Sphere Volume Calculator
Find the volume of a sphere from its radius, together with its surface area, diameter and great-circle circumference.
How it works
Volume = 4⁄3 · π · r³ · Surface area = 4πr² · Diameter = 2r · Circumference = 2πr
The sphere is the shape that encloses the most volume for the least surface area, which is why bubbles and planets are round. Its volume grows with the cube of the radius, 4⁄3·πr³, while its surface area grows with the square, 4πr². A neat link ties them together: the volume equals the radius times one third of the surface area, V = r·(4πr²)/3.
Worked example
For radius 6: volume = 4⁄3 × π × 6³ = 4⁄3 × π × 216 = 288π ≈ 904.7787 cubic units. The surface area is 4π × 6² = 144π ≈ 452.3893, the diameter is 12, and the great-circle circumference is 2π × 6 = 12π ≈ 37.6991.
Sources: Sphere — Wikipedia
Frequently asked questions
How does doubling the radius change the volume?
Volume scales with the cube of the radius, so doubling r multiplies the volume by 2³ = 8. A ball twice as wide holds eight times as much, even though its surface area only quadruples.
Can I calculate from the diameter instead?
Yes — just halve it first. If you know the diameter d, the radius is r = d ÷ 2, then apply 4⁄3·πr³. This calculator also reports the diameter alongside the radius for convenience.
What is the great-circle circumference?
It is the circumference of the largest circle you can draw on the sphere — one passing through the centre, like the equator on a globe. It equals 2πr, the same as a flat circle of that radius.
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This calculator is for educational purposes. Double-check important results before acting on them.