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Introduction

QUICK LINKS


Introduction

Circumference and Area of Circles

INTRO
Remembering all the different parts of a circle and what they represent can sometimes feel a little out of reach. That’s why we like to think about them in terms of our favorite type of circle...pizza!
These are different formulas we can use to find these different values:
Circle PartPizzaFormula
CircumferenceCrust
AreaAmount of Pizza
DiameterDistance Across
RadiusSlice Length
Check out our
Calculator
or explore our
Lesson
and
Practice
sections to learn more about circles and test your understanding.

You can also use the Quick Links menu on the left to jump to a section of your choice.

You can also use the Quick Links dropdown above to jump to a section of your choice.

CALCULATOR

Circumference & Area of Circles Calculator

Step 1. Identify the unknown.

What are you trying to solve for?
pizza

Step 2. Identify the given.

What is the value of the ?

Step 3. Select the correct formula(s).

We can use the following formula(s) to solve for the circumference using the area:

Step 4. Plug in the given and solve for the unknown.

(1) Since there isn’t an equation that takes us directly from area to circumference, we first have to solve for the radius:
(2) Now that we know the radius is equal to, we can plug it into the second equation to solve for the circumference:
Our answer is .
KEY STEPS

How to Find Circumference & Area of Circles

Step 1. Identify the unknown.

What are you trying to solve for?
Since the unknown is the circumference, you need to solve for the distance around the circle, which is like the crust of a pizza.

Step 2. Identify the given.

What information do you already have?

Step 3. Select the correct formula(s).

You can use the following formula(s) to solve for the circumference the given the radius:

Step 4. Plug in the given and solve for the unknown.

Plug in the given value into the formula and solve for the unknown using inverse operations as needed.
LESSON
Diameter Formula

Diameter Formula

The diameter represents the width of a circle or, in pizza terms, the distance across a pizza.

If we divide the diameter in half, we get the radius. The radius represents half of the width of a circle, or in pizza terms, the length of a slice of pizza.
The diameter and radius are very important because we need at least one of them to solve for the circumference and area of a circle.
If we’re given the radius, we can easily find the diameter: . If we’re given the diameter we can easily find the radius: .
Continue to see an example of each case!

EXAMPLE 1

Let's say we know our circle has radius . What is the diameter?

Step 1. Identify the unknown.

We're looking for the diameter so that's our unknown.
pizza

Step 2. Identify the given.

pizza

Step 3. Select the correct formula(s).

We can use the following formula(s) to solve for the diameter using the radius:

Step 4. Plug in the given and solve for the unknown.

(1) Since there isn’t an equation that takes us directly from radius to diameter, we first have to solve for the radius:
(2) Now that we know the radius is equal to, we can plug it into the second equation to solve for the diameter:
Our answer is .

EXAMPLE 2

Nice work! Now, let's say we know our circle has diameter . What is the radius?

Step 1. Identify the unknown.

We're looking for the radius so that's our unknown.
pizza

Step 2. Identify the given.

pizza

Step 3. Select the correct formula(s).

We can use the following formula(s) to solve for the radius using the diameter:

Step 4. Plug in the given and solve for the unknown.

(1) Since there isn’t an equation that takes us directly from diameter to radius, we first have to solve for the radius:
(2) Now that we know the radius is equal to, we can plug it into the second equation to solve for the radius:
Our answer is .
Awesome! Expand the
Practice
below to try some more problems or expand the next
Lesson
to explore what we do when we're finding the circumference of a circle.
PRACTICE
Diameter Formula

Practice: Diameter Formula

Question 1 of 4:
pizza

Step 1. Identify the unknown.

What are we trying to solve for?

Step 2. Identify the given.

What information do we already have?

Step 3. Select the correct formula(s).

Which of the following formulas should we use to solve for the diameter using the radius?
Nice! Now that we have our formula, we're ready to plug in and solve.
Question 1 of 4:

Step 4. Plug in the given and solve for the unknown.

Nice work! Now all you have to do is solve:
Great job! Our answer is .

LESSON
Circumference Formula

Circumference Formula

The circumference represents the distance around a circle, or in pizza terms, the crust.

Since the diameter is just radius, we can use either one to find the circumference of a circle.Continue below to walkthrough examples of how to find the circumference of a circle given the radius or diameter and vice versa!

EXAMPLE 1

Let's say we know our circle has radius . What is the circumference?

Step 1. Identify the unknown.

We're looking for the circumference so that's our unknown.
pizza

Step 2. Identify the given.

pizza

Step 3. Select the correct formula(s).

We can use the following formula(s) to solve for the circumference using the radius:

Step 4. Plug in the given and solve for the unknown.

(1) Since there isn’t an equation that takes us directly from radius to circumference, we first have to solve for the radius:
(2) Now that we know the radius is equal to, we can plug it into the second equation to solve for the circumference:
Our answer is .

EXAMPLE 2

Amazing job! Now, let's say we know our circle has circumference . What is the radius?

Step 1. Identify the unknown.

We're looking for the radius so that's our unknown.
pizza

Step 2. Identify the given.

pizza

Step 3. Select the correct formula(s).

We can use the following formula(s) to solve for the radius using the circumference:

Step 4. Plug in the given and solve for the unknown.

(1) Since there isn’t an equation that takes us directly from circumference to radius, we first have to solve for the radius:
(2) Now that we know the radius is equal to, we can plug it into the second equation to solve for the radius:
Our answer is .

EXAMPLE 3

Nice work! Next, imagine our circle has diameter . What is the circumference?

Step 1. Identify the unknown.

We're looking for the circumference so that's our unknown.
pizza

Step 2. Identify the given.

pizza

Step 3. Select the correct formula(s).

We can use the following formula(s) to solve for the circumference using the diameter:

Step 4. Plug in the given and solve for the unknown.

(1) Since there isn’t an equation that takes us directly from diameter to circumference, we first have to solve for the radius:
(2) Now that we know the radius is equal to, we can plug it into the second equation to solve for the circumference:
Our answer is .

EXAMPLE 4

Alright! Last one - say our circle has circumference . What is the diameter?

Step 1. Identify the unknown.

We're looking for the diameter so that's our unknown.
pizza

Step 2. Identify the given.

pizza

Step 3. Select the correct formula(s).

We can use the following formula(s) to solve for the diameter using the circumference:

Step 4. Plug in the given and solve for the unknown.

(1) Since there isn’t an equation that takes us directly from circumference to diameter, we first have to solve for the radius:
(2) Now that we know the radius is equal to, we can plug it into the second equation to solve for the diameter:
Our answer is .
Awesome! Expand the
Practice
below to try some more problems or expand the next
Lesson
to explore what we do when we're finding the area of a circle.
PRACTICE
Circumference Formula

Practice: Circumference Formula

Question 1 of 4:
pizza

Step 1. Identify the unknown.

What are we trying to solve for?

Step 2. Identify the given.

What information do we already have?

Step 3. Select the correct formula(s).

Which of the following formulas should we use to solve for the circumference using the radius?
Nice! Now that we have our formula, we're ready to plug in and solve.
Question 1 of 4:

Step 4. Plug in the given and solve for the unknown.

Nice work! Now all you have to do is solve:
Great job! Our answer is .

LESSON
Area Formula

Area Formula

The area represents the total amount of space inside a circle or, in pizza terms, the total amount of pizza.

The formula for the area of a circle is:If we’re given the radius, we can easily find the area.
If instead, we’re given the diameter, we first have to make a pit stop to find the radius using . Once we have the radius, we can plug it into the circle area formula and solve!
Continue below to walkthrough examples of how to find the area of a circle given the radius or diameter and vice versa!

EXAMPLE 1

Let's start with a circle with radius . What is the area?

Step 1. Identify the unknown.

We're looking for the area so that's our unknown.
pizza

Step 2. Identify the given.

pizza

Step 3. Select the correct formula(s).

We can use the following formula(s) to solve for the area using the radius:

Step 4. Plug in the given and solve for the unknown.

(1) Since there isn’t an equation that takes us directly from radius to area, we first have to solve for the radius:
(2) Now that we know the radius is equal to, we can plug it into the second equation to solve for the area:
Our answer is .

EXAMPLE 2

Exactly! Now, let's say the circle with area . What is the radius?

Step 1. Identify the unknown.

We're looking for the radius so that's our unknown.
pizza

Step 2. Identify the given.

pizza

Step 3. Select the correct formula(s).

We can use the following formula(s) to solve for the radius using the area:

Step 4. Plug in the given and solve for the unknown.

(1) Since there isn’t an equation that takes us directly from area to radius, we first have to solve for the radius:
(2) Now that we know the radius is equal to, we can plug it into the second equation to solve for the radius:
Our answer is .

EXAMPLE 3

Perfect! Next, imagine the circle has diameter . What is the area?

Step 1. Identify the unknown.

We're looking for the area so that's our unknown.
pizza

Step 2. Identify the given.

pizza

Step 3. Select the correct formula(s).

We can use the following formula(s) to solve for the area using the diameter:

Step 4. Plug in the given and solve for the unknown.

(1) Since there isn’t an equation that takes us directly from diameter to area, we first have to solve for the radius:
(2) Now that we know the radius is equal to, we can plug it into the second equation to solve for the area:
Our answer is .

EXAMPLE 4

Amazing! Finally, say the circle has area . What is the diameter?

Step 1. Identify the unknown.

We're looking for the diameter so that's our unknown.
pizza

Step 2. Identify the given.

pizza

Step 3. Select the correct formula(s).

We can use the following formula(s) to solve for the diameter using the area:

Step 4. Plug in the given and solve for the unknown.

(1) Since there isn’t an equation that takes us directly from area to diameter, we first have to solve for the radius:
(2) Now that we know the radius is equal to, we can plug it into the second equation to solve for the diameter:
Our answer is .
Awesome! If you’d like to practice additional problems finding the area of circles, expand the
Practice
below before closing out this lesson! ⚡
PRACTICE
Area Formula

Practice: Area Formula

Question 1 of 4:
pizza

Step 1. Identify the unknown.

What are we trying to solve for?

Step 2. Identify the given.

What information do we already have?

Step 3. Select the correct formula(s).

Which of the following formulas should we use to solve for the area using the radius?
Nice! Now that we have our formula, we're ready to plug in and solve.
Question 1 of 4:

Step 4. Plug in the given and solve for the unknown.

Nice work! Now all you have to do is solve:
Great job! Our answer is .

CONCLUSION
Amazing work, look at you go! Thanks for checking out this lesson ☺️🙏. Where to next?
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