Circumference

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Circumference of a circle

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 2 $π$ .

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 OEIS: A000796). 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:

{C}=\pi \cdot {d}=2\pi \cdot {r}.\!

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.