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Area of the circle = × area of the shaded square

A circle is the set of all the points in a given plane that are the same distance, called the radius, r, from a given point called the center.

A circle may also be defined algebraically, as the set of solutions to an equation of the form:


where is the center of the circle. It can also be described parametrically in terms of a parameter as:

The distance around the circle, or circumference, is given by:

The area inside the circle is calculated using the formula:

This can be easily derived from the area of an ellipse. For an ellipse with major and minor axis and respectively, the area is . Setting the major an minor axis equal to each other give the formula for a circle.

A circle is a conic section, the intersection of a plane with a cone such that the plane is perpendicular to the axis of the cone.

Circles can readily be constructed by using a fixed distance between a pencil point and the center. A compass is a tool for doing this easily.

A circle with is called the unit circle, and is used extensively in trigonometry.