By Karl Wallulis, Updated Aug 30, 2022
Understanding a sphere’s size involves two fundamental measures: its volume (the space it occupies) and its surface area (the total area of its outer surface). When you know either the radius or diameter, you can compute both values quickly with simple mathematical formulas.
If you have the diameter (the straight line across the sphere), divide it by two. If you only have the circumference (the distance around the sphere), divide that value by 2π.
Raise the radius to the third power (multiply it by itself twice). For instance, 3³ = 3 × 3 × 3 = 27.
Use the formula V = (4/3) π r³. With π approximated as 3.1416, the coefficient (4/3) π is about 4.1888. Multiply this constant by the radius cubed to obtain the volume.
Square the radius (radius × radius).
Apply the formula A = 4 π r². Here, 4π is approximately 12.5664. Multiply this by the radius squared to get the surface area.
These straightforward calculations allow engineers, scientists, and hobbyists alike to determine a sphere’s size with precision.
