What is a cylinder?
A cylinder is a three-dimensional geometric shape with two parallel and congruent circular bases connected by a curved surface. A right circular cylinder is commonly described using two dimensions: the radius of its circular base and its height.
Cylinder calculations are commonly used in geometry, engineering, construction, manufacturing, packaging, storage, tanks, pipes, columns, containers, and many other practical applications.
How to calculate the volume of a cylinder
The volume of a cylinder represents the amount of three-dimensional space enclosed inside it. To calculate cylinder volume, multiply the area of the circular base by the cylinder height.
Cylinder volume formula
V = πr²h
Where:
- V = cylinder volume
- r = radius of the circular base
- h = height of the cylinder
- π ≈ 3.14159265359
For example, if the radius is 2 meters and the height is 5 meters:
V = π × 2² × 5
V = 20π ≈ 62.832 m³
How to calculate the base area
Each end of a cylinder is a circle. The area of a circle is calculated using the radius squared multiplied by π.
Base area formula
A = πr²
Because a cylinder has two identical circular bases, this area is used twice when calculating total surface area.
Cylinder surface area formulas
Cylinder surface area can be divided into the curved surface area and the two circular base areas.
Curved surface area
CSA = 2πrh
This measures only the curved outside surface and does not include the two circular bases.
Total surface area
TSA = 2πr(r+h)
This includes the curved surface and both circular bases.
Radius and diameter of a cylinder
The radius is the distance from the center of the circular base to its edge. The diameter passes through the center of the circle from one side to the other.
Diameter formula
d = 2r
If you know the diameter but need the radius, divide the diameter by 2:
r = d ÷ 2
Cylinder calculation example
Suppose a cylinder has a radius of 2 meters and a height of 5 meters. The main measurements are:
| Measurement | Formula | Result |
|---|---|---|
| Volume | π × 2² × 5 | ≈ 62.832 m³ |
| Base area | π × 2² | ≈ 12.566 m² |
| Curved surface area | 2π × 2 × 5 | ≈ 62.832 m² |
| Total surface area | 2π × 2 × 7 | ≈ 87.965 m² |
Common uses of cylinder calculations
Cylinder calculations are useful in many practical situations. Engineers and construction professionals may use cylinder volume calculations for tanks, pipes, silos, columns, containers, and other cylindrical structures.
Surface area calculations can be useful when estimating coating, insulation, paint, wrapping, material requirements, or the exposed area of a cylindrical object.
Frequently asked questions
What is the formula for the volume of a cylinder?
The volume of a cylinder is V = πr²h, where r is the radius and h is the height.
What is the formula for cylinder surface area?
The total surface area is TSA = 2πr(r+h). This includes the curved surface and both circular bases.
What is the curved surface area of a cylinder?
The curved surface area is CSA = 2πrh. It excludes the two circular bases.
Can I calculate a cylinder using diameter?
Yes. If the diameter is known, divide it by two to find the radius before using the cylinder formulas.
Which units does this calculator support?
You can enter dimensions in millimeters, centimeters, meters, inches, or feet.
What is the difference between volume and surface area?
Volume measures the three-dimensional space inside a cylinder and uses cubic units. Surface area measures the outside area and uses square units.