A circle is the set of points on a plane that are all the same distance away from a center point.

A circle is the set of points on a plane that are all the same distance from a center point. Or, you could think of a circle as the part of the plane that lies inside those points. A circle is flat – it has no thickness. But every circle has a radius, a diameter, a circumference, and an area.

The geometry of a circle

The radius of a circle is the distance from the center point to any point on the edge of the circle. You can see it in the picture of the purple circle. The diameter of a circle is twice the radius. It’s the distance all the way across the circle at its widest point. The circumference of a circle (from “circa”, the Latin word for “around”) is the distance around the edge of the circle.

And the area of the circle is all of the points on the plane inside the circle, taken together. A cool thing about circles is that once we know how long one of these is, we can figure out all of the others. If we know the radius of a circle, we can figure out its diameter, its circumference, and its area. Or if we know the circumference, we can figure out the radius, the diameter, and the area. And we can prove that this will always work, for any circle.

Say we know that the radius of a certain circle is 10 centimeters. Click on the links to see how to calculate the diameter, the circumference, and the area of that circle.

What if we draw a circle as a solid, not just in one plane, but all of the points in any direction that are the same distance from the center point? Then we have a sphere.