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How to Calculate a 15-Degree Angle

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The arc that a 15-degree angle forms represents just a small fraction of a circle's circumference. The fraction between the arc length and the circle's total length exactly equals the fraction between the angle size and the degree measure of the total circle. The circumference itself is directly related to a separate length -- the radius of the circle. The ratio between the circumference and the radius is twice the constant pi.

Multiply the angle's radius by 6.283, which is approximately twice pi. For this example, imagine a radius of 6 inches:

6 x 6.283 = 37.698. This is the circle's total circumference.

Multiply the circumference by 15:

37.698 x 15 = 565.47.

Divide the result by 360, the total number of degrees in the circle:

565.47 / 360 = 1.57 inches. This is the length of the angle's associated arc.

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About the Author

Ryan Menezes is a professional writer and blogger. He has a Bachelor of Science in journalism from Boston University and has written for the American Civil Liberties Union, the marketing firm InSegment and the project management service Assembla. He is also a member of Mensa and the American Parliamentary Debate Association.