Stellar Luminosity Formula
Calculate a star's total energy output using the Stefan-Boltzmann law.
Relates luminosity to radius and temperature.
The Formula
L = 4πR²σT⁴
The luminosity formula calculates the total power output of a star. It depends on the star's surface area and its surface temperature.
Variables
| Symbol | Meaning |
|---|---|
| L | Luminosity — total energy radiated per second (watts) |
| R | Radius of the star (meters) |
| σ | Stefan-Boltzmann constant (5.67 × 10⁻⁸ W/m²K⁴) |
| T | Surface temperature of the star (Kelvin) |
| π | Pi (approximately 3.14159) |
Example 1
Find the luminosity of the Sun
R = 6.96 × 10⁸ m, T = 5778 K
L = 4π × (6.96 × 10⁸)² × 5.67 × 10⁻⁸ × (5778)⁴
L = 4π × 4.844 × 10¹⁷ × 5.67 × 10⁻⁸ × 1.115 × 10¹⁵
L ≈ 3.85 × 10²⁶ watts
Example 2
A star has twice the Sun's radius and 1.5 times its temperature
L/L☉ = (R/R☉)² × (T/T☉)⁴
L/L☉ = (2)² × (1.5)⁴ = 4 × 5.0625
L ≈ 20.25 times the Sun's luminosity
When to Use It
Use the stellar luminosity formula when:
- Comparing the energy output of different stars
- Estimating a star's brightness from its size and temperature
- Classifying stars on the Hertzsprung-Russell diagram
- Studying stellar evolution and energy production