Mass-Luminosity Relation Calculator Formula
Understand the math behind the mass-luminosity relation calculator. Each variable explained with a worked example.
Formulas Used
Luminosity (L_sun)
luminosity_solar = pow(mass_solar, 3.5)Luminosity (W)
luminosity_watts = pow(mass_solar, 3.5) * 3.828e26Variables
| Variable | Description | Default |
|---|---|---|
mass_solar | Stellar Mass(M_sun) | 1 |
How It Works
Mass-Luminosity Relation
For main-sequence stars, luminosity increases steeply with mass:
L / L_sun ≈ (M / M_sun)^3.5
This is an empirical fit. The exponent varies from about 2.3 for very low-mass stars to about 4 for massive stars, with 3.5 being a good average.
A 10 M_sun star is ~3162 times as luminous as the Sun.
Worked Example
A 2 solar-mass star.
mass_solar = 2
- 01L/L_sun = 2^3.5
- 02= 2^3 × 2^0.5 = 8 × 1.414 = 11.31
- 03About 11.3 times the Sun's luminosity.
Ready to run the numbers?
Open Mass-Luminosity Relation Calculator