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.

ANSI 25 sprocket dimensions: pitch, outside and root diameters from 9 to 120 teeth

The ANSI 25 chain (ANSI B29.1) has a pitch of 0.250 in (6.4 mm) and a roller of 0.130 in (3.3 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	18.6	21.8	15.3	15.0	Draw
10	20.5	23.9	17.2	17.2	Draw
11	22.5	25.9	19.2	19.0	Draw
12	24.5	28.0	21.2	21.2	Draw
13	26.5	30.0	23.2	23.0	Draw
14	28.5	32.0	25.2	25.2	Draw
15	30.5	34.0	27.2	27.1	Draw
16	32.5	36.1	29.2	29.2	Draw
17	34.6	38.1	31.3	31.1	Draw
18	36.6	40.1	33.3	33.3	Draw
19	38.6	42.2	35.3	35.1	Draw
20	40.6	44.2	37.3	37.3	Draw
21	42.6	46.2	39.3	39.2	Draw
22	44.6	48.2	41.3	41.3	Draw
23	46.6	50.3	43.3	43.2	Draw
24	48.6	52.3	45.3	45.3	Draw
25	50.7	54.3	47.4	47.3	Draw
26	52.7	56.3	49.4	49.4	Draw
27	54.7	58.4	51.4	51.3	Draw
28	56.7	60.4	53.4	53.4	Draw
29	58.7	62.4	55.4	55.3	Draw
30	60.7	64.4	57.4	57.4	Draw
31	62.8	66.4	59.5	59.4	Draw
32	64.8	68.5	61.5	61.5	Draw
33	66.8	70.5	63.5	63.4	Draw
34	68.8	72.5	65.5	65.5	Draw
35	70.8	74.5	67.5	67.5	Draw
36	72.9	76.6	69.6	69.6	Draw
37	74.9	78.6	71.6	71.5	Draw
38	76.9	80.6	73.6	73.6	Draw
39	78.9	82.6	75.6	75.5	Draw
40	80.9	84.6	77.6	77.6	Draw
41	83.0	86.7	79.7	79.6	Draw
42	85.0	88.7	81.7	81.7	Draw
43	87.0	90.7	83.7	83.6	Draw
44	89.0	92.7	85.7	85.7	Draw
45	91.0	94.8	87.7	87.7	Draw
46	93.1	96.8	89.7	89.7	Draw
47	95.1	98.8	91.8	91.7	Draw
48	97.1	100.8	93.8	93.8	Draw
49	99.1	102.8	95.8	95.8	Draw
50	101.1	104.9	97.8	97.8	Draw
51	103.1	106.9	99.8	99.8	Draw
52	105.2	108.9	101.9	101.9	Draw
53	107.2	110.9	103.9	103.8	Draw
54	109.2	113.0	105.9	105.9	Draw
55	111.2	115.0	107.9	107.9	Draw
56	113.3	117.0	109.9	109.9	Draw
57	115.3	119.0	112.0	111.9	Draw
58	117.3	121.0	114.0	114.0	Draw
59	119.3	123.1	116.0	116.0	Draw
60	121.3	125.1	118.0	118.0	Draw
61	123.4	127.1	120.0	120.0	Draw
62	125.4	129.1	122.1	122.1	Draw
63	127.4	131.2	124.1	124.1	Draw
64	129.4	133.2	126.1	126.1	Draw
65	131.4	135.2	128.1	128.1	Draw
66	133.5	137.2	130.2	130.2	Draw
67	135.5	139.2	132.2	132.1	Draw
68	137.5	141.3	134.2	134.2	Draw
69	139.5	143.3	136.2	136.2	Draw
70	141.5	145.3	138.2	138.2	Draw
71	143.6	147.3	140.3	140.2	Draw
72	145.6	149.3	142.3	142.3	Draw
73	147.6	151.4	144.3	144.3	Draw
74	149.6	153.4	146.3	146.3	Draw
75	151.6	155.4	148.3	148.3	Draw
76	153.7	157.4	150.4	150.4	Draw
77	155.7	159.5	152.4	152.3	Draw
78	157.7	161.5	154.4	154.4	Draw
79	159.7	163.5	156.4	156.4	Draw
80	161.7	165.5	158.4	158.4	Draw
81	163.8	167.5	160.5	160.4	Draw
82	165.8	169.6	162.5	162.5	Draw
83	167.8	171.6	164.5	164.5	Draw
84	169.8	173.6	166.5	166.5	Draw
85	171.8	175.6	168.5	168.5	Draw
86	173.9	177.7	170.6	170.6	Draw
87	175.9	179.7	172.6	172.6	Draw
88	177.9	181.7	174.6	174.6	Draw
89	179.9	183.7	176.6	176.6	Draw
90	182.0	185.7	178.6	178.6	Draw
91	184.0	187.8	180.7	180.6	Draw
92	186.0	189.8	182.7	182.7	Draw
93	188.0	191.8	184.7	184.7	Draw
94	190.0	193.8	186.7	186.7	Draw
95	192.1	195.8	188.8	188.7	Draw
96	194.1	197.9	190.8	190.8	Draw
97	196.1	199.9	192.8	192.8	Draw
98	198.1	201.9	194.8	194.8	Draw
99	200.1	203.9	196.8	196.8	Draw
100	202.2	206.0	198.9	198.9	Draw
101	204.2	208.0	200.9	200.9	Draw
102	206.2	210.0	202.9	202.9	Draw
103	208.2	212.0	204.9	204.9	Draw
104	210.2	214.0	206.9	206.9	Draw
105	212.3	216.1	209.0	208.9	Draw
106	214.3	218.1	211.0	211.0	Draw
107	216.3	220.1	213.0	213.0	Draw
108	218.3	222.1	215.0	215.0	Draw
109	220.3	224.1	217.0	217.0	Draw
110	222.4	226.2	219.1	219.1	Draw
111	224.4	228.2	221.1	221.1	Draw
112	226.4	230.2	223.1	223.1	Draw
113	228.4	232.2	225.1	225.1	Draw
114	230.5	234.3	227.2	227.2	Draw
115	232.5	236.3	229.2	229.2	Draw
116	234.5	238.3	231.2	231.2	Draw
117	236.5	240.3	233.2	233.2	Draw
118	238.5	242.3	235.2	235.2	Draw
119	240.6	244.4	237.3	237.2	Draw
120	242.6	246.4	239.3	239.3	Draw

Dimensions in mm. 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.