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) * 3.828e26

Variables

VariableDescriptionDefault
mass_solarStellar 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
  1. 01L/L_sun = 2^3.5
  2. 02= 2^3 × 2^0.5 = 8 × 1.414 = 11.31
  3. 03About 11.3 times the Sun's luminosity.