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

Other circle topics

General

• Circle definition
• Radius of a circle
• Diameter of a circle
• Circumference of a circle
• Parts of a circle (diagram)
• Semicircle definition
• Tangent
• Secant
• Chord
• Intersecting chords theorem
• Intersecting secant lengths theorem
• Intersecting secant angles theorem
• Area of a circle
• Concentric circles
• Annulus
• Area of an annulus
• Sector of a circle
• Area of a circle sector
• Segment of a circle
• Area of a circle segment (given central angle)
• Area of a circle segment (given segment height)

Equations of a circle

• Basic Equation of a Circle (Center at origin)
• General Equation of a Circle (Center anywhere)
• Parametric Equation of a Circle

Angles in a circle

• Inscribed angle
• Central angle
• Central angle theorem

Arcs

• Arc
• Arc length
• Arc angle measure
• Adjacent arcs
• Major/minor arcs
• Intercepted Arc
• Sector of a circle
• Radius of an arc or segment, given height/width
• Sagitta - height of an arc or segment