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Video:How to Find the Perimeter of a Circle

with Jen D'Amore

Finding the perimeter, or circumference, of a circle is a basic math skill that is easy to master. Here is a step-by-step demonstration on how to find the perimeter of a circle.See Transcript

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Transcript:How to Find the Perimeter of a Circle

Hi, I'm Jen D'Amore for About.com and this video is all about how to find the perimeter, or circumference, of a circle.

Can Use Two Formulas to Find the Perimeter of a Circle

The circumference is the length or distance of the outside of a circle. To find it we'll need to also know the radius or diameter of the circle. But once you know one, you could figure out the other, since the diameter is twice the radius, and the radius is half of the diameter.

So, you have your choice in formulas, depending on which one you want to use. Here's the first: C equals pi times d, or since the radius is half of the diameter, C equals pi 2 r.

C is the circumference, r is the radius, d is diameter and pi equals 3.1415926 (even though pi continues infinitely, we can cut it at 7 decimal places).

Use Pi to Find the Perimeter of a Circle

So why does this formula work? And where did pi come from? Pi is a lower-case greek letter that represents the irrational constant 3.141592653589. It is irrational because it cannot be expressed as a simple fraction, as it changes so irrationally as it stretches to infinity. But we'll just keep it to seven decimal places.

If your calculator has a pi key you can just use that. That will keep you from having to type in all those extra numbers.

According to Archimedes, the great mathematician, Pi is the ratio of a circle's circumference to it's diameter, so, if the diameter is 1, the circumference is pi, which is why we see it in our circle-solving equations.

Examples of Finding the Perimeter of a Circle

Plugging that into the equation you can see it more clearly. Pi x 1 = pi -- if your diameter is 2 meters, plug that into the equation C = 2 pi = 6.2 meters. If the diameter of the circle is 20 feet, 20pi = 62.83 feet.

As you can see, it doesn't matter what unit of measurement your using, inches, feet, miles or meters -- you can plug any into the formula to find the circumference in whatever unit you prefer, as long as you stay consistent.

If you're only given the radius, first double it to find the diameter, then plug it into the equation: r = 5 cm, 2r = d, 2(5) = 10 cm = d. Now you can plug into your equation: 10(pi) = 31.415 cm. Of course, you could save a step and use the other formula I mentioned for finding circumference, C = pi 2 r. In this case, plug the radius directly into the equation.

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