Sphere Calculator

Known value

Value

Result

Volume523.598776
Surface area314.159265
Radius5
Diameter10
Great circle area78.539816
Equator length31.415927

One number is enough

Every property of a sphere from any one known value: radius, diameter, volume or surface area.

A sphere is described by a single number, so any known quantity leads to all the others. You can enter the volume or the surface area instead of the radius and get the radius back — which is what problems ask for just as often.

Note how the two scale differently: volume goes as the cube of the radius while area goes as the square. Double the radius and area quadruples while volume grows eightfold — the same reason large animals lose heat more slowly than small ones.

What this calculator shows

Volume and surface area
Radius and diameter, even when you supplied volume or area
The area of a great circle and the equatorial circumference

What to keep in mind

The formulas are exact: V = 4/3 πr³ and S = 4πr², with no approximation.
Going back from volume uses a cube root and from area a square root.

FAQs

How do I find the radius from the volume?

Take the cube root of 3V/4π. Switch the selector to volume and the calculator does it for you.

Why is the surface 4πr²?

It is exactly four great circles. Archimedes proved it long before calculus existed.

What is the difference between a sphere and a ball?

A sphere is the surface; a ball is the surface plus everything inside. So a sphere has area, and a ball also has volume.

How does volume scale with radius?

Cubically. A ten percent larger radius means a 33 percent larger volume — worth remembering when choosing containers.

Worked example

A sphere of radius 5

Input: Radius 5

Output: Volume 523.6, surface area 314.16

Note: The surface is exactly four times the great circle — a result Archimedes valued enough to want a sphere and cylinder carved on his tomb.

Useful links

All tools in Math & Statistics

Sphere Calculator

Result

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Cone Calculator

Circle Calculator

Useful links