# Math Made Easy—How to Find the Circumference of a Circle

## Geometry Help

## Circumference of Circle

Understanding what the circumference of a circle is, as well as how to calculate the circumference of a circle is a relatively easy geometry principle. By following the circumference problems and solutions in the **Geometry Help Online** section below, you should easily be able grasp the concept of circumference.

By following along with the examples given and taking the online * Math Made Easy!* geometry quiz for circumference of a circle, you will be able to complete your geometry homework on this topic in a snap.

## Circumference of Circle Formula

The circumference of a circle is merely the distance around a circle. Sometimes it is referred to as the perimeter, although the term *perimeter* is usually reserved for the measure of a distance around a polygon.

**The equation for the circumference of a circle can be written in two ways:**

- C = 2πr
- C = πd

Where: r represents the radius of the circle and d represents a circle's diameter.

Recall that the radius is the distance from the center of the circle to a point on the edge of a circle and the diameter is the largest distance across a circle. The diameter is always twice the length of the radius.

When calculating the circumference with a known radius use the first version of the circumference formula shown; when the diameter is known use the second version of the circumference formula shown.

## Modern Day Uses for Circumference

Did you know that the circumference of the Earth was first calculated more than 2200 years ago by the Greek mathematician, Eratosthenes?

**Knowing how to calculate circumference is used in many fields of study, including:**

- engineers
- architects
- carpenters
- artists

## High School Geometry Help - Terms

**Circle Terms to Know:**

**Pi**: symbol for pi is π and it equals about 3.14**Radius**: The distance from the center of a circle to an edge**Radii**: The plural for radius.**Diameter**: The distance from one edge of a circle to another edge going through the center.**Circumference**: The distance around a circle; the perimeter of a circle.

## Math Made Easy! Tip

If you have trouble remembering geometry terms, it helps to think of other words from the same root with which you may be more familiar.

For example, the Latin root of the word circumference is *circum, *meaning* around*. *Circum* is now considered a prefix also meaning *around* or *round about*.

**Here is a list of words that come from the root/prefix circum that can help you remember that circumference the distance of measure around a circle:**

- Circus - (from the root
*circum*) usually held in a*circular*arena - Circle - (from the root
*circum*) a*round*shape - Circumvent - to go
*around*or bypass; to avoid - Circumstances - conditions
*surrounding*and event - Circumnavigate - to fly or sail
*around*

## Geometry Help Online: Circumference

Check out 4 common types of geometry homework problems and solutions involving the circumference of circles.

## #1 Find the Circumference of a Circle Given the Radius

**Problem:** Find the circumference of a circle with a radius of 20 cm.

**Solution:** Plug in 20 for r in the formula C = 2 πr and solve.

- C = (2)(π)(20)
- C = 40π
- C = 125.6

**Answer:** A circle with a diameter of 20 cm. has a circumference of 125.6 cm.

## #2 Find the Circumference of a Circle Given the Diameter

**Problem: **Find the circumference of a circle with a diameter of 36 in.

**Solution: **Simply plug in 36 for d in the formula C = πd and solve.

- C = (π)(36)
- C = (3.14)(36)
- C = 113

**Answer: **The circumference of a circle with a diameter of 36 in. is 113 in.

## #3 Find the Radius of a Circle Given the Circumference

**Problem: **What is the radius of a circle with a circumference of 132 ft.?

**Solution: **Since we are trying to determine the radius, plug in the known circumference, 132, for C in the formula C = 2πr and solve.

- 132 = 2πr
- 66 = πr
*(divide both sides by 2)* - 66 = (3.14)r
- r = 21
*(divide both sides by 3.14)*

**Answer: **A circle with a circumference of 132 ft. has a radius of about 21 ft.

## #4 Find the Circumference of a Circle Given the Area

**Problem:** Find the circumference of a circle that has an area of 78.5 m. squared.

**Solution: **This is a two-step problem. First, since we know the area of the circle we can figure out the radius of the circle by plugging in 78.5 for A in the area of a circle formula A = πr^{2} and solving:

- 78.5 = πr
^{2} - 78.5 = (3.14)r
^{2} - 25 = r
^{2}*(divide both sides by 3.14)* - r = 5
*(take the square root of both sides)*

Now that we know the radius is equal to 5 m. we can substitute 5 in for r in the formula C = 2πr and solve:

- C = 2π(5)
- C = (2)(3.14)(5)
- C = 31.4

**Answer: **A circle with an area of 78.5 m. squared has a circumference of 31.4 m.

## Do you need more geometry help online?

If you still need help with other **geometry problems about the circumference of a circle**, please ask in the comment section below. I'll be glad to help out and may even include circumference math problem in the problem/solution section above.

## Comments

LOL, my daughter (the smarter one) figured that out. I am following you so that I'll be sure to be able to find you again. Dd is doing fairly OK in geometry this semester, but last semester (algebra) most of her homework sessions ended in tears. She got a 45 on an algebra assignment that she, my husband and I all worked on together for three hours. LOL, we thought between the three of us she'd get at least a C. We will need you again for sure! Thank you!

Thank you so much, KTrapp, you are a life saver! I was able to go over your answer with my daughter this morning before school, and we both get it now! She and I are both "arts and letters" type people and have a hard time with math. I feel terrible when she asks me for help. I try to help but truthfully she is ahead of me in the math dept. I see those symbols and letters (like the m) and my brain just freezes up. Thanks so much for helping us both! You are wonderful!

I am trying to help my 7th grade daughter learn how to figure the circumference of a circle when all that is known is the area, but I'm the blind leading the blind, LOL. I'm looking at the last example, and I am not understanding at all. The example you give has an area of 78.5 m squared. What do we do if the area in her question is not m or squared? What does the m stand for? The area in her question is 200.96. How does that plug into the formula? I do not get it at all! Thank you!

I GET IT

You havn't really explained what you do in the equations if you could just do that this article would be even more helpful :)

k, k, k! I didn't need this stuff! I skated. But in California, you have to pass English and math to graduate. Ewwwwww. I would have flunked the math for sure!

I am pulling my hair out, but I do remember how to do this.

Of all math forms, geometry is the one that I have found most useful in my everyday life. These are little skills that we need to be reminded of from time to time. It also helps that I understand the importance of math and have a better attitude towards it now than I did when I was in high school! Voted up and useful.

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