Planet Density Calculator Formula
Understand the math behind the planet density calculator. Each variable explained with a worked example.
Formulas Used
Mean Density
density = 3 * mass / (4 * pi * pow(radius, 3))Density (g/cm3)
density_gcc = 3 * mass / (4 * pi * pow(radius, 3)) / 1000Variables
| Variable | Description | Default |
|---|---|---|
mass | Planet Mass(kg) | 5.972e+24 |
radius | Planet Radius(m) | 6371000 |
How It Works
Mean Bulk Density of a Planet
The average density is found by dividing the total mass by the total volume.
Formula
rho = M / V = 3M / (4 pi R cubed)
Density helps distinguish rocky planets (about 5 g/cm3) from gas giants (about 1 g/cm3). Earth's mean density is about 5.51 g/cm3.
Worked Example
Earth: M = 5.972e24 kg, R = 6.371e6 m.
- 01rho = 3M / (4 pi R cubed)
- 02R cubed = (6.371e6)^3 = 2.586e20
- 034 pi R cubed = 3.254e21
- 04rho = 3 * 5.972e24 / 3.254e21
- 05rho = 5 504 kg/m3 = 5.50 g/cm3
Frequently Asked Questions
Why is Earth denser than Mars?
Earth has a larger iron core relative to its size. Mars, being smaller, lost more of its internal heat and has a proportionally smaller core.
Can density reveal a planet's composition?
Yes. A density above about 5 g/cm3 suggests an iron-rich rocky body. Below about 2 g/cm3 indicates a gas or ice giant.
Which planet has the lowest density?
Saturn, with a mean density of about 0.687 g/cm3, less than water.
Ready to run the numbers?
Open Planet Density Calculator