White Dwarf Radius Calculator Formula
Understand the math behind the white dwarf radius calculator. Each variable explained with a worked example.
Formulas Used
Radius (R_sun)
radius_solar = 0.0126 * pow(mass_solar, -1/3)Radius (km)
radius_km = 0.0126 * pow(mass_solar, -1/3) * 695700Radius (R_Earth)
radius_earth = 0.0126 * pow(mass_solar, -1/3) * 695700 / 6371Variables
| Variable | Description | Default |
|---|---|---|
mass_solar | White Dwarf Mass(M_sun) | 0.6 |
How It Works
White Dwarf Mass-Radius Relation
White dwarfs are supported by electron degeneracy pressure. An unusual property: more massive white dwarfs are smaller.
Approximate Relation
R / R_sun ≈ 0.0126 × (M/M_sun)^(-1/3)
A 0.6 M_sun white dwarf is roughly Earth-sized. As mass approaches the Chandrasekhar limit (1.4 M_sun), the radius shrinks toward zero.
Worked Example
A 0.6 M_sun white dwarf.
- 01R/R_sun = 0.0126 × 0.6^(-1/3)
- 020.6^(-1/3) = 1/(0.6^(1/3)) = 1/0.8434 = 1.1856
- 03R/R_sun = 0.0126 × 1.1856 = 0.01494
- 04R = 0.01494 × 695700 = 10 394 km ≈ 1.63 R_Earth
Frequently Asked Questions
Why are heavier white dwarfs smaller?
More mass means stronger gravity, compressing the degenerate electron gas further. This is the opposite of normal stars.
What is a typical white dwarf mass?
About 0.6 M_sun. Most white dwarfs fall between 0.5 and 0.8 M_sun.
How dense is a white dwarf?
About 10^6 kg/m³ on average (a million times water). A teaspoon would weigh about a tonne.
Ready to run the numbers?
Open White Dwarf Radius Calculator