactive power
4.15692kVAR

This load uses 5.54256 kW of real power. The supply must carry 6.9282 kVA of apparent power; the difference is reactive power (4.15692 kVAR).

Educational estimate — check the assumptions below.

About this calculator

In AC circuits, the power that does useful work (kW) is less than voltage × current (kVA) when the power factor is below 1, as it is for motors and other inductive loads. This calculator gives real, apparent and reactive power, or the current a load will draw — for both single-phase and balanced three-phase supplies.

Formula

Three-phase: P = √3 × VL × I × cos φ    S = √3 × VL × I

Single-phase: P = V × I × cos φ    S = V × I

Q = √(S² − P²)

P = real power (W), S = apparent power (VA), Q = reactive power (VAR), VL = line-to-line voltage, cos φ = power factor.

Worked example

  • Three-phase, 400 V, 10 A, PF 0.8: P = 1.732 × 400 × 10 × 0.8 = 5.54 kW; S = 6.93 kVA; Q = 4.16 kVAR.
  • Current for a 15 kW three-phase load at 400 V, PF 0.85: I = 15 000 ÷ (1.732 × 400 × 0.85) = 25.5 A.
  • Single-phase 230 V, 10 A, PF 1: 2.3 kW.

Assumptions and limitations

  • Three-phase results assume a balanced load (equal current in each line) and sinusoidal voltage and current.
  • For a motor, the kW entered or calculated is electrical input power. Motor nameplate kW is output power — divide by the motor efficiency to get input power.
  • Harmonics from drives and electronic loads are not included.

Safety note

This calculator does not size cables, breakers or protection. Electrical installations must be designed and installed by qualified persons according to your local wiring regulations.

References

  • Standard AC power relations for single-phase and balanced three-phase systems (IEC 60050 definitions of active, reactive and apparent power).