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:

  1. Get the total load kW (or sum of loads).
  2. Get the power factor (measured or typical for the load type).
  3. Compute kVA = kW ÷ PF.
  4. 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.