Circumference of Circle Formula

Circumference of Circle Formula

Formula

All Formulas

Summary

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

Formula Terms
Expression Description
Circumference of the circle
The circle constant (pi), where
The radius of the circle

How to use

To calculate the circumference of a circle, multiply the circle constant (pi) by two times the radius of 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.

Explanation

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.

Definition of π (pi).
Definition of (pi)

To derive the formula, substitute for the diameter in the definition of and rearrange the equation to solve for the circumference.

Related Formulas

The area of a circle is given by the geometric constant π (pi) multiplied by the radius of the circle squared (A = πr²).