# Cylinder Volume Calculator

Luis Anaya

15 Jan 2021

A cylinder is a three-dimensional shape formed from two, flat circular bases and one curved surface that connects those bases to create the three-dimensional cylinder.

The cylinder's volume is the total amount of space that the cylindrical shape takes up.

Calculating the volume of a cylinder can be helpful if you need to know how much of something you could fit inside the cylinder, for example so you could order the correct amount of material to completely fill a cylinder without having excess waste left over.

The formula to calculate the volume of a cylinder is:

V = π * r² * h

Where:

V = Volume of cylinder

π = pi (pi has the value 3.141592 which is the ratio a circle's circumference to its diameter)

r = radius of cylinder

h = height of cylinder

### Cylinder Geometry

In geometric terms the base, top and the connecting surface in between are called faces.

Therefore we can described a cylinder as having 3 faces:

- 1. Circular base
- 2. Circular top
- 3. Curved surface

Where those faces meet is called an edge. A cylinder has two edges:

- 1. Where the base connects to the curved surface
- 2. Where the curved surface connects to the top

Three dimensional shapes have a third property called a vertex. A vertex is a corner where multiple edges meet. A cylinder does not have any vertices.

### Example Calculations

#### Example 1

A cylinder has a radius of 5 and a height of 10.

Substituting those values into the cylinder volume formula gives:

V = π * 5² * 10

V = π * 25 * 10

V = 785

The volume of the cylinder is 785.

#### Example 2

A cylinder has a radius of 12 and a height of 6.

Substituting those values into the cylinder volume formula gives:

V = π * 12² * 6

V = π * 144 * 6

V = 2714

The volume of the cylinder is 2714.

### Units of Volume

In the examples above no units are specified. Let's assume we are measuring the cylinder radius and height in centimetres. The calculated volume would therefore be measured in cubic centimetres, denoted cm3.

Updating our earlier example, a cylinder has a radius of 5cm and a height of 10cm.

Substituting those values into the cylinder volume formula gives:

V = π * 5² * 10

V = π * 25 * 10

V = 785 cm³

But when you buy can of drink, for example, the volume is not reported in terms of cm3, it tends to be reported in terms of centilitres (cl). There are ten cm3 in one centilitre. Therefore the volume of the example cylinder measured in centilitres is:

V = 785 / 10

V = 78.5 cl

### Examples of cylinders

The calculator on this page is accurate for right, circular cylinders, which are characterised by perfectly circular bases with both bases being perfectly aligned. However there are other types of cylinder, some which have different formulas for calculating their volume:

#### Oblique Cylinder

#### Elliptical Cylinder

#### Hollow Cylinder

### FAQs

Have a question about our this calculator? See our list of frequently asked questions below.

- What is the formula for calculating the volume of a cylinder?
- V = π * r² * h.
- What is the formula for calculating the radius of a cylinder?
- r = SQRRT(V / (π * h)).
- What is the formula for calculating the height of a cylinder?
- h = V / (π * r²).
- How many faces does a cylinder have?
- A cylinder has 3 faces.
- How many edges does a cylinder have?
- A cylinder has 2 edges.
- How many vertices does a cylinder have?
- A cylinder has no vertices.