Surface Area of a Sphere

Calculates the surface area of a sphere as 4 × π × radius², exactly four times the area πr² of a circle with the same radius.

Explanation

The surface area of a sphere is the area of its curved outer skin, and it depends on nothing but the radius.

S = 4 \pi r^2

$S$ — the surface area
$r$ — the radius
$\pi$ — pi

Example

With the default radius $r = 5$ :

S = 4 \pi \times 5^2 = 100\pi \approx 314.1593

The surface area is about 314.1593.

Exactly four circles

A circle of the same radius has area $\pi r^2$ , so the sphere's skin measures precisely four times as much. The numbers bear this out: a circle of radius 5 has area about 78.5398, and four of those come to 314.1593. Picture peeling the sphere and flattening the pieces onto circles of the same radius; they fill exactly four of them.

Watch out

The surface area is $4\pi r^2$ while the volume is $\dfrac{4}{3}\pi r^3$ . Both carry a 4 and a $\pi$ , which invites mix-ups, but the surface area squares the radius and the volume cubes it. The units differ accordingly: cm² for the surface, cm³ for the volume. The radius must be a positive number.