Cylinder Volume Calculator
Calculate the volume of a cylinder using radius and height. Perfect for engineering, manufacturing, plumbing, and packaging applications where you need to determine capacity or material requirements.
Calculate Cylinder Volume
Enter the radius and height of your cylinder:
V = Ο Γ radiusΒ² Γ height
Ο β 3.14159 (use Math.PI for precision)
Understanding Cylinder Volume
A cylinder is a three-dimensional solid with two parallel circular bases connected by a curved lateral surface. The volume of a cylinder represents the total space enclosed by its surfaces and is calculated by multiplying the area of the circular base by the height.
Cylinder Properties
π² Cylinder Definition
A cylinder is a three-dimensional shape with two parallel circular bases of equal size connected by a curved surface. The line joining the centers of the two bases is called the axis.
π Volume Formula
V = ΟrΒ²h
Where Ο β 3.14159, r is the radius, and h is the height
The volume equals the area of the base multiplied by the height
π Surface Area
Total Surface Area = 2ΟrΒ² + 2Οrh
Two circular bases + lateral surface area
Lateral surface area = circumference Γ height
π‘ Pro Tip: The volume formula V = ΟrΒ²h comes from the fact that a cylinder can be "unrolled" into a rectangle with width equal to the circumference (2Οr) and height equal to the cylinder's height. The area of this rectangle equals the lateral surface area.
Common Cylinder Examples
| Radius | Height | Volume | Real-World Example |
|---|---|---|---|
| 5 cm | 10 cm | 785.4 cmΒ³ | Standard bucket |
| 7.5 cm | 15 cm | 2,356 cmΒ³ | Large paint can |
| 10 cm | 20 cm | 6,283 cmΒ³ | Storage drum |
| 15 cm | 30 cm | 21,206 cmΒ³ | Industrial tank |
| 2.5 cm | 5 cm | 98.2 cmΒ³ | Coffee can |
| 3 cm | 8 cm | 226.2 cmΒ³ | Soup can |
Volume vs Capacity
π Geometric Volume
The mathematical volume of the cylinder
Includes the exact internal space
Measured in cubic units (cmΒ³, mΒ³, ftΒ³)
Used for material calculations
π₯ Liquid Capacity
The amount of liquid the cylinder can hold
Slightly less than geometric volume
Measured in liters, gallons, fluid ounces
Used for filling calculations
βοΈ Material Volume
The volume of material needed to make the cylinder
Includes wall thickness for hollow cylinders
Used in manufacturing calculations
Real-World Applications
π Manufacturing & Engineering
Storage tank capacity calculations
Pipe volume for fluid flow systems
Pressure vessel design
Heat exchanger sizing
Material requirements planning
ποΈ Construction & Plumbing
Water tank and reservoir sizing
Drainage pipe volume calculations
Concrete column capacity
HVAC ductwork design
Well and borehole volumes
π Home & Kitchen
Paint can volume for coverage
Cooking oil container capacity
Beverage can and bottle sizing
Spray can propellant calculations
Cleaning product containers
π Automotive & Transportation
Fuel tank capacity calculations
Oil can and lubricant containers
Compressed gas cylinder volumes
Tire air volume calculations
Engine cylinder displacement
Liquid Volume Conversions
| Volume (Liters) | US Gallons | UK Gallons | Fluid Ounces | Cups |
|---|---|---|---|---|
| 1 L | 0.264 gal | 0.220 gal | 33.8 fl oz | 4.23 cups |
| 5 L | 1.321 gal | 1.099 gal | 169.1 fl oz | 21.13 cups |
| 10 L | 2.642 gal | 2.199 gal | 338.1 fl oz | 42.27 cups |
| 20 L | 5.283 gal | 4.399 gal | 676.3 fl oz | 84.54 cups |
| 50 L | 13.209 gal | 10.997 gal | 1,690.7 fl oz | 211.34 cups |
Special Cylinder Types
π² Right Cylinder
The most common type with bases perpendicular to the axis
Height measured along the axis
All our calculations use right cylinders
π Oblique Cylinder
Bases are not perpendicular to the axis
Height measured perpendicular to bases
More complex volume calculations
π― Hollow Cylinder
Cylinder with a hole through the center
Volume = outer volume - inner volume
Used for pipes and tubes
Engineering Considerations
π οΈ Material Thickness
For hollow cylinders (pipes, tubes)
Inner radius = outer radius - thickness
Volume calculations must account for this
π‘οΈ Temperature Effects
Materials expand with temperature
Coefficient of thermal expansion
Affects both dimensions and volume
βοΈ Weight Calculations
Weight = volume Γ density
Different materials have different densities
Important for structural engineering