kVA / kW / PF Calculator

The distinction between apparent power (kVA) and real power (kW) matters because AC generators, transformers, and conductors are limited by current — and current carries both useful power and the reactive "sloshing" that never does work. Oliver Heaviside's 1880s reformulation of Maxwell's equations using vector notation gave engineers the mathematical tools to describe this cleanly: impedance as a complex quantity, and power as the real part of V·I* (the complex conjugate product).

Nameplate ratings on utility equipment have been in kVA (not kW) since the early 20th century for exactly this reason. A 500 kVA transformer can supply 500 kW only to a unity-PF load; at PF = 0.8, the real power maxes out at 400 kW while the transformer is already thermally loaded. Generator sets are sized the same way — a 100 kW genset delivers only 80 kW at 0.8 PF without exceeding its alternator current rating.

Modern data centers and UPS systems encountered this trade-off in reverse in the 2000s: early three-phase UPS systems rated in kVA at 0.8 leading PF didn't match the unity-PF loads of modern server PSUs with active PFC, leaving stranded kVA capacity. The 2010s saw UPS manufacturers re-rate products in both kVA and kW at PF = 1.0 to match the real load, ending years of oversized UPS purchases.

Enter any two of apparent power (S in kVA), power factor, or real power (P in kW); the tool derives the third and computes reactive power Q = √(S² − P²) and phase angle φ = arccos(PF). The power triangle visualization shows S as the hypotenuse, P horizontal, Q vertical.

Use this for generator/UPS/transformer sizing: the equipment's thermal limit is the kVA rating, and the usable kW depends on your load's PF. For three-phase loads, line quantities give S = √3 · V_LL · I_L. Everything runs client-side; no values leave your browser.