Finding the Radius: Formula & Concept

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Segment Relationships in Circles

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
Your next lesson will play in 10 seconds
  • 0:04 What Is the Radius?
  • 0:36 What About the Diameter?
  • 0:59 Finding Radius Using…
  • 1:55 Finding the Radius…
  • 3:14 Lesson Summary
Save Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Speed Speed Audio mode

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In some problems, the radius is easy to spot, but in others, the radius requires the use of some formulas. Learn how the formulas for circumference and area can help you in figuring out the radius of a circle or sphere.

What Is the Radius?

So, what exactly is the radius? The radius tells you how big a particular circle is. It starts at the center of a circle and goes to the edge of the circle. How long the radius is determines how large the circle is. A larger radius means a larger circle.

Notice that a smaller circle has a shorter, or smaller, radius than a larger circle. You can test it for yourself, too. Find any two circles of different sizes and measure their radiuses and compare. Which radius is larger? Which is smaller?

What About the Diameter?

There's another term related to the radius that you need to know, and that is diameter. The diameter is twice as long as the radius and is the distance from edge to edge of the circle passing through the center. If the radius is 2 inches long, then the diameter will be 4 inches long. It's always double. Let us now see how the various formulas for circles will help us find the radius.

Finding the Radius Using Circumference

We've just been given the circumference of a particular circle, and we now need to find the radius of the circle. How do we proceed?

First, we need the formula for circumference, which is C=2*pi*r. Once we have the formula, we can plug in our numbers for circumference and the constant pi to solve for r. We will use our algebra skills to rewrite the equation so r is by itself. Follow along with our steps.

We start with our circumference formula, which is C = 2*pi*r. Our next step is plugging in all the numbers we know. We know the circumference is 8 and we know the constant pi is always 3.14. After that, we simplify by multiplying the 2 by pi. After that, we divide by 6.28 so that r is by itself. When r is by itself, we have solved for the radius and now know how large the radius is. In this case, our radius is 1.27 meters.

To unlock this lesson you must be a Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use

Become a member and start learning now.
Become a Member  Back
What teachers are saying about
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account