How to Calculate the Outside Length of a Circle

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Determining the outside distance of a circle is a common arithmetic problem. In order to determine the outside length of a circle, certain measurements of the circle must be known beforehand, including the radius or diameter of a circle.

Place a small dot in the center of a piece of paper. Place the point of the compass on the dot.

Use a sweeping motion to keep the point of the compass in place while sweeping the attached pencil in a smooth arc to create a circle.

Use a ruler to measure the distance from the center dot you already created in the circle to one of the outside edges of the circle. This is the radius of the circle. Ideally, you should record the radius in centimeters (or metric), but any unit of measurement can be used.

Record the radius of the circle on your paper using a small letter 'r' as the symbol for the radius. For example, r=5 cm. Do not forget to record the units.

Use the radius of the circle you drew to calculate the circumference of the circle using the formula C=2 ? r.

Use a calculator to multiply 2 * ? * r. Alternately, you can use the shortened equivalent of pi which is ?=3.14. By using 3.14, you are able to multiple the circumference without the aid of a calculator.

In our example, the circumference (c) of the circle with a radius of 5 cm would be 31.41592 cm when you use a calculator to multiply 2 * ? * 5. Notice that if you calculate by hand, there is a slight difference due to rounding errors giving the answer 31.4 cm.

Tips

• Alternately, you can determine the diameter of your circle by measuring the distance all the way across the circle, making sure to intersect the middle point. A diameter (d) is twice the radius of a circle. In out example, that would give our circle a diameter = 10 cm. The formula for determining the circumference of a circle using the diameter is
c = ? d.

Warnings

• For a more thorough understanding of pi, please visit the Math forum at http://mathforum.org/dr.math/FAQ/FAQ.pi.html. Without understanding the relationship of the circumference of a circle to the diameter of a circle, you may get confused with more difficult geometry problems.