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Circumference of a circle - derivation

This page describes how to derive the formula for the circumference of a circle.

Recall that the definition of pi (π) is the circumference c of any circle divided by its diameter d. Put as an equation, pi is defined as Rearranging this to solve for c we get The diameter of a circle is twice its radius, so substituting 2r for d

If you know the area

Recall that the area of a circle is given by Solving this for r So The circumference c of a circle is Substituting r Squaring both sides to lose the radical Solving for c:

Other circle topics

General

Equations of a circle

Angles in a circle

Arcs