How to Find the Circumference of a Circle

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You can find the circumference of a circle by using the measurement of its diameter, radius or area. The circumference of a circle is the distance around the circle's edge from one point, meeting back at that point. Knowing how to calculate a circle's circumference can be useful in math class but also in real-life situations such as craft projects and construction tasks.

Understanding the Circle

Reviewing the features of a circle before you begin is a good way to avoid calculating incorrectly. A circle is a symmetrical, round, two-dimensional figure. The circumference, or distance around the circle, includes a series of points that are all equidistant from the exact center of the circle. The diameter is a line segment that passes from one point on the circle's edge directly through the middle of the circle to a point on the circle's opposite edge. The radius is a line segment that extends from one point on the edge of the circle inward to the center of the circle. The area of a circle is the space inside the circle.

Using the Diameter

The diameter is the simplest measurement for finding the circumference of a circle, and it requires the fewest steps. Start with the formula C = πd (circumference = 3.14 x diameter). If you enter π (pi) into your calculator, you will get the longer, more accurate value for pi. But you can also use the acceptable approximation for π, which is 3.14. If the diameter of a wheel is 10 inches, for example, your equation would read C = 3.14 x 10, which equals a circumference of 31.4 inches.

Using the Radius

The radius of a circle, half of its diameter, can help you find the circumference in a couple of steps. First, double the radius to get the diameter (radius x 2, or radius + radius). One you have the diameter, you can use the equation C = πd. If you want to know the circumference of a cookie that has a radius of 2 inches, for instance, start by doubling the radius to get the diameter: 2 x 2 = 4. Next use the diameter in the equation C = πd: C = 3.14 x 4. The circumference of the cookie is 12.56 inches.

Using the Area

Using the area to find the circumference of a circle is slightly more complex. First you must find the radius, then the diameter and then the circumference. If you know that the area inside a circle is equal to 153.86 square inches, use the following equation to find the radius: A = π(r x r). Your equation would look like this: 153.86 = 3.14(r x r). Divide both sides of the equation by 3.14, then find the square root of both sides. The radius will be 7 inches. Now you can double the radius to get 14 and use the equation C = πd. If C = 3.14 x 14, then C = 43.96 inches.

References

About the Author

Rachel Pancare taught elementary school for seven years before moving into the K-12 publishing industry. Pancare holds a Master of Science in childhood education from Bank Street College and a Bachelor of Arts in English from Skidmore College.

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  • Spike Mafford/Photodisc/Getty Images

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