Diameters
(KS3, Year 7)

The Lesson

The diameter is the line through the centre of the circle that has its endpoints on the circle. The diameter also refers to the length of this line. The diameter is often denoted by d. The image below shows what we mean by the diameter:

diameter

Dictionary Definition

The Oxford English Dictionary defines the diameter as "a straight line passing through the centre of a circle (or sphere), and terminated at each end by its circumference (or surface)."

Examples of the Diameter

The circle below has a diameter of 5 cm. This is the length of the line that touches opposite sides of the circle and passes through the centre.

diameter of 5 cm The circle below has a diameter of 12 inches.

diameter of 12 inches

How to Find the Diameter

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

How to Find the Diameter from the Radius

The diameter is twice the radius. If the diameter is d and the radius is r (as shown in the image below), then we can find the diameter using the formula:

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

How to Find the Diameter from the Circumference

The diameter is the circumference divided by π. If the diameter is d and the circumference is C (as shown in the image below), then we can find the diameter using the formula:

diameter equals circumference divide by pi
Read more about how to find the diameter from the circumference

How to Find the Diameter from the Area

The diameter is twice the square root of the area divided by π. If the diameter is d and the area is A (as shown in the image below), then we can find the diameter using the formula:

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

Interactive Widget

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

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.

Euclid's Definition of the Diameter

Euclid defined the diameter his book, Elements.

Euclid Definition 17: "A diameter of the circle is any straight line drawn through the center and terminated in both directions by the circumference of the circle, and such a straight line also bisects the circle".

Diameter of a Sphere

A circle is not the only shape that has a diameter. A sphere also has a diameter. The diameter of a sphere is the line segment through the center of the sphere that ends on opposite points on the surface of the sphere. The image below shows what we mean by the diameter of a sphere. It is labelled d:

diameter in a sphere

The Diameter in Other Shapes

The diameter 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 diameter. The base of both shapes is a circle. The diameter of the base (as shown in the image below) is labelled r:

diameter in a cone and cylinder
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See Also

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