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

The ANSI 120 chain (ANSI B29.1) has a pitch of 1.500 in (38.1 mm) and a roller of 0.875 in (22.2 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 4.39 5.06 3.51 3.44 Draw
10 4.85 5.55 3.98 3.98 Draw
11 5.32 6.03 4.45 4.40 Draw
12 5.80 6.51 4.92 4.92 Draw
13 6.27 6.99 5.39 5.35 Draw
14 6.74 7.47 5.87 5.87 Draw
15 7.21 7.95 6.34 6.30 Draw
16 7.69 8.43 6.81 6.81 Draw
17 8.16 8.91 7.29 7.25 Draw
18 8.64 9.38 7.76 7.76 Draw
19 9.11 9.86 8.24 8.21 Draw
20 9.59 10.34 8.71 8.71 Draw
21 10.06 10.82 9.19 9.16 Draw
22 10.54 11.30 9.67 9.67 Draw
23 11.02 11.78 10.14 10.12 Draw
24 11.49 12.25 10.62 10.62 Draw
25 11.97 12.73 11.09 11.07 Draw
26 12.44 13.21 11.57 11.57 Draw
27 12.92 13.69 12.05 12.02 Draw
28 13.40 14.17 12.52 12.52 Draw
29 13.87 14.64 13.00 12.98 Draw
30 14.35 15.12 13.48 13.48 Draw
31 14.83 15.60 13.95 13.93 Draw
32 15.30 16.08 14.43 14.43 Draw
33 15.78 16.56 14.91 14.89 Draw
34 16.26 17.03 15.38 15.38 Draw
35 16.73 17.51 15.86 15.84 Draw
36 17.21 17.99 16.34 16.34 Draw
37 17.69 18.47 16.81 16.80 Draw
38 18.16 18.95 17.29 17.29 Draw
39 18.64 19.42 17.77 17.75 Draw
40 19.12 19.90 18.24 18.24 Draw
41 19.60 20.38 18.72 18.71 Draw
42 20.07 20.86 19.20 19.20 Draw
43 20.55 21.33 19.67 19.66 Draw
44 21.03 21.81 20.15 20.15 Draw
45 21.50 22.29 20.63 20.62 Draw
46 21.98 22.77 21.11 21.11 Draw
47 22.46 23.24 21.58 21.57 Draw
48 22.93 23.72 22.06 22.06 Draw
49 23.41 24.20 22.54 22.52 Draw
50 23.89 24.68 23.01 23.01 Draw
51 24.37 25.16 23.49 23.48 Draw
52 24.84 25.63 23.97 23.97 Draw
53 25.32 26.11 24.45 24.43 Draw
54 25.80 26.59 24.92 24.92 Draw
55 26.27 27.07 25.40 25.39 Draw
56 26.75 27.54 25.88 25.88 Draw
57 27.23 28.02 26.35 26.34 Draw
58 27.71 28.50 26.83 26.83 Draw
59 28.18 28.98 27.31 27.30 Draw
60 28.66 29.45 27.79 27.79 Draw
61 29.14 29.93 28.26 28.25 Draw
62 29.62 30.41 28.74 28.74 Draw
63 30.09 30.89 29.22 29.21 Draw
64 30.57 31.36 29.70 29.70 Draw
65 31.05 31.84 30.17 30.16 Draw
66 31.52 32.32 30.65 30.65 Draw
67 32.00 32.80 31.13 31.12 Draw
68 32.48 33.27 31.60 31.60 Draw
69 32.96 33.75 32.08 32.07 Draw
70 33.43 34.23 32.56 32.56 Draw
71 33.91 34.71 33.04 33.03 Draw
72 34.39 35.18 33.51 33.51 Draw
73 34.87 35.66 33.99 33.98 Draw
74 35.34 36.14 34.47 34.47 Draw
75 35.82 36.62 34.95 34.94 Draw
76 36.30 37.09 35.42 35.42 Draw
77 36.77 37.57 35.90 35.89 Draw
78 37.25 38.05 36.38 36.38 Draw
79 37.73 38.53 36.85 36.85 Draw
80 38.21 39.00 37.33 37.33 Draw
81 38.68 39.48 37.81 37.80 Draw
82 39.16 39.96 38.29 38.29 Draw
83 39.64 40.44 38.76 38.76 Draw
84 40.12 40.91 39.24 39.24 Draw
85 40.59 41.39 39.72 39.71 Draw
86 41.07 41.87 40.20 40.20 Draw
87 41.55 42.35 40.67 40.67 Draw
88 42.03 42.82 41.15 41.15 Draw
89 42.50 43.30 41.63 41.62 Draw
90 42.98 43.78 42.11 42.11 Draw
91 43.46 44.26 42.58 42.58 Draw
92 43.94 44.73 43.06 43.06 Draw
93 44.41 45.21 43.54 43.53 Draw
94 44.89 45.69 44.02 44.02 Draw
95 45.37 46.17 44.49 44.49 Draw
96 45.84 46.64 44.97 44.97 Draw
97 46.32 47.12 45.45 45.44 Draw
98 46.80 47.60 45.92 45.92 Draw
99 47.28 48.08 46.40 46.40 Draw
100 47.75 48.55 46.88 46.88 Draw
101 48.23 49.03 47.36 47.35 Draw
102 48.71 49.51 47.83 47.83 Draw
103 49.19 49.99 48.31 48.31 Draw
104 49.66 50.46 48.79 48.79 Draw
105 50.14 50.94 49.27 49.26 Draw
106 50.62 51.42 49.74 49.74 Draw
107 51.10 51.90 50.22 50.22 Draw
108 51.57 52.37 50.70 50.70 Draw
109 52.05 52.85 51.18 51.17 Draw
110 52.53 53.33 51.65 51.65 Draw
111 53.01 53.81 52.13 52.13 Draw
112 53.48 54.28 52.61 52.61 Draw
113 53.96 54.76 53.09 53.08 Draw
114 54.44 55.24 53.56 53.56 Draw
115 54.92 55.72 54.04 54.04 Draw
116 55.39 56.19 54.52 54.52 Draw
117 55.87 56.67 55.00 54.99 Draw
118 56.35 57.15 55.47 55.47 Draw
119 56.82 57.63 55.95 55.94 Draw
120 57.30 58.10 56.43 56.43 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.