Surface Area of a Sphere Formula
Geometry Formulas: Area, Volume, Perimeter
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
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See Also
- Square Footage Calculator - Width × length in feet to square feet
- Square Feet to Square Meters (Sq Ft to Sq M) - Convert Square Feet to Square Meters
- Square Meters to Square Feet (Sq M to Sq Ft) - Convert Square Meters to Square Feet
- Gravel Calculator - Area to cubic yards, tons and coverage
- Topsoil Calculator - Cubic yards, weight and coverage for any area
- Multiplication Facts - Any two numbers from 1 to 9, with the working shown
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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 |
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