How to Find and Calculate the Weight of a Sphere

The same sized spheres with unlike densities will weigh differently.
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A sphere's weight can be found through means other than scales. A sphere is a three-dimensional object with properties derived from the circle — such as its volume formula, 4/3 * pi * radius^3, which has both the math constant pi, the ratio of a circle's circumference to its diameter, which is approximately 3.142, and a radius, the distance from the center to the sphere's edge, based on the circle's radius. With the sphere's volume, you can find its weight by the sphere's density, a ratio of weight-to-volume, without having to weigh anything.

    Cube the sphere's radius and then multiply it by 4/3pi to calculate its volume. For this example, let the radius be 10 cm. Cubing 10 cm results in 1,000 cm^3, and multiplying 1,000 by 4/3pi results in approximately 4,188.79 cm^3.

    Find the density of the sphere. In this example, let the density be 100 mg/cm^3.

    Multiply the sphere's volume by its density to calculate its weight. Concluding this example, 4,188.79 cm^3 multiplied by 100 mg/cm^3 results in 418,879 mg.


    • Spheres that are real and small enough can also be weighed on conventional scales.