## Circumference & Area of Circles

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 Part | Pizza | Formula |

Circumference | Crust | $CC =2πr=πd $ |

Area | Amount of Pizza | $A=πr_{2}$ |

Diameter | Distance Across | $d=2r$ |

Radius | Slice Length | $r$ |

Continue to explore the circle formulas in more detail, starting with the formula for diameter.

### Circumference & Area of Circles Calculator

#### Step 1. Identify the unknown.

What are you trying to solve for?

$C=?$

#### 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:

$(1)A(2)C =πr_{2}(solve for radius)=2πr $

#### 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:

$A0π0 r =πr_{2}=πr_{2}=r_{2}=π0 $

(2) Now that we know the radius is equal to$0$, we can plug it into the second equation to solve for the circumference:

$CCC =2πr=2π×0=0π≈0 $

Our answer is $r=π0 ≈0$.

### Recap 🧢 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:

$C =2πr $

#### 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.

Continue to explore the circle formulas in more detail, starting with the formula for diameter ⬇️.You can also use the Quick Links menu on the left to jump to the section you’d like to explore!

### 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: $d=2r$. If we’re given the diameter we can easily find the radius: $r=2d $.

Continue to see an example of each case!Let's say we know our circle has radius $5$. What is the diameter?

#### Step 1. Identify the unknown.

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

$d=?$

#### Step 2. Identify the given.

#### Step 3. Select the correct formula(s).

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

$d =2r $

#### 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:

$ddd =2r=2×5=10 $

(2) Now that we know the radius is equal to$0$, we can plug it into the second equation to solve for the diameter:

Our answer is $d=10$.

Nice work! Now, let's say we know our circle has diameter $24$. What is the radius?

#### Step 1. Identify the unknown.

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

$r=?$

#### Step 2. Identify the given.

#### Step 3. Select the correct formula(s).

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

$d =2r $

#### 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:

$d24r =2r=2r=12 $

(2) Now that we know the radius is equal to$0$, we can plug it into the second equation to solve for the radius:

Our answer is $r=12$.

Great job! Get in some extra practice here ⬇️ or skip ahead to learn more about circumference.

### Practice: Diameter Formula

Question 1 of 4:

#### 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 .

### Circumference Formula

The circumference represents the distance around a circle, or in pizza terms, the crust.Since the diameter is just $2×$ radius, we can use either one to find the circumference of a circle.$C=πd =π(2r )=2πr$Continue below to walkthrough examples of how to find the circumference of a circle given the radius or diameter and vice versa!Let's say we know our circle has radius $7$. What is the circumference?

#### Step 1. Identify the unknown.

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

$C=?$

#### Step 2. Identify the given.

#### Step 3. Select the correct formula(s).

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

$C =2πr $

#### 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:

$CCC =2πr=2π×7=14π $

(2) Now that we know the radius is equal to$0$, we can plug it into the second equation to solve for the circumference:

Our answer is $C=14π≈43.98$.

Amazing job! Now, let's say we know our circle has circumference $60$. What is the radius?

#### Step 1. Identify the unknown.

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

$r=?$

#### Step 2. Identify the given.

#### Step 3. Select the correct formula(s).

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

$C =2πr $

#### 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:

$C60r =2πr=2πr=π30 $

(2) Now that we know the radius is equal to$0$, we can plug it into the second equation to solve for the radius:

Our answer is $r=π30 ≈9.55$.

Nice work! Next, imagine our circle has diameter $16$. What is the circumference?

#### Step 1. Identify the unknown.

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

$C=?$

#### Step 2. Identify the given.

#### Step 3. Select the correct formula(s).

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

$C =πd $

#### 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:

$CCC =πd=π×16=16π $

(2) Now that we know the radius is equal to$0$, we can plug it into the second equation to solve for the circumference:

Our answer is $C=16π≈50.27$.

Alright! Last one - say our circle has circumference $48$. What is the diameter?

#### Step 1. Identify the unknown.

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

$d=?$

#### Step 2. Identify the given.

#### Step 3. Select the correct formula(s).

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

$C =πd $

#### 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:

$C48d =πd=πd=π48 $

(2) Now that we know the radius is equal to$0$, we can plug it into the second equation to solve for the diameter:

Our answer is $d=π48 ≈15.28$.

Practice with some additional problems or keep scrolling to learn more about how to find the area of a circle. Let's move on to our final formula - the area formula 🔥🔥.

### Practice: Circumference Formula

Question 1 of 4:

#### 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 .

### 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:$A=πr_{2}$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 $d=2r$. 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!

Let's start with a circle with radius $2$. What is the area?

#### Step 1. Identify the unknown.

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

$A=?$

#### Step 2. Identify the given.

#### Step 3. Select the correct formula(s).

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

$A =πr_{2} $

#### 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:

$AAA =πr_{2}=π×(2)_{2}=4π $

(2) Now that we know the radius is equal to$0$, we can plug it into the second equation to solve for the area:

Our answer is $A=4π≈12.57$.

Exactly! Now, let's say the circle with area $36$. What is the radius?

#### Step 1. Identify the unknown.

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

$r=?$

#### Step 2. Identify the given.

#### Step 3. Select the correct formula(s).

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

$A =πr_{2} $

#### 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:

$A36π36 r =πr_{2}=πr_{2}=r_{2}=π36 $

(2) Now that we know the radius is equal to$0$, we can plug it into the second equation to solve for the radius:

Our answer is $r=π36 ≈3.39$.

Perfect! Next, imagine the circle has diameter $8$. What is the area?

#### Step 1. Identify the unknown.

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

$A=?$

#### Step 2. Identify the given.

#### Step 3. Select the correct formula(s).

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

$(1)d(2)A =2r(solve for radius)=πr_{2} $

#### 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:

$d8r =2r=2r=4 $

(2) Now that we know the radius is equal to$0$, we can plug it into the second equation to solve for the area:

$AAA =πr_{2}=π×(0)_{2}=0π≈0 $

Our answer is $r=4$.

Amazing! Finally, say the circle has area $25$. What is the diameter?

#### Step 1. Identify the unknown.

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

$d=?$

#### Step 2. Identify the given.

#### Step 3. Select the correct formula(s).

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

$(1)A(2)d =πr_{2}(solve for radius)=2r $

#### 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:

$A25π25 r =πr_{2}=πr_{2}=r_{2}=π25 $

(2) Now that we know the radius is equal to$0$, we can plug it into the second equation to solve for the diameter:

$ddd =2r=2×0=0 $

Our answer is $r=π25 ≈2.82$.

If you’d like to practice additional problems using the area formula, take a moment to complete the quick practice below before finishing this lesson! ⚡

### Practice: Area Formula

Question 1 of 4:

#### 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 .

When you feel like you've mastered this lesson, click for a celebration ⬇️!