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The circumference (from Latin circumferentia, meaning "carrying around") of a closed curve or circular object is the linear distance around its edge.[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.

Circumference of a circle[edit]

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 diameter is 1, its circumference is π.
When a circle's radius is 1—called a unit circle—its circumference is 2π.

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 letter π. The numerical value of π is 3.14159 26535 89793 ... (see OEISA000796). Pi is defined as the ratio of a circle's circumference C to its diameter d:

 \pi = \frac{C}{d}

Or, equivalently, as the ratio of the circumference to twice the radius. The above formula can be rearranged to solve for the circumference:


The use of the mathematical constant π is ubiquitous in mathematics, engineering, and science. The constant ratio of circumference to radius {C}/{r} = 2\pi also has many uses in mathematics, engineering, and science. These uses include but are not limited to radians, computer programming, and physical constants. The Greek letter τ (tau) is sometimes used to represent this constant, but is not generally accepted as proper notation.

Circumference of an ellipse[edit]

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

Circumference of a graph[edit]

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

See also[edit]


External links[edit]