Surface Area of a Sphere Formula

Geometry Formulas: Area, Volume, Perimeter
Formula:

What is the formula for the surface area of a sphere?

Answer

Surface area of a sphere
S = 4 · π · r²

Here r is the radius. The result comes out in square units.

Where the formula comes from

S = 4 · π · r²

Exactly four times the area of the circle you would get by slicing the sphere through the middle — another of Archimedes’ results, and the reason a globe’s surface is four times its own shadow.

Worked examples

Let r = 3. Then the surface area of a sphere ≈ 113.1 square units.

Let r = 5.5. Then the surface area of a sphere ≈ 380.13 square units.

The common mistake

Reaching for the volume formula because both mention r and π. The surface has r squared and a 4; the volume has r cubed and a 4/3. One comes out in m², the other in m³.

Other quantities: Sphere

Related Calculations

See Also

Geometry Formulas: Area, Volume, Perimeter

These are the formulas for the area, perimeter, circumference, volume and surface area of the standard shapes — 31 of them. Each page shows not only the formula but where it comes from, what every letter stands for, two worked examples and the mistake that this particular shape invites. For example, it can help you find out what is the formula for the surface area of a sphere? (The answer is: S = 4 · π · r²). Pick the pair — "Area of a circle", for instance — and hit the "Find out" button.
Geometry Formulas: Area, Volume, Perimeter
Formula:

Values from the Formula

If r =Surface area
1≈ 12.57 square units
2≈ 50.27 square units
3≈ 113.1 square units
4≈ 201.06 square units
5≈ 314.16 square units
10≈ 1,256.64 square units

FAQ

What is the formula for the surface area of a sphere?

Surface area of a sphere S = 4 · π · r²

Where does this formula come from?

Exactly four times the area of the circle you would get by slicing the sphere through the middle — another of Archimedes’ results, and the reason a globe’s surface is four times its own shadow.

What is the most common mistake here?

Reaching for the volume formula because both mention r and π. The surface has r squared and a 4; the volume has r cubed and a 4/3. One comes out in m², the other in m³.

How do I use this formula?

Put your own numbers in place of the letters. With r = 5.5, for instance, the formula S = 4 · π · r² gives ≈ 380.13 square units.

See Also