What it is
The Stefan-Boltzmann Radiation Calculator finds the total thermal power radiated by a surface. According to the Stefan-Boltzmann law, a body emits power proportional to the fourth power of its absolute temperature, scaled by its emissivity and surface area. This universal physics tool applies to stars, heated metal, building surfaces, the human body, and any radiating object.
How to use it
Enter three values: the emissivity (a dimensionless number from 0 for a perfect reflector to 1 for an ideal black body), the surface area in square metres, and the absolute temperature in kelvin. Remember to convert Celsius to kelvin by adding 273.15. The calculator returns the radiated power in watts.
The formula explained
The equation is $$P = \varepsilon \cdot \sigma \cdot A \cdot T^{4}$$ where \(P\) is radiated power in watts, \(\varepsilon\) is emissivity, \(\sigma\) is the Stefan-Boltzmann constant (\(5.670374419 \times 10^{-8}\ \text{W}\cdot\text{m}^{-2}\cdot\text{K}^{-4}\)), \(A\) is area in square metres, and \(T\) is absolute temperature in kelvin. Because temperature is raised to the fourth power, doubling \(T\) increases radiated power sixteenfold.
Worked example
For human skin at 305 K with area 1.8 m² and emissivity 0.98: \(T^{4} = 305^{4} = 8{,}653{,}650{,}625\). Then $$P = 0.98 \times 5.670374419 \times 10^{-8} \times 1.8 \times 8{,}653{,}650{,}625 \approx 865.6\ \text{W}$$ This is the gross outward radiation; net loss to the surroundings subtracts the inward radiation absorbed from the environment.
FAQ
Why kelvin and not Celsius? The law uses absolute temperature; using Celsius would give nonsense because \(T^{4}\) requires a true zero scale.
What is emissivity? It measures how efficiently a surface radiates compared with a perfect black body. Polished metals have low values (~0.05); skin, water and matte paints are near 0.95–0.98.
Is this the net heat loss? No. This is gross emitted power. Net radiative exchange is \(P_{\text{net}} = \varepsilon \sigma A (T^{4} - T_{\text{surroundings}}^{4})\).
