How to Calculate the Volume of a Cylinder
The volume of a cylinder tells you how much space it occupies—or how much liquid it can hold. It's one of the most useful geometry formulas in engineering, cooking, and manufacturing.
The Formula
Volume = π × r² × h
Where:
- r = radius of the circular base
- h = height of the cylinder
- π ≈ 3.14159
Step-by-Step Example
Find the volume of a cylinder with radius 4 cm and height 15 cm.
- Square the radius: 4² = 16
- Multiply by π: 16 × 3.14159 = 50.265
- Multiply by height: 50.265 × 15 = 753.98 cm³
Real-World Applications
- Water tanks: A cylindrical tank with r = 1.5 m and h = 3 m holds π × 2.25 × 3 = 21.21 m³ ≈ 21,210 liters
- Engine cylinders: Engine displacement is calculated as the total volume of all cylinders
- Cooking: Calculating how much a pot or pan can hold
Volume in Different Units
| Radius | Height | Volume |
|---|---|---|
| 5 cm | 10 cm | 785.4 cm³ |
| 10 cm | 20 cm | 6,283 cm³ |
| 1 m | 2 m | 6.28 m³ |
| 3 in | 12 in | 339.3 in³ |
Converting Volume to Liters
1 cm³ = 1 mL = 0.001 liter. So a cylinder with volume 785.4 cm³ holds 785.4 mL or 0.785 liters.
Use our cylinder volume calculator for any dimensions.