Physics

Luminosity Calculator

Find a star's luminosity from its radius and temperature.

Calculated Output

Luminosity (W) 3.843932540746749e+26

Luminosity (L☉) 1.004

Formula: L = 4π·R²·σ·T⁴

Step-by-Step Breakdown

1. Values used:

2. Radius = 1 R☉

3. Surface temperature = 5,778 K

5. Luminosity = 3.843932540746749e+26W

6. Luminosity = 1.004L☉

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The math behind it

L = 4π·R²·σ·T⁴, combining surface area with the Stefan–Boltzmann law.

The Sun (1 R☉, 5778 K) → about 3.85 × 10²⁶ W (1 L☉).

Why does temperature dominate?

Luminosity rises with T⁴, so hot stars are vastly more luminous.