For a balanced three-phase load, apparent power is S = √3 × VLL × I, real power is P = S × power factor, and reactive power is Q = S × sin(arccos pf). This calculator returns all three from the line-to-line voltage, line current and power factor.
Reviewed: June 20, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: balanced three-phase power relations, recomputed in code.
The power triangle
Apparent power (kVA) is the total the supply must carry; real power (kW) does useful work; reactive power (kVAR) sloshes back and forth with the magnetic fields of motors and transformers. They form a right triangle, with the power factor equal to cosφ = P/S. The √3 (≈ 1.732) appears because, in a balanced system, line-to-line voltage is √3 times the phase voltage.
Worked examples
400 V, 10 A, pf 0.8:
480 V, 100 A, pf 0.9:
230 V, 5 A, unity pf:
At unity power factor, real power equals apparent power and reactive power is zero. As the power factor drops, kVAR grows, so the supply carries more kVA for the same useful kW — which is why power-factor correction saves capacity.
Frequently Asked Questions
S = √3·V_LL·I; P = S·pf; Q = S·sin(arccos pf).
kW = √3·V·I·pf ÷ 1000. 400 V, 10 A, 0.8 ≈ 5.54 kW.
kVA total, kW real (does work), kVAR reactive. kVA² = kW² + kVAR².
Line-to-line voltage is √3 × phase voltage in a balanced system.
cosφ between V and I, 0–1. Unity = all real power, no reactive.