Planetary Density Calculator
ρ = 3M / 4πR³ — bulk density is the single number that constrains what a planet is made of, without ever landing on it.
density as a planetary X-ray 🖖
We have never drilled more than 12 km into Earth, yet we know its core is iron. The trick is bulk density: ρ = 3M/(4πR³). Mass comes from timing orbits of moons or spacecraft; radius from occultations or radar altimetry. The resulting density, cross-referenced against equations of state for rock, ice, and iron at high pressure, narrows down what mix of materials must be inside. A density below ~2 g/cm³ rules out a significant rock fraction. Above ~5 g/cm³, a large iron core is nearly unavoidable. Seismology and moment-of-inertia measurements refine the picture — but density alone does most of the work before any probe is sent.
what packing tells you about a world 🖖
Density just measures how much material is crammed into a given space, in grams per cubic centimetre. Comparing that one number across worlds lets you guess what a planet is made of without ever landing. A striking case: Saturn's average density is only about 0.69 g/cm³, less than water, so a big enough ocean would let it float, while rocky Earth at 5.51 g/cm³ is the densest planet in the Solar System.
gravity fakes a planet's density 🖖
Large planets squeeze themselves: their own gravity compresses the interior, so the measured bulk density runs higher than the material's natural value. Astronomers correct for this to recover the uncompressed density. Do it, and Mercury, not Earth, comes out densest at roughly 5.3 g/cm³ versus Earth's ~4.4, betraying an outsized iron core that fills about 85% of its radius.
Example problems
- Example 1 - Mercury — 5.43 g/cm³, anomalously iron-rich core (83% of radius)
- Example 2 - venus sample case
- Example 3 - Earth — 5.51 g/cm³, rocky with a large iron-nickel core
- Example 4 - mars sample case
- Example 5 - jupiter sample case
- Example 6 - Saturn — 0.69 g/cm³, less dense than water; would float
- Example 7 - uranus sample case
- Example 8 - neptune sample case
- Example 9 - moon sample case
- Example 10 - pluto sample case