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12B sprocket dimensions: pitch, outside and root diameters from 9 to 120 teeth

The 12B chain (ISO 606 B series) has a pitch of 19.1 mm and a roller of 12.1 mm. These two numbers set every diameter of the sprocket that runs it.

The table gives, for every tooth count, the diameters a sprocket cut from plate must have: the pitch diameter the rollers sit on, the outside diameter at the tooth tips, the root diameter at the bottom of the gaps and the measurement a caliper reads across the gaps. Every row opens the sprocket generator with that chain and tooth count, for the 1:1 template and the DXF.

Teeth Pitch Ø, d Outside Ø, da Root Ø, df Caliper check
9 2.19 2.49 1.72 1.68 Draw
10 2.43 2.74 1.95 1.95 Draw
11 2.66 2.98 2.19 2.16 Draw
12 2.90 3.22 2.42 2.42 Draw
13 3.13 3.46 2.66 2.64 Draw
14 3.37 3.70 2.90 2.90 Draw
15 3.61 3.94 3.13 3.11 Draw
16 3.84 4.18 3.37 3.37 Draw
17 4.08 4.41 3.61 3.59 Draw
18 4.32 4.65 3.84 3.84 Draw
19 4.56 4.89 4.08 4.07 Draw
20 4.79 5.13 4.32 4.32 Draw
21 5.03 5.37 4.56 4.54 Draw
22 5.27 5.61 4.79 4.79 Draw
23 5.51 5.85 5.03 5.02 Draw
24 5.75 6.09 5.27 5.27 Draw
25 5.98 6.33 5.51 5.50 Draw
26 6.22 6.57 5.75 5.75 Draw
27 6.46 6.81 5.99 5.97 Draw
28 6.70 7.05 6.22 6.22 Draw
29 6.94 7.28 6.46 6.45 Draw
30 7.18 7.52 6.70 6.70 Draw
31 7.41 7.76 6.94 6.93 Draw
32 7.65 8.00 7.18 7.18 Draw
33 7.89 8.24 7.41 7.41 Draw
34 8.13 8.48 7.65 7.65 Draw
35 8.37 8.72 7.89 7.88 Draw
36 8.61 8.96 8.13 8.13 Draw
37 8.84 9.20 8.37 8.36 Draw
38 9.08 9.43 8.61 8.61 Draw
39 9.32 9.67 8.85 8.84 Draw
40 9.56 9.91 9.08 9.08 Draw
41 9.80 10.15 9.32 9.32 Draw
42 10.04 10.39 9.56 9.56 Draw
43 10.27 10.63 9.80 9.79 Draw
44 10.51 10.87 10.04 10.04 Draw
45 10.75 11.11 10.28 10.27 Draw
46 10.99 11.35 10.52 10.52 Draw
47 11.23 11.58 10.75 10.75 Draw
48 11.47 11.82 10.99 10.99 Draw
49 11.71 12.06 11.23 11.22 Draw
50 11.94 12.30 11.47 11.47 Draw
51 12.18 12.54 11.71 11.70 Draw
52 12.42 12.78 11.95 11.95 Draw
53 12.66 13.02 12.19 12.18 Draw
54 12.90 13.26 12.42 12.42 Draw
55 13.14 13.50 12.66 12.66 Draw
56 13.38 13.73 12.90 12.90 Draw
57 13.61 13.97 13.14 13.13 Draw
58 13.85 14.21 13.38 13.38 Draw
59 14.09 14.45 13.62 13.61 Draw
60 14.33 14.69 13.86 13.86 Draw
61 14.57 14.93 14.09 14.09 Draw
62 14.81 15.17 14.33 14.33 Draw
63 15.05 15.41 14.57 14.57 Draw
64 15.29 15.64 14.81 14.81 Draw
65 15.52 15.88 15.05 15.04 Draw
66 15.76 16.12 15.29 15.29 Draw
67 16.00 16.36 15.53 15.52 Draw
68 16.24 16.60 15.76 15.76 Draw
69 16.48 16.84 16.00 16.00 Draw
70 16.72 17.08 16.24 16.24 Draw
71 16.96 17.32 16.48 16.48 Draw
72 17.19 17.55 16.72 16.72 Draw
73 17.43 17.79 16.96 16.95 Draw
74 17.67 18.03 17.20 17.20 Draw
75 17.91 18.27 17.43 17.43 Draw
76 18.15 18.51 17.67 17.67 Draw
77 18.39 18.75 17.91 17.91 Draw
78 18.63 18.99 18.15 18.15 Draw
79 18.86 19.23 18.39 18.39 Draw
80 19.10 19.46 18.63 18.63 Draw
81 19.34 19.70 18.87 18.86 Draw
82 19.58 19.94 19.11 19.11 Draw
83 19.82 20.18 19.34 19.34 Draw
84 20.06 20.42 19.58 19.58 Draw
85 20.30 20.66 19.82 19.82 Draw
86 20.54 20.90 20.06 20.06 Draw
87 20.77 21.14 20.30 20.30 Draw
88 21.01 21.37 20.54 20.54 Draw
89 21.25 21.61 20.78 20.77 Draw
90 21.49 21.85 21.02 21.02 Draw
91 21.73 22.09 21.25 21.25 Draw
92 21.97 22.33 21.49 21.49 Draw
93 22.21 22.57 21.73 21.73 Draw
94 22.45 22.81 21.97 21.97 Draw
95 22.68 23.05 22.21 22.21 Draw
96 22.92 23.28 22.45 22.45 Draw
97 23.16 23.52 22.69 22.68 Draw
98 23.40 23.76 22.92 22.92 Draw
99 23.64 24.00 23.16 23.16 Draw
100 23.88 24.24 23.40 23.40 Draw
101 24.12 24.48 23.64 23.64 Draw
102 24.35 24.72 23.88 23.88 Draw
103 24.59 24.96 24.12 24.12 Draw
104 24.83 25.19 24.36 24.36 Draw
105 25.07 25.43 24.60 24.59 Draw
106 25.31 25.67 24.83 24.83 Draw
107 25.55 25.91 25.07 25.07 Draw
108 25.79 26.15 25.31 25.31 Draw
109 26.03 26.39 25.55 25.55 Draw
110 26.26 26.63 25.79 25.79 Draw
111 26.50 26.87 26.03 26.02 Draw
112 26.74 27.10 26.27 26.27 Draw
113 26.98 27.34 26.51 26.50 Draw
114 27.22 27.58 26.74 26.74 Draw
115 27.46 27.82 26.98 26.98 Draw
116 27.70 28.06 27.22 27.22 Draw
117 27.94 28.30 27.46 27.46 Draw
118 28.17 28.54 27.70 27.70 Draw
119 28.41 28.78 27.94 27.93 Draw
120 28.65 29.01 28.18 28.18 Draw

Dimensions in in. The outside diameter is the middle of the ISO 606 range; ANSI catalogues print a slightly larger figure, for the tighter ANSI tooth, and the pitch and root diameters are the same. The caliper check is the root diameter on an even tooth count and d × cos(90°/z) − d1 on an odd one, read across the two gaps nearest to opposite.

How the numbers are worked out

Pitch diameter
d = p / sin(180° / z) p is the chain pitch and z the number of teeth.
Outside diameter
da = d − d1 + p × (1.125 − 0.8 / z) d1 is the roller diameter. The middle of the ISO 606 range, from d + p (1 − 1.6/z) − d1 to d + 1.25 p − d1.
Root diameter
df = d − d1 The bottom of the tooth gap, which is what the chain sits on.
Caliper check
even z: df ; odd z: d × cos(90° / z) − d1 On an even tooth count one gap faces another and the caliper reads df; on an odd one it reads across the two gaps nearest to opposite.

Questions

What is the pitch diameter of a 20-tooth %{chain} sprocket?
%{d20}: d = p / sin(180° / 20) with p = %{pitch}. The outside diameter is %{da20} and the root diameter %{df20}.
How do I check a %{chain} sprocket after cutting it?
With a caliper across the tooth gaps. On an even tooth count it reads the root diameter, d − d1 with d1 = %{roller}; on an odd one, across the two gaps nearest to opposite, it reads d × cos(90°/z) − d1. The table gives the figure for every tooth count.
Why is the outside diameter in the table different from the catalogue?
The table is the middle of the ISO 606 range, which is the nominal a plasma or laser cut should aim at. ANSI catalogues print the outside diameter of the tighter ANSI tooth, a few tenths of a millimetre larger; the pitch and root diameters, which are what the chain sits on, are the same.