# Finding the Diameter Using the Circumference

The diameter of a circle is the line segment that connects two points on the circle and passes through the center. The diameter is also defined as the chord that passes through the center of the circumference. The length of the diameter can be calculated using both the length of the radius and the length of the circumference.

Here, we will learn about the formulas that we can use to calculate the lengths of diameters of circles. Then, we will apply these formulas to solve some problems.

##### PRECALCULUS

Relevant for

Learning to find the diameter using the circumference.

See examples

##### PRECALCULUS

Relevant for

Learning to find the diameter using the circumference.

See examples

## Formula for the diameter using the circumference

To calculate the length of the diameter of circles, we can use both the length of the radius and the length of the circumference.

### Finding the diameter of the circle using the radius

The length of the diameter is exactly twice the length of the radius. So if we know the length of the radius, we can find the length of the diameter using the following formula:

$latex d=2r$

where r is the length of the radius.

### Finding the diameter using the circumference

Generally, the diameter is used to calculate the circumference, therefore, it is also possible to calculate the length of the diameter if we have the circumference. The formula for the circumference is:

$latex C= \pi d$

Therefore, the formula for the diameter of a circle is:

$latex d = \frac{C}{\pi}$

where C is the length of the circumference and π is a mathematical constant that has an approximate value of 3.1416.

The formulas for the diameter of circles are applied to solve the following examples. Each exercise has its respective solution, but it is recommended that you try to solve the problems yourself before looking at the answer.

### EXAMPLE 1

What is the diameter of the circumference that has a radius of 7 m?

We have the value $latex r=7$. We use this value in the first formula for the diameter:

$latex d=2r$

$latex d=2(7)$

$latex d=14$

The diameter is equal to 14 m.

### EXAMPLE 2

If a circle has a radius of 14.5 m, what is its diameter?

We have the length $latex r=14.5$. Therefore, we use this value in the diameter formula:

$latex d=2r$

$latex d=2(14.5)$

$latex d=29$

The length of the diameter is 29 m.

### EXAMPLE 3

What is the length of the diameter of a circle that has a length of 25 m?

We have the length $latex C = 25$. Therefore, we use this value in the second diameter formula given above:

$latex d=\frac{C}{\pi}$

$latex d=\frac{25}{\pi}$

$latex d=7.96$

The length of the diameter is 7.96 m.

### EXAMPLE 4

If a circle has a length of 42 m, what is its diameter?

We substitute the length $latex C = 42$ in the second formula for the diameter:

$latex d=\frac{C}{\pi}$

$latex d=\frac{42}{\pi}$

$latex d=13.37$

The diameter is equal to 13.37 m.

## Finding the diameter using the circumference and radius – Practice problems

Use what you have learned about circumference diameters and solve the following practice problems. Select an answer and check it to see if you got the correct one.