Definition:
The number of square units that will exactly cover the surface of a sphere.

Try this
Drag the orange dot to adjust the radius of the sphere and note how the area changes.

The surface area of a sphere is given by the formula
Where r is the radius of the sphere. In the figure above, drag the orange dot to change the radius of the sphere
and note how the formula is used to calculate the surface area.

This formula was discovered over two thousand years ago by the Greek philosopher Archemedes.
He also realized that the surface area of a sphere is exactly equal to the area of the curved wall of its circumscribed
cylinder, which is the smallest cylinder that can contain the sphere.
See Surface area of a cylinder.

If you know the surface area

By rearranging the above formula you can find the radius:
where a is the surface area.

Interesting facts

For a given volume, the sphere is the shape that has the smallest surface area. This why it appears in nature so much, such as water drops, bubbles and planets.

The surface area of a sphere is exactly four times the area of a circle with the same radius. You can see this in the area formula, since the area of a circle is
and the surface area of a sphere is

Things to try

In the figure above, click "hide details".

Drag the orange dot to resize the sphere.

Calculate the volume of the sphere

Click "show details" to check your answer.

In the figure above, click "reset" then uncheck "show radius"

Drag the orange dot to resize the sphere.

Calculate the radius of the sphere from the volume