

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
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