What Is a Radius?

What Is a Radius?

A radius is the line segment from the center 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 center 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

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)