HesapHanem

Planet Density Calculator

Find the mean density of a celestial body.

How it is calculated

The tool treats the body as a perfect sphere: V = (4/3) × π × r³ and ρ = M ÷ V. Mass M is in kilograms, radius r is in metres, and the answer is in kg/m³, rounded to two decimals. Both values must be greater than zero. Scientific notation such as 5.972e24 is accepted, which is handy for planetary masses. Because the real radius used is the mean radius, a flattened or irregular body (a fast-spinning planet, a small asteroid) will not match its true volume exactly. To convert to g/cm³, divide the result by 1000.

Worked example

Using Earth: mass 5.972e24 kg, radius 6,371,000 m. Step 1: r³ = 6,371,000³ ≈ 2.586 × 1020 m³. Step 2: V = 4/3 × π × r³ ≈ 1.0832 × 1021 m³. Step 3: ρ = 5.972 × 1024 ÷ 1.0832 × 1021 = 5,513.26 kg/m³, which is about 5.51 g/cm³.

Try this example →

Common mistakes

  • Entering the radius in kilometres while the mass is in kilograms; a radius of 6371 instead of 6,371,000 makes the density a billion times too large.
  • Entering the diameter instead of the radius, which makes the density eight times too small.
  • Typing mass in Earth masses or solar masses without converting to kilograms.
  • Reading kg/m³ as g/cm³: water is 1000 kg/m³ but 1 g/cm³.
  • Assuming the result is the density at the surface or core; it is a single average over the whole body.

About this calculator

This calculator finds a celestial body's mean density, ρ = M / ((4/3)·π·r³), by dividing its mass by the volume of a sphere with its radius — a single number that reveals a great deal about what a planet or moon is made of even when its interior can't be observed directly. Earth's mean density of about 5.51 g/cm³ points to a substantial iron-nickel core, while Saturn's density of just 0.69 g/cm³ (lower than water) reflects a body made almost entirely of hydrogen and helium gas.

Astronomers use mean density as a first diagnostic when characterizing a newly discovered exoplanet from its measured mass and radius, distinguishing likely rocky “super-Earths” from gas- or ice-dominated “mini-Neptunes” before any spectroscopic data is available. Planetary scientists studying solar-system bodies, astronomy students, and enthusiasts following exoplanet discovery announcements all use this calculator to turn a raw mass-and-radius measurement into a clue about composition.

Was this helpful?

You can pick up to 3 reactions.

Comments (1)

  • Editorial team

    Water at 1,000 kg/m3 makes a handy yardstick. Earth, with a mass of 5.972e24 kg and a mean radius of 6,371,000 m, comes out near 5,500, the densest of the major planets. Saturn, using about 5.683e26 kg and 58,232,000 m, lands near 690, lighter than water. Compare your result with a published value for the same body. Which planet or moon did you try, and did it match?

Popular calculators

Loan Calculator

Monthly payment, total interest and full amortization schedule.

Percentage Calculator

Percent change, percent of, and ratio calculations.

Discount Calculator

Calculate final price, savings, and discount amount.

BMI Calculator

Body mass index from height and weight (metric or imperial).

Age Calculator

Compute your exact age in years, months and days from a birth date.

Compound Interest Calculator

Calculate the final amount and interest earned with compounding.

All Calculators