ElectroHub

kVA to kW Calculator & Conversion Formula

kW = kVA × power factor, and that is the whole of it. Horsepower is where the conversion goes wrong: hp is shaft output, so the electrical kW has to be multiplied by the motor's efficiency on the way out, not merely divided by 0.7355. Generators, UPS units and transformers are rated in kVA precisely because the maker cannot know the power factor of whatever gets plugged in.

kVA ↔ kW ↔ horsepower

kW = kVA × power factor — that conversion needs nothing else. Going on to horsepower needs the efficiency too, because horsepower is shaft output while kW at the terminals is electrical input, and the motor keeps the difference.

Apparent
Real
Reactive
Shaft
  • The 6.00 kVAr is the part of the supply's capacity doing no work. Correcting the power factor to unity would free that capacity without changing the 8.00 kW being consumed.
kVAkW at 0.8 pfkW at 0.9 pfkW at unity
544.55
108910
151213.515
252022.525
50404550
1008090100
250200225250
500400450500
Common trap: A generator or UPS is rated in kVA because what limits it is current, and current does not care about power factor. Sizing a 10 kW load onto a 10 kVA set works only at unity power factor — at 0.8 the set delivers 8 kW and trips on the ninth.

The formula

kW = kVA × pf ; kVAr = √(kVA² − kW²) ; hp = kW × η / 0.7355

kVA
apparent power — what the supply has to carry
kW
real power — what does work and what the meter bills
kVAr
reactive power — carried but never consumed
pf
power factor, cos φ, between 0 and 1
η
motor efficiency as a fraction — needed only for horsepower

Worked example

A 10 kVA supply at 0.8 power factor, feeding a motor of 88 % efficiency.

  1. kW = 10 × 0.8 = 8.0 kW
  2. kVAr = √(10² − 8²) = √36 = 6.0 kVAr
  3. Shaft power = 8.0 × 0.88 = 7.04 kW
  4. hp = 7.04 / 0.7355

8 kW real, 6 kVAr reactive, and 9.57 metric horsepower at the shaft.

Where you'll use it

Sizing a DG set or UPS against a load stated in kW, reading a transformer nameplate, and the standard exam question on the power triangle. The 2 kVA of headroom that disappears between a 10 kVA set and an 8 kW load is not a rounding error — it is the reactive power the set still has to carry.

The laws behind it

Parts this applies to

Resistor (fixed)Capacitor (aluminium electrolytic)Capacitor (tantalum)LED (light-emitting diode)MOSFETRectifier DiodeSchottky DiodeZener Diode

Related calculators

kVA to Amps Calculator & FormulaI = kVA × 1000 / (√3 × V) [three phase]HP to kW Converter & FormulakW = hp × 0.7355 (metric)Power Triangle CalculatorS² = P² + Q²Power Factor Correction CalculatorQ_c = P × (tan φ₁ − tan φ₂), where φ = arccos(pf)Motor Full Load Current CalculatorI = kW × 1000 / (√3 × V × η × cos φ) [three phase]