kVA to kW Calculator
Convert apparent power in kVA to real power in kW and reactive power in kVAR using your load's power factor.
Calculator Inputs
Power Triangle Results
How to use this calculator
- Choose your calculation direction. Decide whether you want to find real power (kW) from kVA, or determine the required apparent capacity (kVA) from a known kilowatt load.
- Enter the power rating. Type the numerical value of apparent power in kVA or real power in kW into the corresponding input field.
- Set the power factor. Input the expected power factor between 0.1 and 1.0 for your equipment (unity power factor is 1.0).
- View the calculated powers. The calculator outputs real power (kW), apparent power (kVA), and reactive power (kVAR) simultaneously.
Remember that real power can never exceed apparent power. To determine the actual circuit current drawn by your equipment in amperes, use our watts to amps calculator, or check component resistance using the Ohm's law calculator.
Formulas
In AC electrical circuits, power has three distinct components:real power (kW) that performs physical work,reactive power (kVAR) that sustains magnetic fields, andapparent power (kVA) that represents total capacity. Together they form the electrical power triangle:
| To find | Formula | Description |
|---|---|---|
| Real power (kW) | kW = kVA × PF | Apparent power multiplied by power factor |
| Apparent power (kVA) | kVA = kW / PF | Real power divided by power factor |
| Reactive power (kVAR) | kVAR = √(kVA² − kW²) | Quadrature component of the power triangle |
| Power factor (PF) | PF = kW / kVA | Ratio of real power to apparent power |
Common mistakes
- Assuming a generator rated in kVA can deliver that same number in kW when operating with inductive motor loads.
- Directly adding kW and kVAR arithmetically rather than vectorially via the Pythagorean theorem (kVA = √(kW² + kVAR²)).
- Entering the power factor as a percentage (such as 85) instead of a decimal fraction (0.85).
- Confusing reactive power in kVAR with total energy consumption in kilowatt-hours (kWh).
Worked Example
1. Standby generator capacity
A facility backup generator has a nameplate rating of 100 kVA. The connected building load runs at an average power factor of 0.8.
- Real power: kW = 100 × 0.8 = 80 kW
- Reactive power: kVAR = √(100² − 80²) = √(10,000 − 6,400) = √3,600 = 60 kVAR
2. Sizing a power supply for a known machinery load
A workshop requires 50 kW of active motor power operating at a power factor of 0.9.
- Formula: kVA = kW / PF
- Calculation: kVA = 50 / 0.9 ≈ 55.56 kVA
3. Purely resistive heating installation
An industrial oven draws 30 kVA with pure resistance elements where the power factor is exactly 1.0.
- Real power: kW = 30 × 1.0 = 30 kW
- Reactive power: kVAR = √(30² − 30²) = 0 kVAR
Once you know your system capacity and expected load currents, check your supply lines using our voltage drop calculator to ensure the conductor sizing meets standard installation guidelines.
Frequently Asked Questions
What is the fundamental difference between kVA and kW?
kVA measures apparent power, which is the total capacity supplied to an AC system. kW measures real power, which is the fraction of that electricity converted into working output like heat, mechanical torque, or lighting. The two values are equal only when the power factor is 1.0.
How do I calculate kW from kVA?
Multiply the apparent power by the power factor: kW = kVA × PF. For example, a 100 kVA generator powering a load with an 0.8 power factor delivers 80 kW of active working power.
How do I calculate kVA if I only know kW?
Divide the real power by the power factor: kVA = kW / PF. If a facility requires 50 kW of working power at a 0.9 power factor, the supply source must provide at least 55.56 kVA.
What is reactive power (kVAR) in simple terms?
Reactive power represents the electrical energy that oscillates between the supply and magnetic coils in inductive gear such as motors and transformers. While it produces no direct mechanical work, it is necessary to maintain operating magnetic fields.
Why do utility companies penalize low power factor?
A lower power factor increases the current flowing through supply lines for the same usable kilowatt load, causing higher conductor losses and voltage sag. Commercial tariffs often add surcharges when power factor drops below a common guideline like 0.85 or 0.90.
Can power factor ever exceed 1.0?
No. Power factor is the mathematical cosine of the phase angle between voltage and current waveforms, meaning it strictly ranges from 0.0 to 1.0 in standard AC power systems.
Disclaimer
This calculator is provided for educational and estimation purposes only. Always consult a licensed electrical professional and adhere to your local electrical codes and standards before making any decisions based on these calculations.
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