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Converters & physics calculator

kVA to kW calculator with power factor, kVAr and current

Convert between apparent power (kVA), real power (kW), reactive power (kVAr) and current for single- and three-phase systems. You also get the power triangle and the capacitor bank needed to correct the power factor.

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Results

100 kVA at power factor 0.8 = 80 kW. A 33.7 kVAr capacitor bank would lift the power factor to 0.95, cutting current from 144 A to 122 A (−29% cable losses) and freeing 15.8 kVA of capacity.
Real power
80kW
power factor 0.8
Apparent power
100kVA
Reactive power
60kVAr
Line current (per phase)
144.3A
I = S ÷ (√3 × 400 V)
Phase angle φ
36.9°
Power in horsepower
107.3hp
Capacitor bank for PF 0.95
33.7kVAr
Current after correction
121.5A
−16% current
kVA after correction
84.21kVA
Power triangle (before → after correction)
Current vs power factor (same kW)

Same apparent power at other power factors

Power factorkWkVArCurrent (A)
11000144.3
0.959531.22144.3
0.99043.59144.3
0.858552.68144.3
0.88060144.3
0.757566.14144.3
0.77071.41144.3

Standard generator / transformer sizes at PF 0.8

kVAkWAmps @ 400 V 3-ph
10814
201629
302443
504072
635091
10080144
160128231
250200361
400320577
630504909
1,0008001,443
1,6001,2802,309
2,5002,0003,608
  • kVA is what cables, transformers and generators must carry; kW is the power that does useful work. The ratio is the power factor.
  • Generators are usually rated in kVA at 0.8 PF, so a 100 kVA genset delivers at most 80 kW of real power.
  • Capacitor sizing assumes a sinusoidal supply. With many drives or inverters (harmonics), use detuned capacitor banks or active filters and have an engineer check for resonance.

How this kVA to kW calculator works

Alternating-current circuits carry two kinds of power. Real (active) power, in kW, does useful work: heat, light, motion. Reactive power, in kVAr, sloshes back and forth to build the magnetic fields of motors and transformers and does no net work. Their vector sum is the apparent power, in kVA, which determines the current that cables, switchgear, transformers and generators must carry. The ratio kW ÷ kVA is the power factor (cos φ).

Enter whichever quantity you know (kVA, kW or current) with the power factor, system type (single-phase, three-phase or DC) and voltage. The calculator returns all the others, draws the power triangle, shows how current rises as power factor falls and sizes the capacitor bank needed to correct the power factor to a target value.

The formulas

kW = kVA × PF kVA = kW ÷ PF kVAr = kVA × sin φ = √(kVA² − kW²) Three-phase: I = kVA × 1,000 ÷ (√3 × V_LL) Single-phase: I = kVA × 1,000 ÷ V Correction: Qc = kW × (tan φ₁ − tan φ₂), φ = arccos(PF)

Worked example: a 100 kVA generator

The default is a 100 kVA three-phase generator at 400 V with the industry-standard rating power factor of 0.8:

  • Real power: 100 × 0.8 = 80 kW
  • Reactive power: 100 × sin(36.9°) = 60 kVAr
  • Current: 100,000 ÷ (1.732 × 400) = 144 A per phase

If the site’s load really ran at PF 0.8, a 33.7 kVAr capacitor bank would lift it to 0.95. The same 80 kW would then need only 84.2 kVA and 122 A. That is 16% less current and about 29% lower cable losses (losses scale with current squared), freeing 16 kVA of generator or transformer capacity.

How to read the results

  • The power triangle: the horizontal leg is kW, the vertical leg kVAr, the hypotenuse kVA. The dashed line shows the kVA after correction: same kW, shorter hypotenuse.
  • Current vs power factor: for the same useful power, current rises steeply below PF 0.8; this is what utilities penalise.
  • Standard sizes table: kW and amps for common generator and transformer ratings at PF 0.8 and your voltage.

Typical power factors

Load Power factor
Resistive heaters, kettles, incandescent lamps 1.00
EV chargers, modern PSUs with PFC, PV inverters 0.95–1.00
LED lighting (quality drivers) 0.90–0.98
Induction motor, full load 0.80–0.90
Induction motor, half load 0.65–0.80
Induction motor, no load 0.20–0.40
Welding transformers, arc furnaces 0.50–0.70
Typical industrial site, uncorrected 0.70–0.85

Amps for common kVA ratings (three-phase)

kVA kW at PF 0.8 Amps at 400 V Amps at 480 V Amps at 208 V
20 16 29 24 56
50 40 72 60 139
100 80 144 120 278
250 200 361 301 694
500 400 722 601 1,388
1,000 800 1,443 1,203 2,776

Tips

  1. Size generators on kVA and starting current. Motor starting can demand 3–7 times running current; soft starters and VFDs reduce it.
  2. Correct power factor at the source. Individual capacitors on large motors reduce current in the whole distribution system, not just at the main board.
  3. Don’t over-correct. A leading power factor at light load can cause over-voltage; automatic stepped banks avoid it.
  4. Check harmonics. Variable-speed drives distort current; plain capacitors can resonate with the network, so use detuned reactors.
  5. For balanced three-phase loads with star/delta details, use the three-phase power calculator.

Limitations

The calculations assume sinusoidal voltage and current and a balanced three-phase load. With non-linear loads the “true power factor” also includes harmonic distortion, which capacitors do not fix. Breaker, cable and capacitor sizing must follow local wiring regulations and manufacturer data.

Method & assumptions

Power triangle: S² = P² + Q², P = S · cos φ, Q = S · sin φ. Current: single-phase I = S ÷ V; three-phase I = S ÷ (√3 · VLL). Correction capacitor: Qc = P · (tan φ1 − tan φ2). Cable losses scale with I², so raising power factor from 0.8 to 0.95 cuts them by about 29%.

Frequently asked questions

How do I convert kVA to kW?
Multiply kVA by the power factor: kW = kVA × PF. At the standard generator rating of PF 0.8, 100 kVA = 80 kW; at PF 0.95, 100 kVA = 95 kW. Only at a power factor of 1 (purely resistive load) are kVA and kW equal.
How do I convert kW to kVA?
Divide by the power factor: kVA = kW ÷ PF. A 7.5 kW motor with a power factor of 0.82 draws 9.15 kVA, and its cables and supply must be sized for that apparent power.
How many amps is 100 kVA?
Three-phase: I = 100,000 ÷ (√3 × V). At 400 V that is 144 A per phase, at 415 V 139 A, at 480 V 120 A and at 208 V 278 A. Single-phase at 230 V: 435 A.
Why are generators rated in kVA instead of kW?
The alternator's windings heat up according to current, which depends on apparent power, regardless of the load's power factor. Manufacturers therefore rate generators in kVA and quote kW at an assumed PF of 0.8; the engine is sized for the kW.
What is a good power factor?
Above 0.95 is considered good. Many utilities charge reactive-energy penalties when the power factor of commercial or industrial customers falls below 0.9–0.95, which is why capacitor banks are installed at motor-heavy sites.
How big a capacitor bank do I need?
Qc = kW × (tan φ1 − tan φ2). To lift an 80 kW load from PF 0.80 to 0.95 you need 80 × (0.750 − 0.329) ≈ 33.7 kVAr. Use detuned banks where there are many drives or inverters.

Sources & references

  1. IEC 60050-131 / IEV — International Electrotechnical Vocabulary: apparent, active and reactive power
  2. Schneider Electric — Electrical Installation Guide, chapter L: Power factor correction
  3. US DOE — Reducing power factor cost (Motor Systems Tip Sheet)

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