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Circles: Radians, arcs and sectors
Measuring angles in radians, circumference & arc lengths and sector areas
Measuring angles in radians, circumference & arc lengths and sector areas
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The ratio of a circle's perimeter to its diameter is constant in all circles. This constant is called π (pi). Since the diameter is twice the radius, the circumference of a circle is
The area of a circle is
where r is the radius of the circle.
A sector is an area enclosed between a circular arc and the two radii of the circle touching each end of the arc:
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The area of a circle is πr2, and there are 360 degrees of rotation in a circle. Therefore, a sector with central angle θ is 360°θ​ of a full circle, and has area