How this calculation works
A sphere contains points at an equal distance from its centre. Enter the radius, not the diameter. Volume uses cubic units and surface area uses square units.
Volume = 4πr³/3; surface area = 4πr²A worked example
A sphere with radius 3 has a volume of approximately 113.097336 cubic units.
Good to know
Uses the stated formula and assumptions. Displayed decimal values are rounded; use consistent units for all inputs.
Surface and volume grow at different speeds
Double a sphere’s radius and its surface area grows by a factor of four, while its volume grows by a factor of eight. As a sphere gets larger, the amount of enclosed space therefore rises faster than its outer surface.
The ratio of surface area to volume is 3/r for a positive radius. That mathematical ratio helps explain why a small and a large spherical model can have very different amounts of surface relative to the space inside them.
This is a solid sphere, not a hollow shell
The volume is the full enclosed volume. To find material in a hollow sphere, subtract the inner sphere’s volume from the outer sphere’s volume using consistently measured radii. Thickness cannot simply be multiplied by total volume.
The input is radius, not diameter. A measured width of 10 units corresponds to radius 5. Surface area is in square units and volume is in cubic units.
A few questions, answered
Does this include a shell thickness?
No. It returns the outer surface area and the full enclosed volume from one radius.
What does radius zero produce?
Zero area and zero volume, the limiting degenerate case.