# Circumference

Template:Pi box Circumference (from Latin circumferentia, meaning "carrying around") is the linear distance around the edge of a closed curve or circular object. The circumference of a circle is of special importance in geometry and trigonometry. Informally "circumference" may also refer to the edge itself rather than to the length of the edge. Circumference is a special case of perimeter: the perimeter is the length around any closed figure, but conventionally "perimeter" is typically used in reference to a polygon while "circumference" typically refers to a continuously differentiable curve.

## Circumference of a circle

File:Circle-withsegments.svg
Circle illustration with circumference (C) in black, diameter (D) in cyan, radius (R) in red, and centre or origin (O) in magenta. Circumference = π × diameter = 2 × π × radius.

The circumference of a circle is the distance around it. The term is used when measuring physical objects, as well as when considering abstract geometric forms.

File:2pi-unrolled.gif
When a circle's radius is 1, its circumference is 2π.
File:Pi-unrolled-720.gif
When a circle's diameter is 1, its circumference is π.

### Relationship with Pi

The circumference of a circle relates to one of the most important mathematical constants in all of mathematics. This constant, pi, is represented by the Greek letter π. The numerical value of π is 3.14159 26535 89793 ... (see ). Pi is defined as the ratio of a circle's circumference to its diameter, or equivalently as the ratio of the circumference to twice the radius. Thus

${C}=\pi \cdot {d}=2\pi \cdot {r}.\!$ The use of the mathematical constant π is ubiquitous in mathematics, engineering, and science. While the constant ratio of circumference to radius ${C}/{r}=2\pi$ also has many uses in mathematics, engineering, and science, it is not formally named. These uses include but are not limited to radians, computer programming, and physical constants.

## Circumference of an ellipse

The circumference of an ellipse can be expressed in terms of the complete elliptic integral of the second kind.

## Circumference of a graph

In graph theory the circumference of a graph refers to the longest cycle contained in that graph.