Power Factor Calculator — AC Power Triangle (P, Q, S, cos φ)

Formula

How this is calculated

In an AC circuit, the load impedance can be partly reactive (inductive motors, capacitors, transformers). Reactive components store and return energy every cycle rather than consuming it, creating a phase difference φ between the voltage and current waveforms. This gives rise to three distinct power quantities.

True (active) power P [kW] is the power actually converted to work or heat — the rate at which the load consumes energy. Reactive power Q [kVAR] is the power exchanged back and forth with reactive elements each cycle; it does no net useful work but must flow through the wiring and supply. Apparent power S [kVA] = V_rms × I_rms is the total burden on the supply — what the generator and cables must handle. These three form the power triangle: S² = P² + Q². The power factor PF = cos(φ) = P / S is a dimensionless ratio from 0 to 1 showing what fraction of apparent power is actually doing useful work. A PF of 1.0 means a purely resistive load; a PF of 0.8 means 80% of the VA drawn is being used productively.

Low power factor (below ~0.85) is penalised by electricity utilities because it increases line currents and equipment ratings without delivering additional real power. Power factor correction — typically adding shunt capacitor banks to counteract inductive motor loads — raises PF toward 1. The vector diagram shows P along the real (horizontal) axis, Q along the reactive (vertical) axis, and S as their vector sum — identical to the phasor representation of the power triangle.