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Woodworking Math Tables, Formulas and Calculators

Polygon Formulas, Calculator and Tables

On the page you'll find formulae for calculating the dimensions and angles necessary to build multi-sided shapes, a Polygon Calculator 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 M will tell you the thickness of the material where the staves or sides of the shape are joined.

Polygon Calculator

Use the polygon calculator below to double check your own calculations.  We strongly recommend that you think through your woodworking calculations carefully and double check your figures before you begin sawing!

Polygon Calculator

To use the polygon calculator, you need to begin with two known values. Select the appropriate combination below.

Number of sides

Outside Dimension D1

Outside Dimension D2

Side length (S)

Bevel angle (B)

I know: The number of sides and dimension D1

I want to find: Length of the sides (S), the bevel angle (B), and dimension D2
I know: The number of sides and dimension D2

I want to find: the number of sides, the length of the sides (S), and dimension D1 
I know: the number of sides and the side length (S)

I want to find: the bevel angle (B) and dimensions D1 and D2
    

 

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
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