An arc and the angle over which the arc sits share a special relationship. An arc is part of the circle's circumference, and the angle over which it extends is termed its central angle. The two properties help define one another with the help of the circle's radius, which equals half the diameter and is the length from the circle's center to any point on its circumference. By working with the radius and the math constant pi, finding the arc length with the angle is a matter of some quick math.
Instructions
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1
Measure the length from the center of the circle to its circumference to find its radius. For this example, let the radius be 3 inches.
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2
Multiply the angle by pi, then divide by 180 to convert the measurement to radians. In this example, let the angle measure 60 degrees. Multiplying 60 by pi equals 60pi, and 60pi divided by 180 equals 1/3pi, or approximately 1.047 radians.
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3
Multiply the angle in radians by the length of the radius to find the arc length. Multiplying 1.047 by 3 equals approximately 3.141 inches.