kVA to kW and kW to kVA
Convert apparent power (kVA) to active power (kW) and back: enter cos φ — for generators, transformers and UPS units.
Formulas
kW = kVA × cos φ; kVA = kW / cos φ.
Apparent power S (kVA) is what generators and transformers are rated in; active power P (kW) is what the consumer pays for. Reactive power Q = √(S²−P²) (kVAr) causes losses.
Typical cos φ values
| Equipment | cos φ |
|---|---|
| Heaters, incandescent lamps | 1.0 |
| Fluorescent lamps | 0.5–0.9 |
| Induction motors | 0.7–0.9 |
| Welding machines | 0.5–0.8 |
| Computers, UPS | 0.6–0.9 |
Example
A 10 kVA generator at cos φ = 0.8 delivers 8 kW. Connecting a 9 kW load overloads it by current even at cos φ = 1 — size by kVA.
Related calculators
- Generator sizing — generator
- UPS sizing — ups
- Power factor correction — power-factor
FAQ
What is the difference between kW and kVA?
kVA is apparent power (S), kW is active power (P). P = S×cosφ. The difference is reactive power, which does no useful work.
How many kW in 10 kVA?
At cos φ = 0.8: 10×0.8 = 8 kW. At cos φ = 1: 10 kW.
Why are generators rated in kVA?
Because generator current depends on apparent power: I = S/(√3·U). The active output depends on the consumer's cos φ.