kVA to kW converter (and kW to kVA)
Converting kVA to kW multiplies apparent power by the power factor to give real power; kW to kVA divides by it. The two figures differ whenever a load draws reactive current, as motors, transformers and many electronic supplies do.
Convert kVA and kW
Updates as the values change. The page address keeps the values for sharing.
The distinction matters most when equipment is rated one way and loads are listed the other. Standby generators are commonly rated in kW at a stated power factor, transformers in kVA, and building loads in a mix of both; the converter also shows the reactive power in kVAR that makes up the difference.
Formulas
kVA to kW
The power factor is the fraction of apparent power that does work. At PF 1 kVA and kW are equal; at PF 0.8 a 100 kVA source delivers 80 kW.
kW to kVA
The supply needed for a given real load grows as the power factor falls: 80 kW at PF 0.8 needs 100 kVA, at PF 0.9 about 89 kVA.
Reactive power
The power triangle: kW and kVAR are the sides at a right angle and kVA the hypotenuse. Power-factor correction capacitors are sized in kVAR.
Voltage and phase do not enter these formulas; they apply equally to single-phase and three-phase systems. The same power factor must describe the whole load being converted.
Worked examples
A 100 kVA generator at the standard 0.8 power factor
Generator sets are commonly rated at PF 0.8, the basis on which their kVA and kW ratings are both stated.
kW = kVA × PFkW = 100 kVA × 0.8 = 80 kWkVAR = √(kVA² − kW²) = √(100² − 80²) = 60 kVAR
The generator delivers 80.0 kW of real power, with 60.0 kVAR of reactive power at full rated output.
45 kW of load at PF 0.9: how many kVA
The real-power total of a building's loads, with an overall power factor from metering.
kVA = kW ÷ PFkVA = 45 kW ÷ 0.9 = 50 kVAkVAR = √(kVA² − kW²) = √(50² − 45²) = 21.794 kVAR
The supply must provide 50.0 kVA.
A 500 kVA transformer serving a load at PF 0.85
A fully loaded transformer at the measured power factor of its load.
kW = kVA × PFkW = 500 kVA × 0.85 = 425 kWkVAR = √(kVA² − kW²) = √(500² − 425²) = 263.391 kVAR
It delivers 425.0 kW and 263.4 kVAR. Raising the power factor to 0.95 with capacitors would let the same transformer serve 475.0 kW.
Conversion tables
| kVA (kVA) | PF 0.70 (kW) | PF 0.80 (kW) | PF 0.85 (kW) | PF 0.90 (kW) | PF 0.95 (kW) | PF 1.00 (kW) |
|---|---|---|---|---|---|---|
| 5 | 3.50 | 4.00 | 4.25 | 4.50 | 4.75 | 5.00 |
| 10 | 7.00 | 8.00 | 8.50 | 9.00 | 9.50 | 10.00 |
| 15 | 10.50 | 12.00 | 12.75 | 13.50 | 14.25 | 15.00 |
| 20 | 14.00 | 16.00 | 17.00 | 18.00 | 19.00 | 20.00 |
| 25 | 17.50 | 20.00 | 21.25 | 22.50 | 23.75 | 25.00 |
| 30 | 21.00 | 24.00 | 25.50 | 27.00 | 28.50 | 30.00 |
| 45 | 31.50 | 36.00 | 38.25 | 40.50 | 42.75 | 45.00 |
| 50 | 35.00 | 40.00 | 42.50 | 45.00 | 47.50 | 50.00 |
| 75 | 52.50 | 60.00 | 63.75 | 67.50 | 71.25 | 75.00 |
| 100 | 70.00 | 80.00 | 85.00 | 90.00 | 95.00 | 100.00 |
| 150 | 105.00 | 120.00 | 127.50 | 135.00 | 142.50 | 150.00 |
| 200 | 140.00 | 160.00 | 170.00 | 180.00 | 190.00 | 200.00 |
| 250 | 175.00 | 200.00 | 212.50 | 225.00 | 237.50 | 250.00 |
| 500 | 350.00 | 400.00 | 425.00 | 450.00 | 475.00 | 500.00 |
| 750 | 525.00 | 600.00 | 637.50 | 675.00 | 712.50 | 750.00 |
| 1,000 | 700.00 | 800.00 | 850.00 | 900.00 | 950.00 | 1,000.00 |
| kW (kW) | PF 0.70 (kVA) | PF 0.80 (kVA) | PF 0.85 (kVA) | PF 0.90 (kVA) | PF 0.95 (kVA) | PF 1.00 (kVA) |
|---|---|---|---|---|---|---|
| 5 | 7.14 | 6.25 | 5.88 | 5.56 | 5.26 | 5.00 |
| 10 | 14.29 | 12.50 | 11.76 | 11.11 | 10.53 | 10.00 |
| 15 | 21.43 | 18.75 | 17.65 | 16.67 | 15.79 | 15.00 |
| 20 | 28.57 | 25.00 | 23.53 | 22.22 | 21.05 | 20.00 |
| 25 | 35.71 | 31.25 | 29.41 | 27.78 | 26.32 | 25.00 |
| 30 | 42.86 | 37.50 | 35.29 | 33.33 | 31.58 | 30.00 |
| 40 | 57.14 | 50.00 | 47.06 | 44.44 | 42.11 | 40.00 |
| 50 | 71.43 | 62.50 | 58.82 | 55.56 | 52.63 | 50.00 |
| 75 | 107.14 | 93.75 | 88.24 | 83.33 | 78.95 | 75.00 |
| 100 | 142.86 | 125.00 | 117.65 | 111.11 | 105.26 | 100.00 |
| 150 | 214.29 | 187.50 | 176.47 | 166.67 | 157.89 | 150.00 |
| 200 | 285.71 | 250.00 | 235.29 | 222.22 | 210.53 | 200.00 |
| 400 | 571.43 | 500.00 | 470.59 | 444.44 | 421.05 | 400.00 |
| 800 | 1,142.86 | 1,000.00 | 941.18 | 888.89 | 842.11 | 800.00 |
Both tables are generated by the engine. Voltage does not affect these conversions, so the tables have no voltage columns.
Common mistakes
Treating kVA and kW as interchangeable
They are equal only at power factor 1. Sizing a generator by matching its kVA rating to a load listed in kW leaves it short by the factor 1 ÷ PF.
Using a motor's full-load power factor at light load
An induction motor's power factor falls well below its nameplate value when it runs lightly loaded. A conversion based on full-load PF understates the kVA such a motor draws.
Applying one load's power factor to a whole building
The overall power factor of mixed loads is not the power factor of any one of them. For a building, it comes from metering or from adding the kW and kVAR of the loads separately.
Forgetting that the conductors carry kVA
Wiring and transformers are loaded by apparent power. A load of 80 kW at PF 0.8 loads them like 100 kVA, even though only 80 kW does useful work.
Frequently asked questions
How many kW is 100 kVA?
At power factor 0.8, 100 kVA is 80 kW; at 0.9 it is 90 kW; at 1 it is 100 kW.
Why are generators rated at 0.8 power factor?
Many loads, especially motors, draw reactive current. Rating at PF 0.8 means the generator's alternator can supply that reactive current at full kW output without overheating.
How is kW converted to kVA?
kVA = kW ÷ PF. For example, 40 kW at PF 0.8 is 50 kVA.
Can kW ever be larger than kVA?
No. Power factor cannot exceed 1, so real power is at most equal to apparent power. A calculation showing more kW than kVA has a unit or entry error.
Does voltage matter when converting kVA to kW?
No. Voltage cancels out of the conversion. It matters only when either figure is turned into current, which the kVA to amps and kW to amps converters do.