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Circles and PiArcs

To find the length of an arc or the area of a sector, we need to know about the corresponding angle at the center of the circle: this is called the central angle.

Notice how the arc, sector and angle all take up the same proportion of a full circle. For example, if the central angle is , it takes up of a full circle.

This means that the length of the arc is also 14 of the whole circumference of the circle, and the area of the sector is 14 of the whole area of the circle.

We can express this relationship in an equation:

arc lengthcircumference=circle area=central angle

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