Sphere Volume Calculator
Enter the radius of a sphere to get its volume, surface area and great-circle circumference, drawn to scale. Click the diameter on the drawing to change it.
Dimensions
SphereResult
Volume of a sphere
A sphere encloses the most volume for its surface of any shape, following the four-thirds rule V = 4⁄3·πr³. Its surface area, 4πr², is exactly four times the area of the circle through its centre.
Editing on the drawing
Click the diameter leader on the figure and type a new value — the radius is set to half and the sphere redraws to scale.
How to find the volume of a sphere
A sphere is the most efficient solid there is: for a given surface area it encloses more volume than any other shape. A single measurement — the radius — describes it completely.
The formulas
The volume follows the four-thirds rule, and the surface area is exactly four times the area of the great circle through the centre.
Worked example
Take a sphere of radius 48.
Four-thirds of π times the radius cubed.
Four times the great-circle area.
The widest way round.
What else the calculator returns
You also get the diameter and the great-circle circumference — the distance around the sphere at its widest. Because a sphere has no flat faces to measure across, the figure uses a diameter leader you can click to edit.
Where it comes up
Sphere volumes describe balls and bearings, domes and spherical tanks, droplets and bubbles, and planets. The four-thirds rule is also why a sphere is the shape liquids take in free fall — it minimises surface for the volume held.
Frequently asked questions
How do you find the volume of a sphere?
Use the four-thirds rule with the radius: V = 4⁄3·πr³.
I have the diameter — what then?
Halve it to get the radius (r = d/2), or type the diameter on the figure and the radius is set for you.
How do I find the radius from the volume?
Rearrange the formula: r = ∛(3V / 4π).
Why is the surface area 4πr²?
It works out to exactly four times the area of the sphere's great circle, πr². The result comes from calculus and holds for every sphere.
What is a great circle?
Any circle drawn on the sphere whose centre is the sphere's own centre — the largest circle that fits on it, such as the equator, with circumference 2πr.