# Circumference of Circle π (pi) Formula

This formula calculates the circumference of a circle in terms of the constant (pi) and the radius of the circle.

Variable | Description |
---|---|

Circumference of the circle | |

The geometric constant (pi), where | |

The radius of the circle |

The circumference of a circle is given by the constant (pi) multiplied by two times the radius the circle. For example, to find the circumference of a circle with a radius of length the formula is:

To find a numeric answer, substitute the value in for the constant and evaluate the multiplication.

The circumference of a circle with a radius of length is equal to units.

The formula for the circumference of a circle in terms of its radius comes from the definition of the constant (pi). The constant is defined as the ratio of *any* circle’s circumference divided by its diameter. This is illustrated in the figure below.

Rearranging the definition of and solving for the circumference you reconstruct the formula on the fly.