Editing Circle (section)

===Radian===
{{main|Radian}}
If a circle of radius {{mvar|r}} is centred at the [[Vertex (geometry)|vertex]] of an [[angle]], and that angle intercepts an [[Circular arc|arc of the circle]] with an [[arc length]] of {{mvar|s}}, then the [[radian]] measure {{theta}} of the angle is the ratio of the arc length to the radius:
<math display="block">\theta = \frac{s}{r}.</math>

The circular arc is said to [[subtend]] the angle, known as the [[central angle]], at the centre of the circle. One radian is the measure of the central angle subtended by a circular arc whose length is equal to its radius. The angle subtended by a complete circle at its centre is a [[complete angle]], which measures {{math|2{{pi}}}} radians, 360 [[Degree (angle)|degrees]], or one [[Turn (angle)|turn]].

Using radians, the formula for the arc length {{mvar|s}} of a circular arc of radius {{mvar|r}} and subtending a central angle of measure {{theta}} is
<math display="block">s = \theta r,</math>

and the formula for the area {{mvar|A}} of a [[circular sector]] of radius {{mvar|r}} and with central angle of measure {{theta}} is
<math display="block">A = \frac{1}{2} \theta r^2.</math>

In the special case {{math|1={{theta}} = 2{{pi}}}}, these formulae yield the circumference of a complete circle and area of a complete disc, respectively.