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Circumference to Diameter: Conversion, Formula, Meaning, Example

Jessica Kaminski

reviewed by Jo-ann Caballes

Updated on October 4, 2024

Circumference and diameter are essential in math, especially when learning about circ to diameter. Kids learn about these measurements early on, helping them understand how to work with circles in different math problems. Knowing how circumference and diameter are related is an essential math skill.

What Is the Circumference to Diameter Calculator?

A circumference to diameter calculator helps you determine how wide a circle is across its middle if you know how long it is around the outside. 

Simply put, if you measure the circle’s edge (circumference) and want to determine its width (diameter), this calculator can do that for you. The formula for this is diameter from circumference = Circumference ÷ π (pi).

Circumference to Diameter Ratio

The diameter of a circle formula from circumference ratio shows how the distance around a circle (the circumference) compares to the distance straight across the circle (the diameter). No matter the circle size, if you divide the circumference by the diameter, you’ll always get the same number, about 3.14. This number is called Pi (π). Pi (π) helps us understand by showing how many times the diameter can fit around the edge of the circle.

What Is The Formula For Circumference With Diameter?

When you know the circumference formula diameter, you can find the distance around a circle (called the circumference). 

The formula is Circumference = π x Diameter.

For this case, Pi (π) is about 3.14. If you have the diameter of the circle, you multiply by 3.14. That is the diameter to circumference formula, which helps us find the length of the circle if stretched out into a single line.

Circumference to Diameter: Formula

This way, the diameter can be measured with the formula: Diameter = Circumference ÷ π.

When you know a circle’s circumference, you can follow this method to find the circumference to diameter formula. First, measure the circumference, which is the distance around the circle. Then, take that number and divide it by 3.14.

This number, Pi (π), helps us understand how circles work. If you divide, you end up with the diameter, the distance straight across from one side to the other. This is how to easily calculate circumference from diameter.

How to Find the Diameter from Circumference

These steps will tell you the diameter of the circle with the circumference given:

1. First, find the circumference, which is the distance around the circle.
2. Use the number Pi (π), which is about 3.14. This number helps with circle calculations.
3. Divide the circumference by 3.14. You now have the diameter, the distance across through the circle’s center.

Example:

Measure the diameter of a circle with a circumference of 12.56 inches.

Solution:

The relation to measuring the diameter from the circumference is given by the formula: Circumference = π × Diameter.

In this example, the circumference is 12.56 inches. Using π = 3.14: Diameter = Circumference ÷ π. Therefore, Diameter = 12.56 ÷ 3.14 = 4 inches.

You can always use this system to determine diameter from the circumference.

Is Diameter Half of the Circumference?

Unlike popular misrepresentations may have you believe, a circle’s diameter is certainly not half of its circumference. The formula is Circumference = π x Diameter.

To understand the difference between diameter vs circumference, remember this: the diameter is the distance across the circle from one side to the other. In contrast, the circumference is the distance around the circle.

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Find the Circumference of the Circle When the Area Is Given

If you only know the area of a circle and need to find the circumference, you can still find the circumference of a circle. Here is how to find the diameter of a circle from the circumference.

Example: The area of a circular garden is 28.26 square meters. What is the length of the perimeter (boundary) of the garden?

Solution:

Step 1: Find the radius using the area formula for a circle:

Area = π × (Radius)²

Given the area is 28.26 square meters:

(Radius)² =    Area/π.

(Radius)² =    28.26/3.14 = 9

(Radius) =  √9 = 3 meters

Step 2: Find the circumference using the radius, which is slightly different from finding the diameter from the circumference:

Circumference=2×π×Radius

Circumference = 2 x 3.14 x 3 = 18.84 meters

So, the boundary of the garden is approximately 18.84 meters.

Circumference to Diameter: Solved Examples

Example 1: What is the circumference to the diameter of a circle if its circumference is 9.42 inches?

Solution:

Use the formula:

Diameter =   Circumference/π

Given: Circumference = 9.42 inches, 𝜋 = 3.14

Diameter =   9.42/3.14  = 3 inches

Example 2: Find the circle’s circumference if the radius is 4.5 inches (Use π = 3.14).

Solution:

Use the formula: Circumference = 2 x π x Radius

Given: Radius = 4.5 inches, π = 3.14

Example 3: Knowing the formula for circumference with diameter, what is the circumference of the circle if the area of the circle is 50.24 square feet?

Solution:

First, find the radius using the area formula: Area = π x Radius²

Rearrange to solve for Radius: Radius =  √Area/π

Given: Area = 50.24 square feet, 𝜋 = 3.14.

Radius =  √50.24/3.14

Then, find the circumference using diameter or radius (whichever was given):

Circumference = 2 x π x Radius

Circumference to Diameter: Practice Math Problems

Circumference to Diameter: worksheets

In this article, you’ve learned about circumference to width, the value of Pi, and working with diameters. To reinforce what you’ve learned, check out Brighterly’s worksheets. You can use them to practice and get better at these cool math ideas.

• Free Circle Worksheet [PDF]
• Area And Circumference Of A Circle Worksheet [PDF]
• Free Area Of A Circle Worksheet [PDF]

Jessica Kaminski

67 articles

Jessica is a a seasoned math tutor with over a decade of experience in the field. With a BSc and Master’s degree in Mathematics, she enjoys nurturing math geniuses, regardless of their age, grade, and skills. Apart from tutoring, Jessica blogs at Brighterly. She also has experience in child psychology, homeschooling and curriculum consultation for schools and EdTech websites.