# 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, substitude the value in for the 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 into the expression.

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 into the expression.

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 into the expression.

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 constant (pi). The constant is defined as the ratio of *any* circles circumference divided by its diameter. This is illustrated in the figure below.

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

Since the diameter is twice the length of the radius, substitute into the equation.

Multiply both sides of the equation by .

The result is the circumference formula in terms of .

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.

The greek letter π (pi) is a geometric constant approximately equal to 3.1456. The numeric value is equal to the length of any circle's circumference divided by its diameter.