Stefan-Boltzmann Calculator Formula

Understand the math behind the stefan-boltzmann calculator. Each variable explained with a worked example.

Formulas Used

Radiated Power

radiated_power = emissivity * 5.6704e-8 * area * pow(temperature, 4)

Radiated Power (kW)

radiated_power_kw = emissivity * 5.6704e-8 * area * pow(temperature, 4) / 1000

Variables

VariableDescriptionDefault
emissivityEmissivity (0-1)1
areaSurface Area()1
temperatureTemperature(K)1000

How It Works

Stefan-Boltzmann Law

Every object radiates thermal energy proportional to the fourth power of its temperature.

Formula

P = epsilon * sigma * A * T^4

where sigma = 5.6704 x 10^-8 W/(m²·K^4) is the Stefan-Boltzmann constant and epsilon is the emissivity (1 for a perfect black body).

Worked Example

A perfect black body (epsilon=1) at 1000 K with 1 m² surface area.

emissivity = 1area = 1temperature = 1000
  1. 01P = epsilon * sigma * A * T^4
  2. 02P = 1 * 5.6704e-8 * 1 * 1000^4
  3. 03P = 5.6704e-8 * 1e12
  4. 04P = 56,704 W = 56.7 kW

Ready to run the numbers?

Open Stefan-Boltzmann Calculator