# Circumference of Circle Formula

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 |

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, substitude 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.

This example demonstrates how to find the circumference of a circle with a radius of using the circumference formula.

Set up the formula and substitute the radius in for the variable .

Substitute in for the circle constant.

Evaluate the multiplication.

The circumference of the circle with a radius of is equal to units or approximately units.

This example demonstrates how to find the circumference of a circle with a radius of using the circumference formula.

Set up the formula and substitute the radius in for the variable .

Substitute in for the circle constant.

Evaluate the multiplication.

The circumference of the circle with a radius of is equal to units or approximately units.

This example demonstrates how to find the circumference of a circle with a radius of using the circumference formula.

Set up the formula and substitute the radius in for the variable .

Substitute in for the circle constant.

Evaluate the multiplication.

The circumference of the circle with a radius of is equal to units or approximately units.

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* circles circumference divided by its radius. This is illustrated in the figure below.

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

Multiply both sides of the equation by .

The result is the circumference formula.

The circle constant τ (tau) is a geometric constant approximately equal to 6.283. The numeric value is defined as the length of any circle's circumference divided by the length of its radius.