kW to kVA Formula: kVA = kW ÷ Power Factor
Introduction #
When this guide fits: You already have load kW and a displacement power factor and need kVA for equipment sizing, spreadsheets, or sanity checks against a meter.
When it is not suitable: You need harmonic-dominated apparent power (IT crest factor, VFD input distortion) resolved with true rms measurements and filter design—displacement PF alone can mislead.
Instant answer: kVA = kW ÷ PF (example: 100 kW ÷ 0.8 = 125 kVA; 250 kW ÷ 0.88 ≈ 284 kVA).
Open kW to kVA — 100 kW · PF 0.8 →
This guide owns the formula and worked examples (including three-phase totals); for live numbers use the calculator above.
The Core Formula #
kVA = kW ÷ Power Factor
Where:
- kVA = apparent power in kilovolt-amperes (what the supply must deliver).
- kW = real power in kilowatts (what the load consumes as useful work).
- Power Factor = ratio of real power to apparent power, between 0 and 1 (use decimal form, e.g. 0.85 not 85%).
So for a given kW, lower power factor means higher kVA. Example: 100 kW at PF 0.8 needs 100 ÷ 0.8 = 125 kVA; at PF 0.9 the same 100 kW needs 100 ÷ 0.9 ≈ 111 kVA.
Phase note: kVA = kW ÷ PF always returns total apparent power from total kW and the matching aggregate PF (single-phase or three-phase totals). It is not a “per-phase-only” formula.
Step-by-Step Examples #
Example 1: 10 kW at 0.8 Power Factor #
Given: Load is 10 kW, power factor 0.8. Find kVA.
Step 1: Identify kW and PF.
kW = 10, PF = 0.8.
Step 2: Apply the formula.
kVA = kW ÷ PF = 10 ÷ 0.8 = 12.5 kVA.
Result: The supply must deliver 12.5 kVA to serve this 10 kW load at 0.8 PF.
Example 2: 50 kW at 0.85 Power Factor #
Given: Load is 50 kW, power factor 0.85. Find kVA.
Step 1: kW = 50, PF = 0.85.
Step 2: kVA = 50 ÷ 0.85 = 58.82 kVA (round to 58.8 kVA for practical use).
Result: Required apparent power is 58.8 kVA.
Example 3: 100 kW at 0.9 Power Factor #
Given: Load is 100 kW, power factor 0.9. Find kVA.
Step 1: kW = 100, PF = 0.9.
Step 2: kVA = 100 ÷ 0.9 = 111.11 kVA (use 111 kVA for sizing).
Result: Required apparent power is 111 kVA.
Power Factor Impact Table #
For a fixed real power of 100 kW, the kVA required depends only on power factor. Lower PF means higher kVA.
| PF | kVA needed for 100 kW |
|---|---|
| 0.7 | 142.8 |
| 0.8 | 125 |
| 0.9 | 111 |
| 1.0 | 100 |
So improving power factor from 0.7 to 0.9 cuts the kVA requirement from 142.8 to 111 for the same 100 kW—smaller transformer or generator and often lower demand charges.
Common Mistakes #
Using percentage instead of decimal. Power factor must be in decimal form in the formula. PF 85% is 0.85. Writing kVA = 100 ÷ 85 is wrong; use kVA = 100 ÷ 0.85.
Forgetting to divide. Some people multiply: kW × PF. The correct relation is kVA = kW ÷ PF. Double-check that you are dividing kW by PF.
Mixing kW and kWh. kW is power (instantaneous rate); kWh is energy (power × time). The formula uses kW. Do not substitute kWh into kVA = kW ÷ PF.
Ignoring three-phase. The formula kVA = kW ÷ PF already returns total kVA from total kW and aggregate PF. For three-phase, total kVA is still total kW ÷ PF; the √3 is inside the per-phase voltage and current when you derive kW or kVA from line quantities.
kVA, kW, and kVAR (right triangle) #
For sinusoidal steady-state, kVA is the hypotenuse of the power triangle: kVA² ≈ kW² + kVAR². The identity kW = kVA × PF and kVA = kW ÷ PF are the same relationship written two ways. When you improve PF by supplying kVAR from capacitors, required kVA from the utility for the same kW drops—until harmonics change the game.
| If you know… | Then… |
|---|---|
| kW and PF | kVA = kW ÷ PF |
| kVA and PF | kW = kVA × PF |
| kW and kVAR | kVA = √(kW² + kVAR²) (sinusoidal model) |
Using the Formula in Practice #
When sizing a transformer or generator from load kW:
- Get the total load kW (or sum of loads).
- Get the power factor (measured or typical for the load type).
- Compute kVA = kW ÷ PF.
- Apply the project's documented growth, duty and contingency criteria; do not treat one generic margin as a universal rule.
For multiple loads with different power factors, either convert each to kVA (each load’s kW ÷ its PF) and add kVA, or compute total kW and a weighted power factor, then total kVA = total kW ÷ weighted PF.
Try our kW to kVA converter for instant results. For the difference between apparent and real power, see kVA vs kW.
Browse Power calculator hub for load and conversion tools.
Related articles #
- When equipment is rated in kVA — nameplate / procurement language
- Transformer Sizing Guide — from kVA estimate to standard size
- Power Factor Guide — where PF comes from on the plant floor
Next steps you should take #
- Copy your metered kW and PF interval (15-minute) for the same window you size equipment—avoid nameplate-only stacks.
- Run the same numbers in the calculator and your spreadsheet to catch divide/multiply typos.
- If THD(I) is high, flag the result as displacement-only and pull in harmonic study before ordering transformers.
- Need kVA vs kW language for procurement? See kVA vs kW and When to use kVA.
- Refresh PF = kW ÷ kVA on the Power factor formula authority page.
Can I ever multiply kW by PF to get kVA?
No for the usual definition: kVA = kW ÷ PF when PF is the cosine of the angle between fundamental voltage and current. Multiplying is a common finger-error that shrinks apparent power dangerously.
Does a higher PF always save money?
Often yes on demand and equipment sizing, but tariff logic varies. Some charges are kW-only; others penalize reactive separately. Read your tariff line items.
Is kW ÷ PF valid for three-phase totals?
Yes for total three-phase kW and a representative lagging PF: total kVA ≈ total kW ÷ PF. Deriving phase currents still uses √3 and line voltage relationships.
Additional example (plant bus snapshot): 250 kW at 0.88 PF → kVA = 250 ÷ 0.88 ≈ 284 kVA. Compare to transformer or UPS nameplate only after applying the project's load, duty and growth criteria—do not apply diversity twice if the kW input is already a measured coincident demand.
Technical sources #
- U.S. Department of Energy electrical science handbook — real, reactive and apparent power relationships.
- Eaton power factor correction guide — power factor and kW/kVA context for industrial systems.
Where √3 shows up when you leave “total kW” language #
The compact relationship kVA ≈ kW ÷ PF is a total three-phase shortcut when you already trust one representative displacement power factor. The moment someone asks for feeder amps, you must publish line-to-line voltage and use I_L = 1000 × kW ÷ (√3 × V_L-L × cos φ) (balanced assumption) or use phase-based math intentionally. Mixing phase voltage with line current without the correct √3 factor is a classic specification error—see What Is 3-Phase Power for a table-first refresher. If harmonics dominate, measured true RMS current overrides triangle estimates.
Try our 3-Phase Power Calculator when the spreadsheet column is amps, not kVA.
Conclusion #
The kW to kVA conversion is kVA = kW ÷ Power Factor. Use decimal PF (e.g. 0.8), divide (do not multiply), and use kW not kWh. Account for power factor when sizing equipment; lower PF increases kVA for the same kW. For quick checks, try our kW to kVA converter.