Diameter

In geometry, a circle is a two-dimensional (2D) shape in which all points on the circle are equidistant from another point called the center. The term "radius" is used to describe the distance from the center to any point on the outside of the circle. The distance from one point on the surface of the circle to another point on the surface of the circle that goes through the center point is called the diameter. The diameter is always double the radius.

Diameter formulas

There are a few different ways to calculate the diameter of a circle based on information that is already known. The easiest way to figure the diameter is if you know the radius, but it is also possible to calculate the diameter if you know the circumference of the circle or the area of the circle.

Example 1

If the radius of a circle is known, the diameter is calculated as:

$D=2R$

Where R is the radius of the circle.

Solve for the diameter of a circle where the radius is 3.5 in.

$D=\left(2\right)3.5$

$D=7\text{ in.}$

Example 2

If the circumference of a circle is known, the formula to calculate the diameter is:

$D=\frac{C}{\pi }$

Where C is the circumference of the circle and π is a constant value, which is approximately equal to 3.14

Solve for the diameter of a circle where the circumference is 24 in.

$D=\frac{24}{\pi }$

$D=7.64\text{ in.}$

Example 3

If the area of the circle is known, the formula to compute the diameter of a circle is:

$D=\sqrt{\frac{4A}{\pi }}$

Where A is the area of the circle

Solve for the diameter of a circle where the area of the circle is 100 cm.

$D=\sqrt{\frac{4\left(100\right)}{\pi }}$

$D=\sqrt{\frac{400}{\pi }}$

$D=\sqrt{127.39}$

$D=11.29\text{ cm}$

Practice using the diameter formula

a. Solve for the diameter of a circle where the radius of the circle is 15 cm.

$D=2\left(15\right)$

$D=30\text{ cm}$

b. Solve for the diameter of a circle where the circumference of the circle is 40 in.

$D=\frac{40}{\pi }$

$D=12.74\text{ in.}$

c. Solve for the diameter of a circle where the area of the circle is 85 cm.

$D=\sqrt{\frac{4\left(85\right)}{\pi }}$

$D=\sqrt{\frac{340}{\pi }}$

$D=\sqrt{108.28}$

$D=10.41\text{ cm}$

d. Solve for the diameter of a circle where the circumference of the circle is 180 in.

$D=\frac{180}{\pi }$

$D=57.32\text{ in.}$

e. Solve for the diameter of a circle where the area of the circle is 20 cm.

$D=\sqrt{\frac{4\left(20\right)}{\pi }}$

$D=\sqrt{\frac{80}{\pi }}$

$D=\sqrt{25.48}$

$D=5.05\text{ cm}$

Topics related to the Diameter

Circle

Chord

π (Pi)

Flashcards covering the Diameter

Basic Geometry Flashcards

Common Core: High School - Geometry Flashcards

Practice tests covering the Diameter

Common Core: High School - Geometry Diagnostic Tests

Intermediate Geometry Diagnostic Tests

Get help learning about diameter

Circles are found in nature and in a wide variety of careers. Therefore, knowing how to find the diameter of a circle is a skill that many people will use in their adult life. Whether your student plans to go into architecture, science, construction, transportation, or even video game design, they will need to know all about circles, including diameter. There are a lot of formulas around diameter in addition to the one above, and it can get confusing to remember some of the terms, like the difference between the radius and the diameter.

Working with a private tutor can help your student in many ways. The 1-on-1 attention a tutor can provide means that your student can have their questions about diameters and other concepts related to circles answered right away and in a way that they understand. Tutors can help your student keep track of all the formulas they need to know for various geometric concepts by teaching them memory tips and tricks that work for them.

If your student is learning about diameter and other related concepts and could use a helping hand, get in touch with the Educational Directors at Varsity Tutors today to see how tutoring can help your student.