Sphere Volume & Surface Area Calculator
Enter a sphere’s radius to get its volume, surface area, diameter and great-circle circumference in one step.
How it works
V = (4/3)·π·r³ · Surface area = 4·π·r² · Circumference = 2·π·r
A sphere is the set of all points a fixed distance (the radius) from a centre. Its volume grows with the cube of the radius, so doubling the radius multiplies the volume eightfold, while its surface area grows with the square of the radius and so quadruples. The great-circle circumference is the distance around the sphere through its widest cross-section — the same as a circle of the same radius.
Worked example
For a radius of 5 units: volume = (4/3)·π·5³ = (4/3)·π·125 ≈ 523.60 units³; surface area = 4·π·5² = 100π ≈ 314.16 units²; the great-circle circumference is 2·π·5 = 10π ≈ 31.42 units.
Sources: Sphere — Wolfram MathWorld
Frequently asked questions
Why does volume grow faster than surface area?
Volume scales with r³ and surface area with r². As the radius grows, volume outpaces surface area — the reason large animals lose heat more slowly than small ones, since heat loss depends on surface area but heat production on volume.
What is the great-circle circumference?
It is the perimeter of the largest circle you can draw on the sphere, one passing through its centre. It equals 2πr, exactly the circumference of a flat circle with the same radius.
How do I work backwards from the volume to the radius?
Rearrange the volume formula: r = ∛(3V / 4π). For a volume of 523.6 units³ this returns r = 5 units.
Related calculators
This calculator is for educational purposes. Double-check important results before acting on them.