Sphere Density Calculator — Mass, Volume & Density of a Sphere
Enter the sphere radius and mass to calculate density, or select a common material and the calculator derives the mass automatically. See whether the sphere floats or sinks in water — all from the formula ρ = m / V.
Material (optional)
cm
g
Less dense than water — this sphere floats
0.95
g/cm³- 1
Volume of sphere
(4 ÷ 3) × π × 5³ = 523.5988V = 4⁄3 π r³ - 2
Density ρ = m ÷ V
500 ÷ 523.5988 = 0.955
How does this calculator work?
Density of a sphere ρ = m / (4⁄3 π r³). Enter mass (g) and radius (cm) to get density in g/cm³, or pick a common material and the mass is derived automatically. Spheres with ρ < 1 g/cm³ float in water; those with ρ > 1 g/cm³ sink.
Formula
How this is calculated
Density is defined as mass per unit volume: ρ = m / V. For a sphere of radius r, the volume is V = 4⁄3 π r³ — the same formula used in geometry. Combining the two gives ρ = m / (4⁄3 π r³). This calculator works in both directions: if you enter mass and radius it gives density; if you pick a known material, it uses the tabulated density to derive the mass of a sphere of your chosen radius.
All inputs use CGS units (centimetres and grams) so that the result is in g/cm³, the most common unit for material density comparisons. The density of pure water at 4 °C is exactly 1.000 g/cm³ by definition; any material with ρ < 1 g/cm³ floats on water and any with ρ > 1 g/cm³ sinks — the Archimedes principle in its simplest form.
The material density values are standard reference values at room temperature (~20 °C) from common engineering tables. Real samples may differ due to alloy composition, porosity, temperature, or impurities. The calculator assumes a solid, uniform sphere with no hollow core.
Frequently asked questions
This calculator assumes a solid sphere. For a hollow sphere, subtract the inner volume (4⁄3 π r_inner³) from the outer volume to get the material volume, then divide the shell mass by that shell volume.
Archimedes' principle states that an object floats when it displaces water with weight equal to its own weight. Because water has a density of 1 g/cm³, any object with average density below 1 g/cm³ floats; above 1 g/cm³ it sinks. For a sphere this depends purely on the ratio m/V.
Yes — the formula is unit-consistent. If you enter the radius in metres and mass in kilograms, the result will be in kg/m³ (multiply by 0.001 to convert to g/cm³). Water is approximately 1000 kg/m³ in SI units.
TG we-Calculate Editorial Team. (2026). Sphere Density Calculator — Mass, Volume & Density of a Sphere [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/sphere-density-calculator
TG we-Calculate Editorial Team. "Sphere Density Calculator — Mass, Volume & Density of a Sphere." TG we-Calculate. 2026. https://we-calculate.com/calculator/sphere-density-calculator.
TG we-Calculate Editorial Team, "Sphere Density Calculator — Mass, Volume & Density of a Sphere," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/sphere-density-calculator
@misc{wecalculate_sphere_density_calculator, title = {Sphere Density Calculator — Mass, Volume & Density of a Sphere}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/sphere-density-calculator}}, year = {2026}, note = {TG we-Calculate} }
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