Stefan-Boltzmann Sun Power Calculator
Enter star radius and temperature to calculate emitted power using the Stefan-Boltzmann law.
Blackbody Radiation and Stellar Luminosity 🖖
Stellar luminosity is inexorably linked to the Stefan-Boltzmann law, L = 4πR²σT⁴. This fundamental thermodynamic principle defines the absolute power radiated by a blackbody relative to its surface area and temperature. Any deviation from this equilibrium indicates a non-ideal radiator. This computational boundary establishes a baseline for comparing stellar output, completely uninfluenced by the arbitrary classifications of stellar taxonomy.
Why temperature beats size 🖖
This tool has only two inputs — how big a star is and how hot its surface is — yet they pull with very different strength. Radius enters as R², but temperature enters as T⁴, so heat is the dominant lever. Make a star twice as hot without changing its size and every square metre radiates 2⁴ = 16 times more power. That steep fourth-power climb is why a small rise in surface temperature can outshine a large gain in size.
Stefan measured the Sun's heat in 1879 🖖
Josef Stefan didn't just state that flux grows as T⁴ — in 1879 he ran the law backwards. Feeding measured sunlight through σT⁴, he estimated the Sun's surface at roughly 5430 °C (about 5700 K), the first credible figure when rival guesses ranged from 1500° to millions of degrees. This calculator performs the same inversion: the flux you compute is exactly the quantity Stefan measured to take the Sun's temperature.
Example problems
- Sun - Sun baseline: L ≈ 1 L☉ using radius and photosphere temperature.
- Sirius A - Sirius A is much hotter than the Sun, strongly increasing surface flux.
- Betelgeuse - Cool but enormous radius can still produce very high luminosity.
- Red Dwarf - Small cool stars emit far less total power than Sun-like stars.