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What is Circumference? - Definition & Equation

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  • 0:00 Circumference
  • 0:32 Circumference Equation
  • 0:47 Diameter Equation
  • 1:20 Radius Equation
  • 2:05 Lesson Summary
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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 this video, you'll learn how to define and find the circumference of a circle using two equations: one that involves the diameter and another that involves the radius.

Circumference

Our earth is a sphere, and if we sliced it in half, we'd end up with a circle. Circumference is the distance around a circle. We can measure the circumference of the earth by measuring the distance we'd cover if we walked the way around the world. To understand circumference, we also need to understand the meaning of diameter and radius.

The diameter is the distance across the center of a circle, shown in green in this image. The radius is the distance from the center to the edge of a circle, shown in red.


The circumference is the distance all the way around the circle.
circumference


Circumference Equation

There are two ways to write the equation for the circumference.


Equation for circumference using the diameter.
circumference


Equation for circumference using the radius.
circumference


You can use either of these equations, depending on whether the problem provides you with the diameter or the radius.

Diameter Equation

There are two ways you can apply the equation for the circumference of a circle using the diameter.

The first is by using the equation to find the circumference given the diameter. For example, if a problem gives you a diameter of 7, you'd plug in the value of the diameter for d and replace pi with 3.14.

Diameter equation 1

The second way to use the equation is when you need to find the diameter given a circumference, such as 21.98 inches. To do this, divide both sides by pi.

Diameter equation 2

Radius Equation

There are also two ways you can apply the equation for the circumference of a circle using the radius.

The first is by using the equation to find the circumference given the radius of a circle. For example, let's say the problem gives you a radius of 6 inches. You'd plug the 6 into the r variable and replace pi with 3.14.


Finding the circumference given the radius.
circumference


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