Find a sphere's density from its mass and diameter. Uses density = mass / volume, where volume = (4/3) x pi x radius^3.
Results
Calculated
Density (g/cm³)
—
Mass ÷ volume
Density (kg/m³)
—
SI equivalent (× 1000)
Volume (cm³)
—
(4/3) × π × radius³
Radius (cm)
—
Diameter ÷ 2
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How to use this calculator
Enter the sphere's mass in grams and its diameter in centimeters, then click Calculate. The calculator finds the radius, computes the sphere's volume, and divides mass by volume to get density. Click Clear to reset the fields and start a new calculation.
The formula
Density is defined as mass per unit volume: density = mass / volume. For a sphere, volume is calculated from the radius using volume = (4/3) × π × radius³. Since diameter is usually easier to measure than radius, this calculator accepts diameter and halves it internally (radius = diameter ÷ 2) before applying the volume formula.
Understanding the inputs
Measure diameter across the widest point of the sphere — for a solid ball, that means spanning it with calipers or a ruler through its center. Mass should be the total mass of the sphere, measured on a scale in grams. This calculator assumes a solid, uniform, perfectly spherical object; hollow spheres or irregular shapes will not give an accurate density with this method.
Interpreting the results
Density in g/cm³ is the primary result, with the equivalent value in kg/m³ shown alongside it (multiply g/cm³ by 1000 to get kg/m³). The volume and radius cards let you verify the intermediate steps. Compare your result to known material densities — water is about 1.0 g/cm³, aluminum about 2.7 g/cm³, and steel about 7.85 g/cm³ — to get a sense of what the sphere might be made of.
Frequently Asked Questions
What is the formula for sphere density?
Density equals mass divided by volume: density = mass / volume. For a sphere, volume is found from the radius using volume = (4/3) × π × radius³. If you measure the diameter instead, divide it by 2 to get the radius first. The result is mass per unit volume, commonly expressed in g/cm³ or kg/m³.
Should I measure radius or diameter?
Either works, but diameter is usually easier to measure directly with calipers or a ruler, since you can span the widest point of the sphere in one motion. This calculator asks for diameter and halves it internally to get the radius used in the volume formula.
Why does my result not match a known material's density?
This calculator assumes a solid, uniform sphere. If the object is hollow, has an internal cavity, contains mixed materials, or your mass or diameter measurement has error, the computed density will differ from the textbook value for a pure, solid version of that material. Small measurement errors are amplified because volume depends on radius cubed.
What are typical densities of common materials?
For reference, water is about 1.0 g/cm³, aluminum about 2.7 g/cm³, steel about 7.85 g/cm³, lead about 11.3 g/cm³, and typical solid plastics range roughly 0.9 to 1.4 g/cm³. Comparing your calculated density to these reference values can help identify what a sphere is likely made of.