kW to kVA Formula Explained (With Step-by-Step Examples)
Introduction #
Converting kW to kVA is required whenever you size transformers, generators, or UPS from a known real power (kW) and power factor. The formula is simple; the mistakes are common. This guide states the formula, works through step-by-step examples, shows how power factor changes the result, and lists errors to avoid.
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.
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 gives single-phase kVA. 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. For sizing equipment, total three-phase kVA = total kW ÷ PF is correct.
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.
- Add margin (e.g. 15–25%) and pick the next standard size.
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.
Use our free kW to kVA converter for instant results. For the difference between kW and kVA and when to use each, see kW vs kVA: What's the Difference?.
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, use the kW to kVA converter.