## The Lesson

A radius is the line segment from the centre of the circle to any point on the circle. The radius also refers to the length of this line. The radius is often denoted by r. The image below shows what we mean by the radius: ## Dictionary Definition

The Oxford English Dictionary defines the radius as "a straight line from the centre of a circle to its circumference, all such lines being equal in length."

The circle below has a radius of 5 cm. This is the length from the centre of the circle to any point on the circle. The circle below has a radius of 8 ft. ## How to Find the Radius

The radius of a circle is related to its diameter, circumference and area.

## How to Find the Radius from the Diameter

The radius is half of the diameter. If the radius is r and the diameter is d (as shown in the image below), then we can find the radius using the formula: ## How to Find the Radius from the Circumference

The radius is the circumference divided by 2π. If the radius is r and the circumference is C (as shown in the image below), then we can find the radius using the formula: ## How to Find the Radius from the Area

The radius is the square root of the area divided by π. If the radius is r and the area is A (as shown in the image below), then we can find the radius using the formula: ## What Is a Circle?

A circle is a shape containing a set of points that are the same radius from the center of the circle. When you know the radius of a sphere, you can find its volume and its surface area. When you know the radius, you can find the volume and surface areas of the shape.