Circle
From Latin: circus - "ring, a round arena"
A line forming a closed loop, every point on which is a fixed distance from a center point.
Try this Drag an orange dot. The circle can be moved by dragging the center point and resized by dragging the point on the circle.

A circle is a type of line. Imagine a straight line segment that is bent around until its ends join. Then arrange that loop until it is exactly circular - that is, all points along that line are the same distance from a center point.

There is a difference between a circle and a disk. A circle is a line, and so, for example, has no area - just as a line has no area. A disk however is a round portion of a plane which has a circular outline. If you draw a circle on paper and cut it out, the round piece is a disk.

Properties of a circle

Center A point inside the circle. All points on the circle are equidistant (same distance) from the center point.
Radius The radius is the distance from the center to any point on the circle. It is half the diameter. See Radius of a circle.
Diameter The distance across the circle. The length of any chord passing through the center. It is twice the radius. See Diameter of a circle.
Circumference The circumference is the distance around the circle. See Circumference of a Circle.
Area Strictly speaking a circle is a line, and so has no area. What is usually meant is the area of the region enclosed by the circle. See Area enclosed by a circle .
Chord A line segment linking any two points on a circle. See Chord definition
Tangent A line passing a circle and touching it at just one point. See Tangent definition
Secant A line that intersects a circle at two points. See Secant definition

Calculator

ENTER ANY ONE VALUE
Radius clear
Diameter clear
Area clear
Circumference clear
   
 

Use the calculator on the right to calculate the properties of a circle.

Enter any single value and the other three will be calculated. For example: enter the radius and press 'Calculate'. The area, diameter and circumference will be calculated.

Similarly, if you enter the area, the radius needed to get that area will be calculated, along with the diameter and circumference.

Pi

In any circle, if you divide the circumference (distance around the circle) by its diameter (distance across the circle), you always get the same number. This number is called Pi and is approximately 3.142. See Definition of pi.

Relation to ellipse

A circle is actually a special case of an ellipse. In an ellipse, if you make the major and minor axis the same length, the result is a circle, with both foci at the center. See Ellipse definition

Circle as a conic section

You can define a circle as the shape created when a plane cuts through a cone at right angles to the cone's axis. For more on this see Conic sections - circle.

Circle as a locus

A circle is the locus of all points a fixed distance from a given (center) point. This definition assumes the plane is composed of an infinite number of points and we select only those that are a fixed distance from the center. (See locus definition.)

Equations of a circle

In coordinate geometry, a circle can be described using sets of equations.
For more on this see Equations of circles and ellipses.

Other circle topics

General

Equations of a circle

Angles in a circle

Arcs

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