kW to kVA and kVA to kW Calculator
How the formula works
kW is the real power that does useful work. kVA is the apparent power that the supply equipment must deliver. The power factor (PF) links the two. Generators, transformers, UPS units and cables are rated in kVA, while motors and heaters are usually rated in kW. So you need to convert in both directions during design.
Formulas
kW to kVA: kVA = kW ÷ PF
kVA to kW: kW = kVA × PF
Current (A) = kVA × 1000 ÷ (k × V)
kVAr = √(kVA² − kW²)
Power factor angle φ = cos⁻¹(PF)
Where
- kW = real power of the load
- kVA = apparent power
- kVAr = reactive power
- PF = power factor (between 0.1 and 1)
- V = line voltage in volts (for example 415 V for three phase or 230 V for single phase)
- k = 1.732 for three phase and 1 for single phase
How to use the calculator
- Select the conversion, either kW to kVA or kVA to kW.
- Select the system and the voltage. Choose Custom if your voltage is not in the list.
- Enter the power value and the power factor, then click Calculate.
- You get the real power, apparent power, load current, reactive power and the power factor angle together.
How to read the result
- A lower power factor gives a higher kVA for the same kW, and so a higher current.
- When the power factor is below 0.9, the calculator shows a low power factor message. Many utilities charge a penalty for low power factor, and capacitor banks are used to correct it.
- Always select equipment with some margin above the calculated value. Check the manufacturer rating and your project specification.
Worked example
Example 1: kW to kVA (three phase)
A three phase, 415 V motor load has a real power of 150 kW at 0.85 power factor. Find the kVA, current and reactive power.
Step 1: Apparent power
kVA = 150 ÷ 0.85 = 176.47 kVA
Step 2: Load current
I = 176.47 × 1000 ÷ (1.732 × 415) = 245.5 A
Step 3: Reactive power
kVAr = √(176.47² − 150²) = 93.0 kVAr
Step 4: Power factor angle
φ = cos⁻¹(0.85) = 31.8°
Result
The load needs about 176.5 kVA and draws about 245.5 A. A 200 kVA generator or transformer would cover it with a margin. Since the power factor is below 0.9, power factor correction can reduce the kVA and the current.
Example 2: kVA to kW (three phase)
A 200 kVA, 415 V three phase generator supplies a load with a power factor of 0.8. How much real power can it deliver?
kW = 200 × 0.8 = 160 kW
I = 200 × 1000 ÷ (1.732 × 415) = 278.2 A
kVAr = √(200² − 160²) = 120 kVAr
φ = cos⁻¹(0.8) = 36.9°
The generator can supply 160 kW at 0.8 power factor. If the power factor improves to 0.95, the same generator can supply 190 kW.
Example 3: kVA to kW (single phase)
A 7.5 kVA, 230 V single phase inverter runs at 0.9 power factor.
kW = 7.5 × 0.9 = 6.75 kW
I = 7.5 × 1000 ÷ (1 × 230) = 32.6 A
kVAr = √(7.5² − 6.75²) = 3.27 kVAr
Common mistakes
- Confusing kW and kVA. kW is real power and kVA is apparent power. They are equal only when the power factor is 1.
- Using the wrong operation. To go from kW to kVA you divide by PF. To go from kVA to kW you multiply by PF.
- Forgetting 1.732 for three phase. The current formula for three phase needs the factor 1.732. Single phase uses 1.
- Using the wrong voltage. For three phase, use the line to line voltage such as 415 V, not the phase voltage of 240 V.
- Assuming a power factor of 1. Motors, transformers and fluorescent lighting have a lower power factor. Use the actual or nameplate value.
- Entering the power factor in percent. Enter 0.85 and not 85.
- Sizing a generator only by kW. Generators are rated in kVA at a given power factor, so check both the kVA and the kW.
- Selecting equipment at exactly the calculated value. Leave a margin for future load, motor starting current and site conditions.
- Ignoring motor efficiency. A motor rated 100 kW at the shaft draws more than 100 kW from the supply. Use the input kW if you know it.
Frequently asked questions
How do I convert kW to kVA?
Divide the kW by the power factor. For example, 100 kW at 0.8 power factor is 100 ÷ 0.8 = 125 kVA.
How do I convert kVA to kW?
Multiply the kVA by the power factor. For example, 125 kVA at 0.8 power factor is 125 × 0.8 = 100 kW.
What is the difference between kW and kVA?
kW is the real power that does useful work, such as turning a motor shaft or producing heat. kVA is the total power the source must supply, which includes the reactive part. The ratio between them is the power factor.
Why is kVA always higher than kW?
Because the power factor is never more than 1. Only at a power factor of 1 are kVA and kW equal.
Which power factor should I use if I do not know it?
Use the nameplate or datasheet value. If it is not available, many designers assume 0.8 for general mixed loads, but you should confirm it for the actual equipment and your project specification.
How do I find the current from kW or kVA?
For a three phase system, I = kVA × 1000 ÷ (1.732 × V). For a single phase system, I = kVA × 1000 ÷ V. This calculator does it for you after you enter the system, voltage, power and power factor.
How can I improve a low power factor?
Install a capacitor bank or an automatic power factor correction panel. This reduces the reactive power, the kVA demand and the current drawn from the supply.
Can I use this to size a generator or transformer?
It gives the kVA and kW of the load. For final sizing, also consider the starting current of motors, diversity, future expansion, altitude and temperature derating, and the manufacturer data.