Neutron Star Density Calculator Formula

Understand the math behind the neutron star density calculator. Each variable explained with a worked example.

Formulas Used

Average Density

density = 3 * mass / (4 * pi * pow(radius, 3))

Relative to Nuclear Density

density_nuclear = (3 * mass / (4 * pi * pow(radius, 3))) / 2.3e17

Variables

VariableDescriptionDefault
massNeutron Star Mass(kg)2.78e+30
radiusNeutron Star Radius(m)10000

How It Works

Neutron Star Density

Formula

rho = 3M / (4π r³)

A typical neutron star (1.4 M_sun, 10 km radius) has an average density near nuclear density (~2.3 × 10¹⁷ kg/m³). A sugar-cube-sized chunk would weigh about a billion tonnes.

Worked Example

A 1.4 M_sun neutron star with r = 10 km.

mass = 2.78e+30radius = 10000
  1. 01rho = 3M / (4π r³)
  2. 024π r³ = 4π × (10000)³ = 1.257e13 m³
  3. 03rho = 3 × 2.78e30 / 1.257e13 = 6.63e17 kg/m³
  4. 04About 2.9 times nuclear density.

Ready to run the numbers?

Open Neutron Star Density Calculator