Main-Sequence Lifetime Calculator Formula
Understand the math behind the main-sequence lifetime calculator. Each variable explained with a worked example.
Formulas Used
Main-Sequence Lifetime
lifetime_yr = 1e10 * pow(mass_solar, -2.5)Lifetime (Gyr)
lifetime_gyr = 1e10 * pow(mass_solar, -2.5) / 1e9Variables
| Variable | Description | Default |
|---|---|---|
mass_solar | Stellar Mass(M_sun) | 1 |
How It Works
Main-Sequence Lifetime
More massive stars burn through their hydrogen fuel much faster because luminosity rises steeply with mass.
Approximate Formula
t ≈ 10¹⁰ × (M/M_sun)^(-2.5) years
This comes from t ∝ M/L and the mass-luminosity relation L ∝ M^3.5 for main-sequence stars.
Worked Example
A star with 2 solar masses.
- 01t = 10^10 × 2^(-2.5)
- 022^(-2.5) = 1/√(2^5) = 1/√32 = 0.1768
- 03t = 10^10 × 0.1768 ≈ 1.77 Gyr
- 04About 1.77 billion years on the main sequence.
Frequently Asked Questions
How long will the Sun remain on the main sequence?
About 10 billion years total. It is currently about 4.6 billion years into its main-sequence life.
Why do massive stars die so quickly?
Luminosity scales roughly as M^3.5, so a 10-solar-mass star is over 3000 times as luminous but only has 10 times the fuel. It runs out in about 30 million years.
What happens after the main sequence?
Stars expand into red giants (or supergiants for massive stars), then end as white dwarfs, neutron stars, or black holes depending on mass.
Ready to run the numbers?
Open Main-Sequence Lifetime Calculator