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kW to kVA Conversion

This is the reverse of the previous conversion. If you know the real power in kW and the power factor, dividing by cos theta gives the apparent power in kVA. For example, 8 kW at 0.8 power factor requires 10 kVA. This is used to determine the required rating of transformers, generators, and other AC power equipment. A lower power factor means you need a larger kVA rating for the same real power.

Written by the Vorzep Team

Energy & Billing Power Conversion
kW to kVA Converter Electrical Engineering · Power Factor PF
kVA = kW / cos θ
Convert between kW (real power) and kVA (apparent power) using the power factor (cos θ). Perfect for generator sizing, transformer selection, and power system analysis.
kW
cos θ
kVA ↗
— kVA —
Real Power (kW) — kW
Power Factor — cos θ
Apparent Power — kVA
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 — kVA (Apparent Power), kW (Real 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: kVA = kW / cos θ. A higher power factor means more efficient power usage. For purely resistive loads, PF = 1, so kW = kVA.
kVA = kW / cos θ · All fields with * are required.

Variables

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

What it means

The conversion from real power (kW) to apparent power (kVA) is kVA = kW / cosθ, where cosθ is the power factor. This is used to size transformers, cables, and generators based on the real power requirement and the expected power factor. A lower power factor requires a larger kVA rating for a given kW. Example: A motor with a 8 kW load and a power factor of 0.8 requires a generator rated at 8/0.8 = 10 kVA. This ensures that the generator can handle the current drawn by the motor, which is higher than for a resistive load of the same wattage.

Worked example

kW to kVA – Practical Example

Real‑World
Scenario: A load is 8 kW with a power factor of 0.8. Find the required kVA rating of the supply.
ParameterValue
kW8
cos θ0.8
FormulakVA = kW / cos θ
1kVA = 8 / 0.8 = 10 kVA
Final Design kVA = 10 kVA ✓ Apparent power
Why: kVA rating must be higher than kW when power factor is less than 1.

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

kW to kVA conversion kVA = kW / cosθ converts real power back to apparent power. This is used to determine the required apparent power rating of equipment for a given real power. Engineers use it to select transformers and cables. This conversion is essential when power factor is known.

  • Determination of apparent power for equipment sizing
  • Power factor correction and system design
  • Feeder and transformer capacity calculation
  • Load analysis and planning
  • Educational understanding of power factor

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  • Published July 10, 2026
  • Last updated August 15, 2026