Main-Sequence Lifetime Calculator Formula

Understand the math behind the main-sequence lifetime calculator. Each variable explained with a worked example.

Use the Main-Sequence Lifetime Calculator

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.

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