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How to Find the Length of the Sides of an Octagon Based on Diameter

    Apothem or Inradius

    • 1). Divide pi by 8 with your calculator. Pi divided by 8 results in approximately 0.393.

    • 2). Calculate the tangent value of 0.393 in radians with your calculator. The tangent function is generally denoted by "tan." The tangent of 0.393 in radians approximately equals 0.414 radians.

    • 3). Multiply the diameter, which is the perpendicular length between two parallel sides, by 0.414 to calculate a side's length. For example, the diameter measures 5 inches and 5 inches multiplied by 0.414 equals 2.07 inches.

    Radius or Circumradius

    • 1). Divide pi by 8 with your calculator. Pi divided by 8 results in approximately 0.393.

    • 2). Calculate the sine value of 0.393 in radians with your calculator --- the sine function is generally denoted as "sin." The sine of 0.393 in radians approximately equals 0.383 radians.

    • 3). Multiply the diameter's length, the distance from vertex to opposite vertex, by 0.383 to calculate a side's length. For example, the diameter is 10 inches --- 10 inches multiplied by 0.383 results in 3.83 inches.



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