Flame Radiative Heat Loss Calculator
Reviewed by Hamza Gujjar, Algorithm Architect & Software Developer
Last updated: July 26, 2026Flame Radiative Heat Loss Calculator
Not all of a flame's heat reaches its intended target directly - a share always radiates away to cooler surroundings, following the same Stefan-Boltzmann law that governs all thermal radiation.
The Formula
Q = ε × σ × A × (Tf4 - Ts4)
Where σ = 5.670374419 × 10-8 W/m²K⁴ is the Stefan-Boltzmann constant, and temperatures must be in Kelvin, not Celsius or Fahrenheit.
Worked Example
A flame at 1,800K with 0.3 emissivity, 0.5 m² of radiating surface, in a 300K surrounding environment:
Q = 0.3 × 5.67e-8 × 0.5 × (1,8004 - 3004) ≈ 89.2 kW
How to Use This Calculator
- Enter the flame's emissivity (0 to 1; sooty luminous flames run higher, clean blue flames lower).
- Enter flame and surrounding temperatures in Kelvin.
- Enter the radiating surface area.
Frequently Asked Questions
Why does the fourth-power relationship matter so much?
Because heat loss scales with temperature to the fourth power, even a modest temperature increase dramatically increases radiative loss - which is exactly why very hot flames radiate disproportionately more than their temperature increase alone would suggest.
Pair this with the Flame Emissivity Calculator if you need to estimate emissivity first.