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How to Find the Radius of a Circle: Definition & Formula

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  • 0:01 What Is a Radius?
  • 0:27 Formula for Radius
  • 0:57 Examples
  • 1:59 Lesson Summary
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Lesson Transcript
Instructor: Karin Gonzalez

Karin has taught middle and high school Health and has a master's degree in social work.

In this lesson, you will discover the definition of a radius. You will also learn how to find the radius of a circle using three different formulas based on diameter, circumference, and area.

What is a Radius?

A radius is a straight line from the center of a circle to the circumference of a circle. If you have two or more of them, they are referred to as radii. All radii in a circle will be the same length. The circumference is the outside perimeter of a circle. It's the distance around a circle. A radius can be a line from any point on the circumference to the center of the circle. If you put two radii together, edge to edge, going through the center of a circle, you would get a diameter.

Formula for Radius

The formulas to find the radius are quite simple. If you know the diameter of the circle, use this formula:

If you don't know the diameter, but you know the circumference, you can use this equation:

If you know the area of the circle, use this equation:

Note that the area of a circle is essentially the total space, measured in square units, inside of the perimeter of a circle.

Examples

Let's look at how we could apply the above equations to radii in real life.

Example 1

A bike wheel has many spokes that lead to the central hub of the wheel. Each spoke of the wheel will be the same distance from the circumference (the outer circular edge of the wheel) to the central hub (the center of circle). If we knew that the diameter of the wheel was 60 inches, we could easily find the radius of the wheel using this equation:

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