How to Find the Perimeter of a Circle

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Perimeter is defined as the distance around a given area. Think of calculating how long a fence would be that completely surrounds your property. Perimeter is generally calculated by adding the lengths of all of the sides. Circles have no straight lines that are easily measured. Therefore, they require a special formula to determine perimeter.

    Learn that the perimeter of a circle has its own special name, called "circumference." The symbol is a capital C. It is calculated using the formula Pi x diameter, or 3.14 x d = C. It can also be calculated by Pi x (2 x radius) = C or 3.14 x (2 x r) = C.

    Learn about Pi. Pi is the result of dividing a circle's circumference by its diameter. No matter the length of the circumference or diameter, Pi is always the same. It is a number that goes on infinitely: 3.1415926 ..... To make it easier to use, it is shortened to 3.14. It is usually represented by the pictured symbol, which is the Greek letter of Pi.

    Review the meaning of diameter. Diameter is the distance of a straight line, drawn through the midpoint of a circle, that connects both sides of the circle. It is represented in the generic formula as d.

    Brush up on radius. The radius is equivalent to half the length of the diameter. It originates at the midpoint of the circle and stops at the perimeter of the circle. It is represented in equations by the letter r.

    Figure out the equation by plugging in the length for d in the equation. For example, if the given length of the diameter is 12 cm, your equation would be 3.14 x 12. The answer or circumference is 37.68 cm.

    Figure out the equation by plugging in the length for r in the equation, or double it for d in the equation. For example, if the given length of the radius is 4 feet, your equation would be 3.14 x (2 x 4). The answer, or circumference, is 25.12 feet.

    Work backward with these formulas, if you know the length of the circumference. Divide the length of the circumference by Pi (3.14) and you get the diameter. Divide the diameter by 2 to find the radius. For example, if the length of the circumference of the circle is 15.7 in., divide that by 3.14 (Pi) and you get 5. The length of the diameter is 5 inches. Divide that by 2, and you find that the length of the radius is 2.5 inches.

    Tips

    • Calculators can help you out when figuring the circumference, but it is better to exercise that brain muscle and work it out by hand.

About the Author

Andrea Coventry has been writing online since 2007. Her expertise includes teaching, working with children and Montessori schools. Her work has appeared in various online publications. Coventry is certified by the American Montessori Society.

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