Sphere Calculator

Created by Georgi Georgiev
Last updated: Aug 20, 2026

1. Find the volume of a sphere
2. Calculate the surface area of a sphere
3. Find the diameter from volume or area
4. Examples for solving a sphere

    Find the volume of a sphere

The formula for the volume of a sphere is:

4/3 x π x (diameter / 2)³

Since (diameter / 2) is just the radius (d = 2 x r), another way to write the equation is as:

4/3 x π x radius³

These same equations are used in our dedicated volume of a sphere calculator. If the area is given instead, first find the diameter using diameter = √(A / π), then calculate the volume using the first equation above.

The unit of the radius or diameter measurement may need to be converted before being used in the equations above, to get the desired output unit. E.g. convert to in, ft, meters, cm to find the volume in cubic inches, cubic feet, cubic meters, cubic centimeters, and so on.

    Calculate the surface area of a sphere

The equation to calculate the surface area of a sphere, sometimes erroneously referred to as the "area of a sphere", is:

Area = 4 * π * (diameter / 2)²

It can be written in terms of the radius as such

Area = 4 * π * radius²

Just like when solving for volume, mind the units used in the calculations to get the outcome in the desired square unit (sq ft, sq in, sq cm, etc.).

    Find the diameter from volume or area

If the radius is given, the diameter is just two times the radius, so this one is very trivial. The diameter can also be calculated from the volume by using the formula:

Diameter = ∛(6 * Volume / π)

It can also be found from the surface area using:

Diameter = √(Area / π)

The result is in the same unit as the input, without the "cubic" or "square" part. So if the volume is in cubic feet (cu ft), the diameter will be in feet (ft). If the area is in square centimeters (sq cm), the diameter will be in centimeters (cm). Our metric converter can help convert between metric and imperial units.

    Examples for solving a sphere

To solve a sphere by its diameter, follow these steps. If the diameter is given as being 4 feet in length, the radius is just 4 / 2 = 2 feet. Then:

Calculate the sphere volume by using the formula above to get 4/3 x 3.14159 x (4/2)³ = 4.1866 x 8 = 33.4928 ft³ (cubic feet).

Calculate the surface area by 4 x 3.14159 x (4 / 2)² = 12.56636 x 4 = 50.26544 ft² (square feet).