The Power Triangle

Real power P (kW) does the work; reactive power Q (kVAR) just sloshes back and forth magnetizing motors and transformers; apparent power S (kVA) is what the utility must actually supply. They form a right triangle, and the power factor is the cosine of its angle. Type into any box, or drag its slider — the rest solve themselves.

Power Quantities
kW
kVAR
kVA
cos θ
deg

Lagging = inductive (motors, transformers). Leading = capacitive.

System → Line Current
V
Power-Factor Correction
cos θ

Adds shunt capacitance to cancel reactive power and shrink the triangle.

Power Triangle
—
P — real Q — reactive S — apparent
Voltage, Current & Instantaneous Power
Voltage v(t) Current i(t) Power p = v·i Average = P
Readout

The Physics

When current lags or leads voltage by an angle θ, the instantaneous power v·i no longer stays positive. Split it and you get two parts: a steady flow that does work, and an oscillating part that averages to zero but still loads the wires.

S² = P² + Q²  ·  P = S·cos θ  ·  Q = S·sin θ  ·  pf = cos θ = P / S

Real power P (kW) is the average of v·i — the part converted to torque, heat, light. Reactive power Q (kVAR) is the amplitude of the part that flows out and back each cycle to build the magnetic and electric fields in motors, transformers, and cables. Apparent power S (kVA) is the vector sum — the volt-amps the source and conductors must carry regardless.

Power factor = P/S tells you how much of the delivered VA actually works. A 0.8 pf load draws 25% more current than a unit-pf load of the same kW — bigger conductors, more losses, and utility demand penalties.

⚡ Correction. A lagging (inductive) load's Q can be cancelled by a capacitor, which supplies leading kVAR locally. Pick a target pf and the panel sizes the capacitor: Qc = P·(tan θold − tan θnew). The triangle's vertical leg shrinks, S drops, and the line current — and your demand charge — fall with it.