Stellar Luminosity Calculator
A star’s luminosity from its radius and surface temperature — in solar luminosities and watts — with the absolute magnitude that follows and where it sits relative to the Sun.
A star radiates as a black body: luminosity is its surface area times σT⁴, so L = 4πR²σT⁴.
How the stellar luminosity calculator works
A star radiates as a black body: luminosity is its surface area times σT⁴, so L = 4πR²σT⁴. Doubling the temperature makes a star sixteen times brighter; doubling the radius four times. In solar units the formula collapses to L ÷ L☉ = (R ÷ R☉)² (T ÷ 5,772)⁴, and the absolute magnitude is 4.83 − 2.5 log₁₀(L ÷ L☉).
Formula: L = 4π R² σ T⁴; M = 4.83 − 2.5 log₁₀(L ÷ L☉)
Worked examples
| Inputs | Luminosity | Note |
|---|---|---|
| 1.2 R☉ at 6,500 K | 2.316 L☉ | 2.32 L☉, M 3.92 |
| The Sun | 1 L☉ | 1 L☉, M 4.83 |
| Betelgeuse-like: 900 R☉ at 3,500 K | 1.10e+5 L☉ | 1.1 × 10⁵ L☉ |
FAQFrequently asked questions
Why does temperature matter so much more than size?
Radiated power goes as the fourth power of temperature: a star 10% hotter is 46% brighter. That is why hot blue stars are enormously luminous despite being only a few times the Sun’s size, and why red giants must be huge to be bright at all.
What is absolute magnitude?
The apparent brightness a star would have at 10 parsecs — a distance-free measure. The Sun is 4.83; each 5 magnitudes lower is 100 times brighter; Deneb is about −8.
How are radius and temperature measured?
Temperature from the spectrum or colour; radius from luminosity and distance, or directly by interferometry and eclipsing binaries for a few hundred stars. Enter either and the formula gives the third.
What does the peak wavelength row mean?
Wien’s law: a black body’s emission peaks at 2.898 million ÷ T nanometres. The Sun peaks near 500 nm (green, appearing white); a 3,500 K red dwarf near 830 nm in the infrared.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G and the speed of light
- IAU 2015 Resolution B3 — nominal solar and planetary conversion constants — the astronomical unit, solar mass and planetary radii
- CSIRO Space and Astronomy — Australia's national science agency
Last checked: September 2026. Constants are CODATA 2018 (G, c) and IAU 2015 nominal values (solar and planetary parameters).