Chandrasekhar Limit — White Dwarf Mass Calculator

The Chandrasekhar limit is the maximum mass a white dwarf star can have before electron degeneracy pressure can no longer support it against gravitational collapse.

Formula:

M_Ch ≈ 3.1462 / μ_e² × (ħc/G)^(3/2) / m_H²

Work that through in solar masses and it collapses to a single memorable line:

M_Ch ≈ 5.83 / μ_e² × M☉

Watch the two coefficients. The 3.1462 belongs to the dimensional form, which returns kilograms; the 5.83 is what is left once the constants are folded in and the answer is already in solar masses. Substituting one for the other is a mistake that quietly doubles the answer, and it is common enough in published write-ups to be worth naming.

Where μ_e is the mean molecular weight per electron, that is, nucleons per electron:

• μ_e = 2 for carbon-oxygen white dwarfs (one electron per two nucleons): M_Ch ≈ 1.46 M☉, the value usually rounded to 1.4
• μ_e = 2 also for oxygen-neon cores. Oxygen-16 and neon-20 both have two nucleons per electron just like carbon-12, so the limit is identical. This one trips people up
• μ_e = 1 for pure hydrogen: M_Ch ≈ 5.83 M☉ (theoretical, since such stars do not exist as white dwarfs)
• μ_e ≈ 2.15 for an iron core (iron-56 has 56 nucleons to 26 electrons): M_Ch ≈ 1.26 M☉, a lower limit, which is part of why iron cores collapse rather than settle

The limit was calculated by Subrahmanyan Chandrasekhar in 1930 while sailing to England at age 19. He was awarded the Nobel Prize in Physics in 1983.

Physical interpretation: When a white dwarf exceeds 1.4 M☉ (typically via mass transfer from a binary companion), electron degeneracy pressure fails. The star can no longer support itself. The entire star ignites in a thermonuclear explosion: a Type Ia supernova.

Type Ia supernovae as standard candles: Because the Chandrasekhar limit is nearly the same for all white dwarfs, Type Ia supernovae reach nearly identical peak luminosities. This makes them extremely valuable as standard candles for measuring cosmic distances — they were used to discover the accelerating expansion of the universe in 1998.

Real white dwarfs: Observed white dwarfs have masses ranging from about 0.5 M☉ to just below 1.4 M☉. Among the most massive found so far is ZTF J1901+1458, reported in 2021 at roughly 1.35 M☉ and squeezed into a body about the size of the Moon.