Three-phase power and power factor
power trianglekW kVA kVARpower factor correction1.732 formulaapparent power
Real, reactive and apparent power, power factor, phase angle and correction kvar — the power triangle as an electrician uses it.
Three-Phase Real Power
Real power drawn by a balanced three-phase load from its line-to-line voltage, line current, and power factor.
Single-Phase Real Power with Power Factor
True power of a single-phase AC load: volts times amps times power factor, the fraction of the current doing real work.
Three-Phase Apparent Power
Apparent power in volt-amperes for a balanced three-phase load — the quantity that sizes transformers, cables and breakers.
Power Factor from Real and Apparent Power
Power factor as the ratio of real power in watts to apparent power in volt-amperes, the share of supplied capacity doing work.
Reactive Power (Power Triangle)
Reactive power in vars from the power triangle, where apparent power is the hypotenuse over real and reactive legs.
Phase Angle from Power Factor
The angle by which current lags or leads voltage, found from the power factor — the link between the ratio and the triangle.
Power-Factor Correction kvar
Size of the capacitor bank in vars needed to lift a load from its existing power factor up to a chosen target power factor.
Power-Factor Correction Capacitance
Capacitance needed across a single-phase load to supply a given number of vars at the supply voltage and frequency.
How they fit together
Volts times amps gives apparent power, kVA — what the conductors, transformer and utility have to carry. Real power, kW, is what does work, and the ratio between them is the power factor, the cosine of the angle between voltage and current. The leftover leg of the triangle is reactive power, kvar, which sloshes back and forth building magnetic fields in motors and transformers and does no useful work at all. The √3 in the three-phase forms is not a fudge: it is the geometry of three voltages 120° apart, and it appears because line voltage is √3 times phase voltage in a wye.
Meter kW when you want energy, kVA when you want to know whether the feeder or transformer is full, and kvar when you are deciding what size capacitor bank to buy. The correction calculation is simply the difference between the reactive power you have and the reactive power you want at the target power factor. Two mistakes. Correcting to unity sounds ideal and is usually wrong — target 0.95, because a bank sized for 1.0 goes capacitive at light load, which raises voltage and can excite resonance with harmonics on the system. And the whole triangle assumes sinusoidal current: with VFDs, LED drivers and switch-mode loads the current is distorted, so the true power factor is displacement power factor times a distortion factor, and adding capacitors to a distorted system corrects nothing while offering harmonics a resonant path.