🔺 Real, Reactive and Apparent Power

Written and maintained by the PhDino author · Last reviewed 21 September 2026 · Checked against 2 independent reference calculations · how PhDino checks its numbers

Real, reactive, and apparent power in a single-phase or balanced three-phase system, and how power factor relates them.

In an AC circuit with any inductive or capacitive load, not all the power the source delivers does useful work. Real power (kW) is what actually does work (heat, mechanical output, light); reactive power (kVAR) sloshes back and forth into magnetic or electric fields without net work; apparent power (kVA) is the vector combination of both, and it's what the source and wiring actually have to be sized for.

Power factor is the ratio of real to apparent power — a power factor of 1.0 means all the delivered power is doing work; anything less means the system is carrying current that isn't contributing useful output, which utilities often penalize with a power-factor charge.

Key formula

S = √3 × V × I  (apparent power, balanced three-phase, line values)
S = V × I  (apparent power, single-phase)
P = S × PF  (real power)
Q = S × √(1 − PF²)  (reactive power)

Variables

V, I

line voltage and line current (for a split-phase 120/240 V home, use 240 V and the current in each of the two hot legs)

PF

power factor (cosine of the angle between voltage and current)

Notes & limitations

• The three quantities P, Q, and S form a right triangle (the "power triangle") — that's the geometric reason Q = S√(1−PF²) works, since PF = P/S = cos(θ).
• Improving power factor (e.g. adding capacitor banks to offset inductive loads like motors) reduces the current the system needs to carry for the same real power delivered — smaller wire, less loss, lower utility penalty.