OrbitLab

Luminosity Calculator

How much light does this star put out?

Radius (solar radii)

Surface temperature (K)

Luminosity

1 L☉

Defaults match the Sun (L = 1 L☉)

What you entered

Radius (solar radii): 1Surface temperature (K): 5778

1
Temperature ratio to the Sun (5778 K)
5778 ÷ 5778= 1
2
L = R² × (T/T☉)⁴
1² × 1⁴= 1 L☉

Result

Luminosity: 1 L☉

A star this size and temperature radiates 1× the Sun's luminosity.

Stellar luminosity from radius and temperature

The Stefan-Boltzmann law: luminosity scales with radius squared and temperature to the fourth power. Temperature dominates.

Radius	Surface temperature	Luminosity	Star type
0.01 R(sun)	10,000 K	8.9720 x 10^-4 L(sun)	White dwarf
0.5 R(sun)	5,778 K	2.5000 x 10^-1 L(sun)	Small main sequence
1 R(sun)	3,000 K	7.2673 x 10^-2 L(sun)	Cool red dwarf-sized
1 R(sun)	5,778 K	1.0000 L(sun)	The Sun
1 R(sun)	10,000 K	8.9720 L(sun)	Hot A-type sized
10 R(sun)	5,778 K	1.0000 x 10^2 L(sun)	Giant
100 R(sun)	3,500 K	1.3464 x 10^3 L(sun)	Red giant

Compare rows three and five: the same radius at 10,000 K instead of 3,000 K is 123 times more luminous, because the fourth power of temperature swamps everything. A red giant is bright only because it is enormous, not because it is hot.

Size and heat both compound

Luminosity depends on the square of a star's radius but the fourth power of its temperature — a star just slightly hotter than the Sun radiates dramatically more energy per unit area, and larger surface area amplifies that further.

Why this puts stars on the H-R diagram

Luminosity and temperature together are exactly the two axes of the Hertzsprung-Russell diagram, the single most important chart in stellar astrophysics for classifying and understanding how stars evolve.

Frequently asked questions

A star has twice the Sun's radius and a surface temperature of 8,000 K (Sun is 5,778 K) — what is its luminosity?

L/L☉ = (R/R☉)² × (T/T☉)⁴ = 2² × (8000/5778)⁴ = 4 × 3.67 = 14.7 solar luminosities.

How does the luminosity calculator relate to the absolute magnitude calculator?

Luminosity gives physical power output (watts or solar luminosities). Absolute magnitude is the same information on a logarithmic scale used by astronomers. M = 4.83 - 2.5 × log10(L/L☉) converts between them.

Why does temperature matter so much more than size?

Luminosity depends on T⁴ but only R². Doubling temperature increases luminosity 16-fold, while doubling radius only increases it 4-fold. This is why blue supergiants (very hot) can outshine red supergiants (very large) despite being smaller.