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) / 1e9

Variables

VariableDescriptionDefault
mass_solarStellar 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.

mass_solar = 2
  1. 01t = 10^10 × 2^(-2.5)
  2. 022^(-2.5) = 1/√(2^5) = 1/√32 = 0.1768
  3. 03t = 10^10 × 0.1768 ≈ 1.77 Gyr
  4. 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.