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kVA to kW Conversion

In AC circuits, apparent power (measured in kVA) includes both real power (kW) and reactive power (kVAR). The power factor, cos theta, tells you what fraction of the apparent power is real, useful power. To convert kVA to kW, you multiply by the power factor. For example, 10 kVA at 0.8 power factor gives 8 kW. This is important for sizing generators, transformers, and UPS systems.

Written by the Vorzep Team

Energy & Billing Power Conversion
kVA to kW Converter Electrical Engineering · Power Factor PF
kW = kVA × cos θ
Convert between kVA (apparent power) and kW (real power) using the power factor (cos θ). Perfect for generator sizing, transformer selection, and power system analysis.
kVA
cos θ
kW ↗
— kW —
Apparent Power — kVA
Power Factor — cos θ
Real Power — kW
Reactive Power — kVAR
Common Power Factors Typical values by equipment
Equipment / Load Typical PF (cos θ) Phase Notes
How to Use This Converter
  1. Select "Solve for": Choose what you want to calculate — kW (Real Power), kVA (Apparent Power), or Power Factor (cos θ).
  2. Enter the required values: The calculator will show the two needed input fields. Enter positive numbers only. Power Factor must be between 0 and 1.
  3. Calculate: Click "Convert" or press Ctrl + Enter. The result and a detailed breakdown will appear.
  4. Swap: Use the "Swap" button to exchange the first two input values (useful for quick checks).
Tip: kW = kVA × cos θ. A higher power factor means more efficient power usage. For purely resistive loads, PF = 1, so kW = kVA.
kW = kVA × cos θ · All fields with * are required.

Variables

Symbol Quantity Unit
kW Real power kW
kVA Apparent power kVA
cos θ Power factor dimensionless

What it means

The conversion from apparent power (kVA) to real power (kW) is given by kW = kVA × cosθ, where cosθ is the power factor. This conversion is essential for sizing electrical equipment and for understanding the actual power consumed. For a purely resistive load, cosθ=1, so kW = kVA. For inductive loads (motors, transformers), the power factor is less than 1. Example: A 10 kVA generator with a load having a power factor of 0.8 can deliver 10 × 0.8 = 8 kW of real power. The remaining 2 kVA is reactive power. This relationship is used to determine the required kVA rating for a given kW load.

Worked example

kVA to kW – Practical Example

Real‑World
Scenario: A generator is rated at 10 kVA with a power factor of 0.8. How much real power (kW) can it deliver?
ParameterValue
kVA10
cos θ0.8
FormulakW = kVA × cos θ
1kW = 10 × 0.8 = 8 kW
Final Design kW = 8 kW ✓ Real power
Why: Real power = apparent power × power factor – important for sizing equipment.

Common mistakes

Watch for unit mismatches (W vs kW, single- vs three-phase) and remember to include power factor or efficiency where the formula requires it.

Applications

kVA to kW conversion kW = kVA × cosθ converts apparent power to real power. This is used to calculate the actual useful power from a transformer or generator rating. Engineers use it to size equipment, to manage power factor, and to avoid overloading. This conversion is common in power system design.

  • Transformer and generator sizing for real power
  • Power factor and load management
  • Electrical installation design and capacity planning
  • Energy efficiency analysis
  • Educational understanding of power factor

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  • Published July 10, 2026
  • Last updated September 25, 2026