## How To Understand Calculating A Circumference

Calculating the circumference of a circle let's you know the distance around the circle. This video will teach you how!

Hi, my name is Charles and I'm one of the math teachers from the Maxim Workshop. I'm just going to now teach you how to do some math. Hi, I'm going to show you how to calculate the circumference of a circle.

First thing we want to do is set out our circle, and just to show you what the circumference and any other variable that might be relevant, how it looks on our circle. So, we've got the origin here and you have the radius which extends from the center of the circle out to the side of the circle. It could go here, it could go there.

Now, the diameter goes from one side to the other and passes through the actual center. So where your radius cuts half of your circle from the origin to the side, your actual diameter starts from one side to the other and also passes through the origin. So, those are the two main things that we're going to use to calculate the circumference of a circle.

Now, the basic idea is that circumference is a measurement of a perimeter so is basically the outside distance of your circle. So, if you were to walk all the way around this circle, it would be the distance that you travelled. So, circumference is given by another equation.

Pi times d. Now d remember, is the length going from one side, passing through the origin, and then going to the opposite side in a straight line. The radius is half that distance.

So, you have Pi times 2r. So, Pi times r2. This is not r squared, this is r times 2, okay? So if we were given measurements for the radius and the diameter, both measurements, then we could calculate the circumference of any given circle.

So, if we take one circle using the diameter as 5 centimeters on a particular circle, we would want to calculate the circumference. So now we're going to first use approximately pi which more accurately equals 3.142 but we're going to approximate it to 3.

Just for easier calculation. Now, if you think about the circumference, it equals pi times d. So circumference here equals 3 times d, 5 centimeters.

Now, that gives us a measurement of 3 times 5 which is 15 centimeters. Now remember, centimeters not centimeters squared because circumference is a length, not an area. Now, there's our first calculation so that's how to calculate the circumference given we know the diameter.

Now, what happens when we don't know the diameter but we know the radius? Well if you think about once you know either radius or diameter, you know the other. So if we were given the radius now of a different circle and it was equal to 10 meters, that would imply that our diameter equals 20 meters. So, again we'll approximate Pi as 3, and we'll try to solve out what the circumference equals.

So, the circumference now, again, is equal to Pi times 2 times r. So, we've got Pi times 2 times the radius. So, we have 3 times 2 which equals 6 times r which is 10 meters.

So that means now we've got six times 10 which is 60 in units of meters. So our circumference on this circle will give us 60 meters. Remember, these are two different circles.

One having the diameter of 5 centimeters, and one having a radius of 10 meters which would imply a diameter of 20 meters. So that's how to calculate the circumference of a circle. .