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))) / 2.3e17Variables
| Variable | Description | Default |
|---|---|---|
mass | Neutron Star Mass(kg) | 2.78e+30 |
radius | Neutron 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
- 01rho = 3M / (4π r³)
- 024π r³ = 4π × (10000)³ = 1.257e13 m³
- 03rho = 3 × 2.78e30 / 1.257e13 = 6.63e17 kg/m³
- 04About 2.9 times nuclear density.
Frequently Asked Questions
What is nuclear density?
About 2.3 × 10¹⁷ kg/m³, the density of an atomic nucleus. Neutron stars are comparable to giant atomic nuclei.
How massive can a neutron star be?
The Tolman-Oppenheimer-Volkoff limit is roughly 2-3 solar masses. Above this, collapse to a black hole is inevitable.
What is a teaspoon of neutron star material?
About 5 ml × ~5e17 kg/m³ = ~2.5 billion tonnes. It would weigh more than Mount Everest.
Ready to run the numbers?
Open Neutron Star Density Calculator