Stellar Luminosity Calculator
Calculate a star's luminosity from its radius and surface temperature using the Stefan-Boltzmann law.
Results in watts and solar luminosities.
A star radiates energy as a blackbody, so its luminosity depends on both its size and temperature. The larger and hotter a star, the more energy it emits.
Stefan-Boltzmann Law:
L = 4πR²σT⁴
Where:
- L = luminosity (watts)
- R = radius (meters)
- σ = Stefan-Boltzmann constant = 5.67 × 10⁻⁸ W/m²/K⁴
- T = surface temperature (Kelvin)
In solar units (much easier to use):
L/L☉ = (R/R☉)² × (T/T☉)⁴
Where L☉ = 3.828 × 10²⁶ W, R☉ = 695,700 km, T☉ = 5,778 K.
Why temperature matters so much: Because of the T⁴ term, temperature has an enormous effect. A star twice as hot as the Sun radiates 2⁴ = 16 times more power per unit area. A star 10 times hotter radiates 10,000 times more per unit area.
Example stars:
- Sun: R = 1 R☉, T = 5,778 K, L = 1 L☉
- Sirius A: R = 1.71 R☉, T = 9,940 K, L ≈ 24 L☉
- Rigel: R ≈ 78 R☉, T ≈ 12,100 K, L ≈ 135,000 L☉
- Betelgeuse: R ≈ 1,000 R☉, T ≈ 3,500 K, L ≈ 126,000 L☉ (large but cool)
- Proxima Centauri: R ≈ 0.15 R☉, T ≈ 3,042 K, L ≈ 0.0017 L☉
This formula shows why giant cool stars can still be very luminous — their enormous surface area compensates for their lower temperature.