Chandrasekhar Limit Calculator
A white dwarf is the dense remnant of a low-mass star, held up not by heat but by the quantum pressure of its packed electrons. There is a ceiling to how much mass this pressure can support, the Chandrasekhar limit, beyond which gravity wins and the star collapses. Remarkably, the limit follows entirely from fundamental constants and the average mass per electron in the star. This calculator evaluates the standard Chandrasekhar mass formula with user-editable constants and electron mean molecular weight, returning the limit in kilograms and solar masses.
Chandrasekhar mass formula
M_Ch = (omega / 2) * sqrt(3 * pi) * (hbar * c / G)^(3/2) * 1 / (mu_e * m_H)^2
Solar masses = M_Ch / 1.989e30
The term (hbar c / G)^(3/2) divided by a squared nucleon mass is the natural mass scale for relativistic degenerate matter. The polytrope constant omega near 2.018 comes from the Lane-Emden solution for an n equals 3 polytrope. With mu_e equal to 2, the result is about 1.4 solar masses.
Chandrasekhar limit facts
- The standard limit is about 1.4 solar masses for mu_e equal to 2.
- Above the limit, electron degeneracy pressure fails and the star collapses.
- Exceeding it can trigger a type Ia supernova, used as a cosmological standard candle.
- The limit does not depend on the white dwarf's radius, a signature of degenerate matter.
- All constants and mu_e are user-editable so you can match any composition or convention.
Chandrasekhar limit: frequently asked questions
What is the Chandrasekhar limit?
The Chandrasekhar limit is the maximum mass a white dwarf star can have before electron degeneracy pressure can no longer support it against gravity. Above this mass the star collapses, triggering a type Ia supernova or forming a neutron star. The standard value is about 1.4 solar masses for a carbon-oxygen white dwarf.
What is the Chandrasekhar mass formula?
M_Ch = (omega / 2) * sqrt(3 pi) * (hbar c / G)^(3/2) * 1 / (mu_e m_H)^2, where omega is approximately 2.018 (a constant from the Lane-Emden n=3 polytrope), hbar is the reduced Planck constant, c the speed of light, G the gravitational constant, mu_e the mean molecular weight per electron, and m_H the hydrogen atom mass.
What is the mean molecular weight per electron?
Mu_e is the average mass per free electron in atomic mass units. For a fully ionized carbon-oxygen white dwarf it is very close to 2, because those nuclei have equal numbers of protons and neutrons so there is about one nucleon mass of two per electron. It is a user-editable input here, defaulting to 2.
Why is the limit about 1.4 solar masses?
Plugging the fundamental constants and mu_e = 2 into the formula yields roughly 1.4 times the mass of the Sun. The exact value depends slightly on composition through mu_e and on relativistic corrections. The limit is independent of the white dwarf's radius, which is a hallmark of degenerate matter.
What units does this calculator use?
All constants are SI: hbar in joule seconds, c in meters per second, G in N m^2 / kg^2, and m_H in kilograms. The constants are user-editable inputs preset to CODATA values, and mu_e and the omega polytrope constant are also editable. The output mass is given in kilograms and in solar masses.
Official sources
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.