Neutron Star Density Calculator
Calculate the average density, surface gravity, and escape velocity of a neutron star from its mass and radius.
Compare to nuclear density.
Neutron stars are the collapsed cores of massive stars that exploded as supernovae. They are among the densest objects in the universe — only black holes are more compact.
Average density:
ρ = M / (4/3 × π × R³)
Surface gravity:
g = GM / R²
Escape velocity:
v_esc = √(2GM / R)
Typical neutron star:
- Mass: 1.4 M☉ = 2.8 × 10³⁰ kg (most measured neutron stars cluster near 1.4 M☉)
- Radius: ~10 km (about the size of a city)
- Average density: ~7 × 10¹⁷ kg/m³ (3× nuclear density)
- Surface gravity: ~2 × 10¹² m/s² (200 billion times Earth’s gravity)
- Escape velocity: ~100,000–150,000 km/s (nearly half the speed of light)
Nuclear density (saturation density): ρ₀ = 2.3 × 10¹⁷ kg/m³ The core of a neutron star exceeds several times nuclear density. At these densities, matter may exist as strange quark matter, hyperons, or other exotic states.
Pulsars: Many neutron stars are observed as pulsars — rotating with periods from milliseconds to seconds, emitting beams of radio waves like a lighthouse. The fastest known pulsar (PSR J1748-2446ad) spins at 716 times per second. At its equator, the surface moves at about 24% of the speed of light.
Maximum mass: The Tolman-Oppenheimer-Volkoff limit is roughly 2.0–2.5 M☉. Above this, electron degeneracy cannot support the star, and it collapses to a black hole.