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How to Determine the Length of a Circumference From the Length of an Arc

A circle's circumference has quite a say in the length of a circle's arc, so it is only fair that an arc length can help in finding a circumference. An arc, a segment of the circumference, works together with its central angle, which is the angle underneath the arc, and the circle's radius to define one another. When you know the arc length and its central angle, you can find the circle's radius and then determine the circle's circumference with the its diameter and the math constant pi, which roughly equals 3.142.

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Instructions

    • 1

      Multiply the central angle by 2 * pi, then divide by 360 to convert the angle from degrees to radians. For an example, the central angle is 45 degrees --- 45 multiplied by 2 * pi approximately equals 282.743, and 282.743 divided by 360 roughly equals 0.785.

    • 2

      Divide the angle in radians into the arc length to calculate the length of the radius. For this example, allow the arc length to measure 2 inches --- dividing 2 inches by 0.785 approximately equals 2.548 inches.

    • 3

      Multiply the radius by 2 to calculate the circle's diameter. In this example, multiplying 2.548 by 2 equals 5.096 inches --- the diameter is 5.096 inches.

    • 4

      Multiply the diameter by pi to calculate the circle's circumference. Concluding this example, multiplying 5.096 inches by pi roughly equals 16.02 inches --- the circle's circumference is 16.02 inches.

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