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.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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