The kVA to kW calculator converts apparent power to real (active) power — and back — using the power factor relationship that lies at the heart of all AC electrical systems. It handles single-phase and three-phase circuits, computes reactive power (kVAR), and lets you derive kVA directly from a voltage and current measurement when you have a clamp meter to hand. A built-in quick-reference table lists common kVA ratings against six typical power factors so you can cross-check transformer, generator, and UPS sizing at a glance.
How it works
Every AC power circuit has three power quantities that form a right-triangle relationship known as the power triangle:
- Real power P (kW) — the portion converted to useful work (heat, light, torque).
- Apparent power S (kVA) — the total power the supply must deliver, combining real and reactive components.
- Reactive power Q (kVAR) — the portion that oscillates between source and inductive / capacitive loads without doing work.
The three are related by: S² = P² + Q², and the power factor is simply PF = P / S.
Single-phase conversion
kW = kVA x PF (to convert apparent to real)
kVA = kW / PF (to convert real to apparent)
If you are measuring directly: S = V x I / 1000 (kVA), then P = S x PF (kW).
Three-phase conversion
For a balanced three-phase system the formula gains the √3 factor:
S = sqrt(3) x V_L x I_L / 1000 kVA
where V_L is the line-to-line voltage and I_L is the line current. Real power then follows: P = S x PF kW. The √3 factor ≈ 1.7321 arises from the 120° phase displacement between the three sinusoidal voltages.
Reactive power
Once you know S (kVA) and P (kW), reactive power is:
Q = sqrt(S² − P²) kVAR
The calculator shows Q in the result cards so you can size power-factor-correction capacitor banks to cancel unwanted reactive current.
Worked example
A three-phase induction motor draws 14.43 A at 400 V (line-to-line) and has a nameplate power factor of 0.85.
- Apparent power: sqrt(3) x 400 x 14.43 / 1000 ≈ 10.0 kVA
- Real power: 10.0 x 0.85 = 8.5 kW
- Reactive power: sqrt(10.0² − 8.5²) ≈ 5.27 kVAR
The motor draws 10 kVA of capacity from the transformer even though it delivers only 8.5 kW of shaft power — the 5.27 kVAR must still flow through cables and switchgear, sizing them for the full apparent-power demand.
| Load | kVA | PF | kW |
|---|---|---|---|
| Small UPS | 1 kVA | 0.9 | 0.90 kW |
| Office server rack | 5 kVA | 0.95 | 4.75 kW |
| Induction motor | 10 kVA | 0.80 | 8.00 kW |
| Generator set | 100 kVA | 0.80 | 80.00 kW |
| Distribution transformer | 500 kVA | 0.90 | 450.00 kW |
All figures are calculated instantly in your browser — no data is uploaded or stored.