Circumference of Circle Formula

Formula

Summary

The circumference of a circle is given by the circle constant (tau) multiplied by the radius.

Variable	Description
	Circumference of the circle
	The circle constant (tau), 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 (tau) multiplied by 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 circle 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 circle constant (tau). The circle constant is defined as the ratio of any circle’s circumference divided by its radius. This is illustrated in the figure below.

Definition of τ (tau). — Figure 1 : Definition of (tau)

Derivation

To derive the formula, start with the definition of the circle constant.

Multiply both sides of the equation by and the result is the circumference formula.