Skip to main content
Mathovia

Electrical / Power & Wattage

Kilowatts (kW) to Kilovolt-Amps (kVA) Conversion Calculator

Calculate apparent power from real power and power factor.

Apparent Power
5.000 kVA
001.251.562.53.133.754.6956.25kWkVA4 kW5 kVA
1 kW = 1.25 kVA

Use the stated electrical relationship and enter values in the displayed units.

Source: Formula conventions follow standard electrical engineering relationships. Verify equipment ratings and local code requirements before installation.
Written by
MPhil in Mathematics, Founder of Mathovia
Updated

Mathematics verification: Mathematical formulas, calculations, worked examples and solutions are reviewed for accuracy before publication. How we check our work

Kilowatts (kW) to Kilovolt-Amps (kVA) Conversion Calculator formula
The Kilowatts (kW) to Kilovolt-Amps (kVA) Conversion formula

Why real power isn’t enough

You know a load needs 4 kW. You go to buy a generator or spec a transformer and find them rated in kVA. The two aren’t interchangeable: a 4 kW generator and a 4 kVA generator are different machines. Apparent power in kVA is what the source’s windings and conductors actually have to carry, and for any load with motors, transformers, or electronic supplies, that’s more than the real power it consumes.

The gap is the power factor. A load at 0.8 power factor pulls 25% more current than its wattage alone would suggest, and that current — not the wattage — is what heats a transformer or loads an alternator. So sizing a source means converting the load’s kW into kVA first.

The kW to kVA formula

is apparent power in kVA, is real power in kW, and is the power factor from 0 to 1. Because , the result is always equal to or greater than the kW you started with. The three quantities form the power triangle, with as the hypotenuse: , where is the reactive power in kVAR.

Worked example

The calculator’s defaults are 4 kW at a power factor of 0.8.

The load does 4 kW of work but demands 5 kVA from the source. The reactive component is kVAR. A generator for this load has to be rated at least 5 kVA, even though a wattmeter on the load would only ever read 4 kW.

Kilowatts (kW) to Kilovolt-Amps (kVA) Conversion Calculator worked example diagram
A visual read of the worked example above — the same numbers the calculator returns for its default inputs.

kW to kVA by power factor

Real powerPF 1.0PF 0.9PF 0.8PF 0.7
2 kW2.0 kVA2.22 kVA2.50 kVA2.86 kVA
4 kW4.0 kVA4.44 kVA5.00 kVA5.71 kVA
10 kW10.0 kVA11.1 kVA12.5 kVA14.3 kVA
25 kW25.0 kVA27.8 kVA31.3 kVA35.7 kVA

At a power factor of 0.7, a source has to be more than 40% larger in kVA than the load’s kW — the reason power factor correction is worth money on a large installation.

Sizing from the result

The kVA figure is the steady-state minimum. Real sizing adds margin:

  • Motor starting can demand three to six times the running kVA for a second or two; a generator has to hold voltage through it.
  • Non-linear loads (drives, LED drivers, IT gear) inject harmonics that raise the effective kVA a generator sees.
  • Growth — leaving 20–25% spare is normal practice.

Common mistakes

  • Using unity power factor for a motor load, which understates the kVA and can overload the source.
  • Sizing a generator to the load’s kW rating while ignoring that its own rating is in kVA.
  • Guessing the power factor when the motor nameplate prints it.

For the reverse, use the kVA to kW calculator. For the volt-amp version, see kW to VA, and for line current, kW to amps.

From kVA to current

Once you have kVA, the current follows from the supply voltage. For a three-phase supply:

A 50 kVA load on a 400 V three-phase supply draws about A per line. That’s the figure cable and breaker sizes are based on.

Correcting the power factor

Capacitors can raise a low power factor, which lowers the kVA needed for the same kW. The reactive power to add is:

where and are the angles whose cosines are the old and new power factors. Raising a 100 kW load from 0.80 to 0.95 needs about kVAR of capacitors. The load’s apparent power falls from 125 kVA to about 105 kVA, freeing 20 kVA of supply capacity.

About the formula: Use the stated electrical relationship and enter values in the displayed units.

Frequently Asked Questions

How do I convert kW to kVA?+

Divide the real power by the power factor: kVA = kW ÷ PF. Since power factor is 1 or less, the kVA figure is always the same size or larger than the kW figure.

What is 4 kW in kVA?+

At a power factor of 0.8, 4 kW ÷ 0.8 = 5 kVA. At unity power factor it would stay 4 kVA; at 0.6 it climbs to 6.67 kVA. The worse the power factor, the more apparent power a source must supply for the same 4 kW of work.

Where do I find my load's real power factor instead of assuming 0.8?+

Motor and HVAC nameplates often print it. A clamp meter that reads true power factor, or a utility bill with power-factor metering, gives a measured value. The 0.8 default stands in for a typical mixed inductive load.

Can I size a generator or UPS from this kVA number?+

It's the right starting quantity, since generators and UPS units are rated in kVA. Then add headroom for motor starting surge, for harmonic loads, and for future growth rather than matching the source exactly to the calculated figure.

Why do transformers and generators get rated in kVA instead of kW?+

Because their limits are heating in the windings and conductors, which is driven by current — and current tracks apparent power, not real power. A kVA rating holds true regardless of the power factor of whatever gets connected.

Does a better power factor let a generator deliver more kW?+

Up to its own kW limit, yes. A 5 kVA generator rated 4 kW at 0.8 can deliver close to 5 kW into a unity-power-factor load, but not beyond its prime-mover kW rating.