What is Diameter? – Definition & Formula

In this lesson, you can find out how important the diameter is to a circle. Also, you can learn about the formulas that were figured out by the mathematicians of old relating to the diameter and how to use them.
What is Diameter?
What exactly is a diameter? It is a crucial measurement of circles. In fact, it is one of the defining measurements of circles. The diameter measures how big the circle is from rim to rim passing through the center. Look at the following diagram to see how this measurement is taken.

A diameter.
diameter
The blue line above is the diameter of the red circle. Notice how it is the line passing through the exact middle of the circle going from one edge of the circle to the other. The diameter measures the circle at its largest point across.

Another definition that is related to the diameter is the radius. It is the measurement from the center of the circle to its edge.

The radius.
diameter
The relation of the radius to the diameter gives us one of the formulas involving the diameter. Let’s see what that is.

Formulas
If you compare the radius to the diameter and you think about their definitions, you will see that the radius is exactly half the diameter and the diameter is twice the radius. Think about it. If the radius is the measurement from the center to the edge, and the diameter is the measurement from edge to edge passing through the center, doesn’t that mean the diameter includes two measurements of the radius in it?

The diameter includes two measurements of the radius in it.
diameter
Because this is true, we have the following formula relating the radius to the diameter.

First formula.
diameter
In math, the typical notation for radius is a lowercase r, while the notation for diameter is a lowercase d. The above formula simply tells us that the diameter is 2 times the radius.

The other formula involving the diameter is the one for the circumference of the circle. The circumference of a circle is the distance around it. If you were to measure the distance it took you to walk all the way around the circle, that measurement would be your circumference.

Second formula.
diameter
The notation for circumference is an uppercase C.

Now, let’s see how we can use these two formulas.

Example – Radius
Our first formula involved the radius. There are two types of problems that you will encounter that relate to this first formula. They are to find the radius given the diameter and to find the diameter given the radius. As you will see, by using your algebra skills, you can easily do these types of problems by using the formula.

So let’s say you were given the radius and asked to find the diameter, you would look at the formula and say to yourself that what you need to do is to multiply the radius by 2 to get your answer. That’s fairly simple. For example, if the radius is 3, then 3 * 2 = 6 is the diameter.

What about if you were given the diameter and asked to find the radius? Well, you would start the same and look at the formula. You would see that because the diameter is twice the radius, the radius is then half the diameter. You would divide the diameter by 2 to get the radius. For example, if the diameter is 8, then 8 / 2 = 4 is the radius.