Circumference (from Latin circumferentia, meaning "carrying around") is the linear distance around the edge of a closed curve or circular object.^{[1]} 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.

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.

When a circle's radius is 1, its circumference is 2π.

When a circle's diameter is 1, its circumference is π.

Relationship with Pi[edit]

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 letterπ. The numerical value of π is 3.14159 26535 89793 ... (see A000796). 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

The use of the mathematical constant π is ubiquitous in mathematics, engineering, and science. While the constant ratio of circumference to radius 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.