How to Calculate the Volume of a Sphere
The sphere is one of the most elegant shapes in geometry, and its volume formula is surprisingly simple for such a three-dimensional object. It appears in physics, engineering, medicine, and everyday life—from balloons to ball bearings.
The Formula
Volume = (4/3) × π × r³
Where r is the radius and π ≈ 3.14159.
Step-by-Step Example
Find the volume of a sphere with radius 6 cm.
- Cube the radius: 6³ = 216
- Multiply by π: 216 × 3.14159 = 678.58
- Multiply by 4/3: 678.58 × (4/3) = 904.78 cm³
Common Sphere Volumes
| Radius | Volume |
|---|---|
| 1 cm | 4.19 cm³ |
| 5 cm | 523.6 cm³ |
| 10 cm | 4,189 cm³ |
| 1 m | 4.19 m³ |
| 12.7 cm (5 in) | 8,579 cm³ |
Sphere Surface Area (Bonus)
The surface area of a sphere is:
SA = 4πr²
For r = 6 cm: 4 × π × 36 = 452.39 cm²
Real-World Applications
- Medicine: Tumor volume estimation uses sphere approximations; a spherical tumor with r = 1 cm has volume ≈ 4.19 cm³
- Earth science: Earth's volume ≈ 1.08 × 10¹² km³ (using r = 6,371 km)
- Manufacturing: Ball bearings, spherical tanks, and pressure vessels
Use our sphere volume calculator to compute any sphere's volume instantly.