How do you calculate a sprocket's pitch diameter and outside diameter?

Pitch diameter is PD = P / sin(180° / N), where P is the chain pitch and N the number of teeth. The approximate outside diameter for a standard full-tooth sprocket is OD = P × (0.6 + cot(180° / N)). The sine form is exact, whereas N × P / π is only an approximation.

What is the caliper diameter of a sprocket, and why do odd teeth differ?

The root diameter is BD = PD − dr, where dr is the roller diameter. For an even tooth count, the tooth spaces are directly opposite, so calipers across them read BD. With an odd count, opposite spaces are offset by half a pitch, so the caliper diameter is CD = PD × cos(90° / N) − dr.

How do I find the chain pitch of an unmarked sprocket?

Count the teeth and measure one diameter. From the outside diameter, P = OD / (0.6 + cot(180° / N)). From the pitch diameter, P = PD × sin(180° / N). Valley readings also depend on the roller size, so this calculator ranks real chains by how closely each would give your measurement.

What does the DXF and SVG export contain?

A true-scale outline of the sprocket in millimetres, built from the ASME B29.1 tooth form: the roller seating curve, working curve, flank and topping curve, with each tooth turned to the standard outside diameter. The DXF uses exact arc and line entities. It does not include a keyway, hub, plate thickness or manufacturing tolerances, so add those and confirm the design with your sprocket maker before cutting.

Sprocket Diameter Calculator

Enter the chain and tooth count to get the pitch, outside, root and caliper diameters, or measure an unmarked sprocket to find which chain it fits.

Presets

Sprocket & Chain

Odd teeth

1. Chain Pitch & Roller

Pitch: 15.875 mm
Roller Ø: 10.16 mm
Inner width: 6.35 mm

2. Number of Teeth (N)Pitch angle 8°

3. Shaft Bore (for CAD)Max hub 210.39 mm

CAD outline export

A true-scale (1:1, millimetres) outline of 45 teeth on 520 chain, drawn with the ASME B29.1 tooth form as exact arcs and lines, turned to the standard outside diameter, plus the bore. Add your keyway, hub, plate thickness and tolerances before cutting.

Why caliper diameter can differ from root diameter

45T is odd, so tooth spaces aren't directly opposite each other. Calipers across the valleys read 217.28 mm, not the true root diameter of 217.42 mm.

Pitch Ø (PD)

227.58mm

Pin circle

Outside Ø (approx.)

236.55mm

Blankturned Ø

Root Ø (BD)

217.42mm

PD − roller Ø

Caliper Ø (CD)

217.28mm

Odd teeth

45T outline with key circles

Pitch circle 227.58 mm
Root circle 217.42 mm
Max hub 210.39 mm
Commercial caliper tolerance +0 / −0.3654 mm. Precision +0 / −0.1827 mm.
Polygon effect: 0.24% speed variation.

520 step chart (42T to 48T)

Sprocket diameters for neighbouring tooth counts
Pitch Ø	Outside Ø	Root Ø	Caliper Ø	Max hub
212.43	221.36	202.27	202.27	195.2
217.48	226.43	207.32	207.18	200.26
222.53	231.49	212.37	212.37	205.32
227.58	236.55	217.42	217.28	210.39
232.63	241.61	222.47	222.47	215.45
237.68	246.67	227.52	227.38	220.51
242.72	251.73	232.56	232.56	225.57

Sprocket Diameter Formulas

A roller chain wraps a sprocket as a regular polygon whose sides are one pitch long, so diameters come from trigonometry rather than a simple multiple of the tooth count. To check a front sprocket against a crankcase after a pitch change, see the chain conversion calculator.

Pitch, outside and root diameter

PD = P / sin(180° / N)

OD ≈ P × (0.6 + cot(180° / N))

BD = PD − d(roller)

P: = chain pitch
N: = number of teeth
d_r: = roller diameter

Caliper diameter, hub and tolerance

CD = BD (even N)

CD = PD × cos(90° / N) − d(roller) (odd N)

MHD = P × (cot(180° / N) − 1) − 0.030 in

Commercial tolerance: +0 / −(0.002 P √N + 0.006) in

Pitch is in inches for the hub and tolerance formulas. If you are not sure of your chain, measure it with the chain size calculator.

Sprocket Pitch and Outside Diameter Chart

Calculated for the two most common pitches: 1/2 inch (ANSI #40) and 5/8 inch (520, 525 and 530 motorcycle chain). To pick a tooth count for a target speed, use the sprocket size calculator.

Pitch and outside diameters for 1/2 inch and 5/8 inch pitch sprockets by tooth count
Teeth	1/2″ pitch PD (mm)	1/2″ pitch OD (mm)	5/8″ pitch PD (mm)	5/8″ pitch OD (mm)
12T	49.07	55.02	61.34	68.77
13T	53.07	59.15	66.33	73.93
14T	57.07	63.26	71.34	79.08
15T	61.08	67.37	76.36	84.21
16T	65.1	71.47	81.37	89.33
17T	69.12	75.56	86.39	94.45
20T	81.18	87.81	101.48	109.76
32T	129.57	136.56	161.96	170.71
36T	145.72	152.78	182.15	190.98
40T	161.87	168.99	202.34	211.24
42T	169.94	177.09	212.43	221.36
45T	182.06	189.24	227.58	236.55
48T	194.18	201.38	242.72	251.73
50T	202.26	209.48	252.82	261.85
60T	242.66	249.95	303.33	312.44

Sprocket Diameter Calculator

Sprocket Diameter Formulas

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Caliper diameter, hub and tolerance

Sprocket Pitch and Outside Diameter Chart

Sprocket Diameter FAQ

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Sprocket Diameter Formulas

Pitch, outside and root diameter

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Sprocket Pitch and Outside Diameter Chart

Sprocket Diameter FAQ

How do you calculate a sprocket's pitch diameter and outside diameter?

What is the caliper diameter of a sprocket, and why do odd teeth differ?

How do I find the chain pitch of an unmarked sprocket?

What does the DXF and SVG export contain?

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