White dwarf radius from mass calculator

It applies the Nauenberg approximation to the inverse mass-radius relation produced by electron degeneracy pressure and returns the radius in metres. The calculation uses a Chandrasekhar limit of 1.44 solar masses and reports an input error above that boundary. It is useful for quick astrophysics checks, teaching, model comparisons, and order-of-magnitude estimates, but it is not a replacement for a detailed stellar-structure model.

Why a more massive white dwarf is smaller

Ordinary objects often become larger when material is added, but a white dwarf follows the opposite trend over most of its stable mass range. Its support comes mainly from electron degeneracy pressure, a quantum-mechanical effect that does not depend on ordinary thermal gas pressure in the same way as a main-sequence star. Adding mass strengthens gravity and forces the degenerate electrons into a more compressed state, so the equilibrium radius falls. This calculator represents that behavior with the Nauenberg mass-radius approximation. Enter the stellar mass as a multiple of the Sun's mass, such as 0.6 for a typical white dwarf, and the result gives the corresponding radius in metres. The returned value is the modeled stellar radius, not a Schwarzschild radius, orbital distance, or observational angular radius. Because the relation is idealized, it is best interpreted as a physically motivated estimate that captures the main inverse trend rather than as an exact prediction for every observed remnant.

How the estimate is calculated

The calculation uses R = 0.0112 R_sun times the square root of [(M_ch/M)^(2/3) minus (M/M_ch)^(2/3)]. Here M is the supplied white dwarf mass, M_ch is fixed at 1.44 solar masses, and the solar radius is fixed at 695,700,000 metres. Keeping the input in solar masses makes the mass ratio dimensionless, while multiplying by the adopted solar radius converts the final answer directly to metres. The formula smoothly decreases as mass increases and reaches zero at the adopted Chandrasekhar boundary. A mass greater than 1.44 is rejected instead of being inserted into the square root, because the expression would cease to describe a stable white dwarf and would produce a non-real mathematical result. The implementation is deterministic: identical input always uses the same constants and arithmetic, with no network lookup, random choice, or time-dependent data. The result therefore works well in reproducible calculations and automated tests.

Assumptions, limits, and interpretation

The Nauenberg relation is a compact approximation for a zero-temperature, non-rotating white dwarf supported by a completely degenerate electron gas. Real stars can differ because of finite temperature, envelope structure, rotation, magnetic fields, chemical composition, crystallization, and general-relativistic effects near the high-mass end. The model also assumes the customary electron molecular-weight choice implicit in the quoted coefficient, making it most appropriate for common carbon-oxygen white dwarfs and useful as a broad estimate for related compositions. Very low-mass remnants may have helium cores and thick envelopes that make their observed radii depart noticeably from this cold relation. Near 1.44 solar masses, small mass changes lead to very large relative radius changes, so the output should not be treated as a precision prediction. Use the estimate to compare theoretical scales, check a calculation, or establish an initial condition. For research-grade inference, compare against evolutionary tracks matched to temperature, composition, atmosphere, and observational uncertainties. Each API request costs $0.002; the browser calculation uses the same deterministic relation.