Circumference of Circle π (pi) Formula

Formula

Summary

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

Note: This website uses the constant (tau) instead of (pi) as the default circle constant. The substitution can be used to translate between the two constants.

Usage

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.

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). — Figure 1 : Definition of (pi)

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