Chandrasekhar mass limit calculator

The Chandrasekhar mass is the maximum mass a non-rotating white dwarf can support against gravity through electron degeneracy pressure alone. Above that limit the star cannot stay in hydrostatic equilibrium as a white dwarf and will collapse toward a denser remnant or trigger a thermonuclear runaway, depending on composition and accretion history. This Chandrasekhar mass limit calculator implements the standard closed-form estimate used in astrophysics courses and order-of-magnitude work: M_Ch equals 5.83 solar masses divided by the square of the mean molecular weight per electron, μ_e. For a fully ionized helium, carbon, or oxygen plasma the usual textbook choice is μ_e equal to two, which yields about 1.46 solar masses—the familiar near-1.4 solar mass figure quoted for Type Ia supernova progenitors and white-dwarf mass ceilings. Enter a positive finite μ_e, and the engine returns the limit in solar masses with the squared μ_e, the fixed prefactor 5.83, and a short formula string.

What the Chandrasekhar limit means and how μ_e enters the formula

Electron degeneracy pressure is a quantum-mechanical support mechanism: fermions cannot occupy the same quantum state, so a dense electron gas resists further compression even when the gas is cold. In a white dwarf the electrons form a nearly fully degenerate Fermi gas while the nuclei provide most of the mass. Balancing the degeneracy-supported pressure gradient against Newtonian gravity leads to a maximum stable mass that scales as one over μ_e squared, where μ_e is the mean mass per free electron in units of the hydrogen mass.

The dimensionless μ_e is typically near two for compositions made of fully ionized helium, carbon, and oxygen, because each nucleon pair contributes roughly one electron; pure hydrogen would give μ_e near one and a higher formal limit, while heavier or partially ionized mixtures shift μ_e upward and lower the mass ceiling. The standard estimate written as M_Ch equals 5.83 over μ_e squared solar masses packages the physical constants, the white-dwarf structure factor, and the usual solar-mass normalization into a single prefactor that textbooks and lecture notes use for quick calculations.

This calculator does not integrate stellar-structure equations, apply general-relativistic corrections, or model rotation and magnetic fields; it answers the single question of what solar-mass limit the classical 5.83 over μ_e squared expression returns for the μ_e you supply. That scope matches homework, exam keys, and pipeline checks that need a transparent, reproducible number rather than a full evolutionary model of a white dwarf.