Sphere Density Calculator

Density is defined as mass divided by volume: ρ = m / V. For a sphere, the volume is V = (4/3)·π·r³, so the combined formula becomes ρ = m / ((4/3)·π·r³) = 3m / (4·π·r³). Simply enter the mass and radius into the calculator above to get the density instantly.

Volume scales with the cube of the radius (V = (4/3)·π·r³), meaning a small change in radius causes a large change in volume. Since density = mass / volume, density is inversely proportional to r³. Doubling the radius of a sphere of the same mass reduces its density by a factor of eight.

Rearranging the sphere density formula gives r = ∛(3m / (4·π·ρ)). Select 'Calculate Radius from Mass and Density' mode in the calculator and enter the known mass and density values.

Rearranging ρ = m / V gives m = ρ · V = ρ · (4/3)·π·r³. Select 'Calculate Mass from Density and Radius' mode in the calculator, enter the density and radius, and the mass will be computed for you.

Water has a density of approximately 1000 kg/m³. A sphere with density less than 1000 kg/m³ will float, while one with density greater than 1000 kg/m³ will sink. Density exactly equal to 1000 kg/m³ results in neutral buoyancy.

For hollow spheres, the effective density is the total mass (shell + any interior material) divided by the total volume enclosed by the outer radius. A hollow sphere has a much lower effective density than a solid sphere of the same material and outer radius, since most of the enclosed volume is empty space.

You can use the water displacement method to find volume: submerge the sphere in water and measure the volume of water displaced. Then weigh the sphere to get its mass. Dividing mass by displaced volume gives the density without needing to measure the radius precisely.

The calculator uses SI units — kilograms (kg) for mass, meters (m) for radius, and kg/m³ for density. Common reference densities include water at ~1000 kg/m³, steel at ~7850 kg/m³, and aluminum at ~2700 kg/m³.