Skip to content
Engineerly

Power & current

kVA to kW Converter (and kVAr)

Convert between kVA, kW and kVAr with the power triangle. Start from any two of kVA, kW and power factor, and optionally add a voltage to get the current that matches the apparent power.

For estimation and education. Not a substitute for a licensed engineer, the applicable codes (IEC 60364, NEC/NFPA 70, BS 7671, local regulations) or manufacturer data. Read the disclaimer.

Power

kVA

0 < PF ≤ 1

Current helper (optional)

System
V

Leave empty to skip.

Result

kVA / kW / kVAr — Engineerly. Estimate for education only; verify against applicable codes and manufacturer data.

Real power
800kW
Apparent power
1,000kVA
Reactive power
600kVAr
Power factor
0.8
Phase angle φ
36.87°
Line current
1,443A

Working, with your numbers

  1. 1. Real power
    kW = kVA × PF
    kW = 1,000 × 0.8
    = 800 kW
  2. 2. Reactive power
    kVAr = √(kVA² − kW²)
    kVAr = √(1,000² − 800²)
    = 600 kVAr
  3. 3. Line current
    I = S / (√3 × V_LL)
    I = 1,000,000 VA / (1.73205 × 400 V)
    = 1,443.4 A

Assumptions

  • Sinusoidal steady state: PF here is the displacement power factor cos φ; harmonic distortion is not included.
  • kVAr is shown as a magnitude; it does not tell you whether the load is lagging (inductive) or leading (capacitive).
  • Current helper assumes a balanced three-phase load and a line-to-line voltage.
Known values: kva-pf
kVA: 1000 kVA
PF: 0.8
Voltage: 400 V

Check before you rely on this

  • Estimation and education only. Not a substitute for a licensed engineer, the applicable code (IEC 60364, NEC/NFPA 70, BS 7671 or local regulations) or manufacturer data.

How to use this calculator

  1. Choose which two quantities you know: kVA and PF, kW and PF, or kW and kVA.
  2. Enter the values. Power factor must be greater than 0 and no more than 1, and kW cannot exceed kVA.
  3. To see the current, choose single- or three-phase and enter the voltage (line-to-line for three-phase).
  4. Read kW, kVA, kVAr, PF and the phase angle, then check the working.

How it works: the formula

kW = kVA × PF kVA = kW / PF kVAr = √(kVA² − kW²) PF = kW / kVA = cos φ I = S / (√3 × V_LL) (three-phase) I = S / V (single-phase)

Real, reactive and apparent power form a right-angled triangle. kW is the adjacent side, kVAr the opposite side and kVA the hypotenuse. The angle φ between kW and kVA is the phase angle between voltage and current.

Variables and units

SymbolMeaningUnit
kWReal (active) power: does useful work and is billed as kWhkW
kVAApparent power: sets the current, and so the cable, transformer and generator sizekVA
kVArReactive power, exchanged with magnetic and electric fieldskVAr
PFPower factor = cos φ—
φPhase angle between voltage and current°

Worked example

A 1000 kVA generator at its rated power factor of 0.8:

kW = 1000 × 0.8 = 800 kW kVAr = √(1000² − 800²) = √360 000 = 600 kVAr φ = acos(0.8) = 36.87° I = 1 000 000 / (1.73205 × 400) = 1443.4 A at 400 V

This is the familiar 3-4-5 triangle scaled by 200. Going the other way, 800 kW at PF 0.8 needs 800 / 0.8 = 1000 kVA of capacity.

Assumptions

  • Steady-state sinusoidal conditions.
  • kVAr is shown as a magnitude, with no sign for leading or lagging.
  • Three-phase current assumes a balanced load.

Limitations

  • With non-linear loads (drives, rectifiers, LED drivers), true power factor is lower than cos φ because of harmonic distortion. Use measured true PF for kW from kVA.
  • Generator kW output is limited by the engine and kVA by the alternator. Running at a PF other than the rated one can be limited by either.

References

Standards and texts that cover this topic. Use the edition adopted in your jurisdiction.

  • IEEE Std 141 ("Red Book") — power factor and the power triangle in industrial distribution.
  • IEEE Std 1459, Definitions for the Measurement of Electric Power Quantities Under Sinusoidal, Nonsinusoidal, Balanced, or Unbalanced Conditions.
  • IEC 60050-131, International Electrotechnical Vocabulary — circuit theory terms for active, reactive and apparent power.

Frequently asked questions

Why are generators and transformers rated in kVA?

Their heating depends on current, and current depends on apparent power, whatever the load's power factor. A kVA rating stays valid for any PF. The kW they can deliver is kVA × PF. Generator sets are usually rated at PF 0.8.

Is kVA always larger than kW?

kVA is never smaller than kW. They are equal only at unity power factor (PF = 1), which purely resistive loads such as heaters get close to.

What is a good power factor?

Many utilities expect 0.9 to 0.95 or better and may charge for reactive energy below a threshold set in the tariff. Induction motors on light load have poor PF. Capacitor banks are the usual fix.

Can I convert kVA to kW without the power factor?

No. The ratio between them is the power factor. If PF is unknown, 0.8 is a common assumption for generator and mixed motor loads, but it is only an assumption. Measure it if the result matters.

Related calculators

  • Three-Phase & Single-Phase Current Calculator — Calculate line current from kW, hp or kVA for three-phase (line-to-line or line-to-neutral) and single-phase supplies, with PF, efficiency and every step shown.
  • Power Factor Correction Capacitor Calculator — Calculate capacitor kVAr to raise power factor, capacitance per phase for star and delta banks at 50 or 60 Hz, and the resulting line current reduction.
  • Generator Sizing Calculator — Size a generator set from a load table: running kW/kVA, diversity, motor starting kVA by DOL, soft starter or VFD, margin, derating and a common kVA rating.

How these formulas were checked: methodology and testing.