Sphere: properties & formulas
A sphere’s surface consists of points at a fixed distance from its center. Its volume grows with the cube of the radius, while surface area grows with the square.
- 1 curved surface
- 0 flat faces
- 0 edges
- 0 vertices
Properties of a sphere
| Flat faces | None; one curved surface |
|---|---|
| Edges / vertices | None |
| Radius | Every surface point is r from the center |
| Great circle | The largest circle on a sphere, with radius r |
| Cross-sections | Always circles (or a single point at a tangent) |
| Symmetry | Infinitely many planes of symmetry |
Sphere formulas
| Volume | V = 4πr³ / 3 |
|---|---|
| Surface area | S = 4πr² |
| Diameter | d = 2r |
| Radius from volume | r = ∛(3V / 4π) |
| Hemisphere volume | V = 2πr³ / 3 |
Sphere volume & surface area calculator
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Use the same unit for every dimension. Changing the unit relabels the measurements; it does not convert them.
From dimensions to an answer
A worked example
A sphere of radius 3 has volume 36π ≈ 113.097 cubic units and surface area 36π ≈ 113.097 square units. The numerical equality does not make the quantities interchangeable.
Sphere: common questions
Wondering about the why? Start here.
How many faces, edges, and vertices does a sphere have?
A sphere has one continuous curved surface and no flat faces, no edges, and no vertices. Every point on its surface is the same distance, the radius, from the center.
How do I calculate a sphere’s volume and surface area?
For radius r, volume is 4πr³/3 and surface area is 4πr². Enter the radius, not the diameter. A sphere with radius 3 has volume 36π cubic units and surface area 36π square units.
Understand volume and surface areaWhat happens when a sphere’s radius doubles?
Its surface area becomes four times as large because area depends on r². Its volume becomes eight times as large because volume depends on r³. These scale factors apply when every length of a similar solid changes by the same factor.
Learn the scaling rules