Radius
(KS3, Year 7)

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:

radius of a circle

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."

Examples of the Radius

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.

circle with radius of 5 cm The circle below has a radius of 8 ft.

circle with a radius of 8 feet

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:

radius is half the diameter
Read more about how to find the radius from the diameter

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:

radius is circumference divided by 2 pi
Read more about how to find the radius from the circumference

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:

radius equals square root of area divided by pi
Read more about how to find the radius from the area

Interactive Widget

Here is an interactive widget to help you learn about the radius.

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.

1 Radius, 2 Radii

The plural of radius is radiuses or radii.

Radius of a Sphere

A circle is not the only shape that has a radius. A sphere also has a radius. The radius of a sphere is the line segment from the center of the sphere to any point on the surface of the sphere. The image below shows what we mean by the radius of a sphere. It is labelled r:

radius in a sphere When you know the radius of a sphere, you can find its volume and its surface area.

The Radius in Other Shapes

The radius appears in other shapes that are not obviously related to circles, for example the cone and cylinder. But if you were to cut through a cone or cylinder, the cross-section would be a circle, which has a radius. The base of both shapes is a circle. The radius of the base (as shown in the image below) is labelled r:

radius in a cone and cylinder When you know the radius, you can find the volume and surface areas of the shape.
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See Also

What is a circle? What is the diameter? What is the circumference? What is the area of a circle? Finding the radius from the diameter Finding the radius from the circumference Finding the radius from the area Learn about the radius ( interactive widget)