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Woodworking Math Tables, Formulas & Calculators - Part III

Polygon Formulas, Calculator and Tables

On the page you'll find formulae for calculating the dimensions and angles necessary to build multi-sided shapes and tables containing dimensions and angles for common sizes of polygons.

Polygon Formulas

Formulas for calculating dimensions and angles used in building regular polygon shapes are listed below.  Please be sure to double-check your calculations carefully and make an appropriate number of test cuts before you begin sawing the stock you've invested in for your project.

 N = Number of sides of the polygon B = 180/N (See Note 1 below) S = sin(B) x D1 S = tan(B) x D2 D1 = S/sin(B) D1 = D2 /cos(B) D2 = S/tan(B) D2 = cos(B) x D1 D4 = D2 - (material thickness x 2) D3 = D4 / cos(B)M = D2 - D3 (see Note 2 below)

Note 1: "B" is the bevel or miter angle setting for saws that calibrate a square cut at zero degree.  For saws that calibrate a square cut at 90 degrees, use the complement of B for the saw's setting. Note 2: Dimension "M" is useful in projects that involve rounding off the corners of a polygon to form a round or cylindrical shape. Dimension Mwill tell you the thickness of the material where the staves or sides of the shape are joined.

Tables

Use the quick reference tables below to double-check angles and dimensions of common sizes of polygons.

 Polygon Angles and Dimensions Number of Sides Bevel Angle Side-to-Side Width Tip-to-Tip Width Side Length Decimal Approx. Fractional Decimal Approx. Fractional Decimal Approx. Fractional 6 30° 5.1962 5-1164 6.0 6 3.0 3 6.0 6 6.9282 6-59/64 3.4641 3-15/32 6.9282 6-63/64 8.0 8 4.0 4 8.0 8 9.2376 9-15/64 4.6188 4-5/8 8.6603 8-21/32 10.0 10 5.0 5 10.0 10 11.5470 11-35/64 5.7735 5-25/32 10.3923 10-25/64 12.0 12 6.0 6 12.0 12 13.8564 13-55/64 6.9282 6-59/64 12.1244 12-1/8 14.0 14 7.0 7 14.0 14 16.1658 16-11/64 8.0829 8-5/64 13.8564 13-55/64 16.0 16 8.0 8 16.0 16 18.4752 18-15/32 9.2376 9-15/64 15.5885 15-19/32 18.0 18 9.0 9 18.0 18 20.7846 20-25/32 10.3923 10-25/32 Side-to-Side Width Tip-to-Tip Width Side Length Number of Sides Bevel Angle Decimal Fractional Equivalent Decimal Fractional Equivalent Decimal Fractional Equivalent 8 22.5° 5.5433 5-35/64 6.0 6 2.2961 2-19/64 6.0 6 6.4944 6-1/2 2.4853 2-31/64 7.391 7-25/64 8.0 8 3.0615 3-1/16 8.0 8 8.6591 8-21/32 3.3137 3-5/16 9.2388 9-15/64 10.0 10 3.8268 3-53/64 10.0 10 10.8239 10-53/64 4.1421 4-9/64 11.0866 12.0 12 4.5922 4-19/32 12.0 12 12.9887 13 4.9706 4-31/32 12.9343 12-15/16 14.0 14 5.3576 5-23/64 14.0 14 15.1535 15-5/32 5.799 5-51/64 14.7821 14-25/32 16.0 16 6.1229 6-5/8 16.0 16 17.3183 17-5/16 6.6274 6-5/8 16.6298 16-5/8 18.0 18 6.8883 6-57/64 18.0 18 19.483 19-31/64 7.4558 7-29/64 Side-to-Side Width Tip-to-Tip Width Side Length Number of Sides Bevel Angle Decimal Fractional Equivalent Decimal Fractional Equivalent Decimal Fractional Equivalent 12 15° 5.7956 5-51/64 6.0 6 1.5529 1-35/64 6.0 6 6.2117 6-7/32 1.6077 1-39/64 7.7274 7-47/64 8.0 8 2.0706 2-5/64 8.0 8 8.2822 8-9/32 2.1436 2-9/64 9.6593 9-21/32 10.0 10 2.5882 2-19/32 10.0 10 10.3528 10-23/64 2.6795 2-43/64 11.5911 11-19/32 12.0 12 3.1058 3-7/64 12.0 12 12.4233 12-27/64 3.2154 3-7/32 13.523 13-33/64 14.0 14 3.6235 3-5/8 14.0 14 14.4939 14-1/2 3.7513 4-3/4 15.4548 15-29/64 16.0 16 4.1411 4-9/64 16.0 16 16.5644 16-9/16 4.2872 4-9/32 17.3867 17-25/64 18.0 18 4.6587 4-21/32 18.0 18 18.635 18-41/64 4.8231 4-53/64 Side-to-Side Width Tip-to-Tip Width Side Length Number of Sides Bevel Angle Decimal Fractional Equivalent Decimal Fractional Equivalent Decimal Fractional Equivalent 16 11.25 5.8847 5-57/64 6.0 6 1.1705 1-11/64 6.0 6 6.1176 6-5/8 1.1935 1-3/16 7.8463 7-27/32 8.0 8 1.5607 1-9/16 8.0 8 8.1567 8-5/32 1.5913 1-19/32 9.8079 9-13/16 10.0 10 1.9509 1-61/64 10.0 10 10.1959 10-13/64 1.9891 2 11.7694 11-49/64 12.0 12 2.3411 2-11/32 12.0 12 12.2351 12-15/64 2.3869 2-25/64 13.731 13-47/64 14.0 14 2.7313 2-47/64 14.0 14 14.2743 14-9/32 2.7848 2-25/32 15.6926 15-11/16 16.0 16 3.1214 3-1/8 16.0 16 16.3135 16-5/16 3.1826 3-3/16 17.6541 17-21/32 18.0 18 3.5116 3-33/64 18.0 18 18.3526 18-23/64 3.5804 3-37/64