How do I tell which ANSI chain I have?

Measure the pitch from one pin center to the next, then the roller diameter and the inside width between the inner plates. The first digits of the ANSI number are the pitch in eighths of an inch, so #40 is 4/8 = 0.500 in. A last digit of 0 is standard chain, 1 is lightweight, and 5 is bushed chain with no rollers.

How do I measure an odd-tooth sprocket?

Measure the caliper diameter across the gaps that are most nearly opposite: Dc = PD·cos(90°/N) − Dr. A 15-tooth #40 sprocket measures 2.080 in instead of its 2.093 in root diameter.

Which plate thickness should I use?

No thicker than the tooth width, 0.93·W − 0.006 in, where W is the chain’s inside width. That is 0.284 in for #40. The thickness list stops there.

Does a #41 sprocket have the same diameter as a #40?

The pitch and outside diameters match because both chains have a 0.500 in pitch. The root diameter differs slightly with the 0.306 in roller, and the tooth is narrower (0.227 in) for #41’s 0.250 in inside width.

How do you calculate sprocket outside diameter?

ASME B29.1 gives OD ≈ p·(0.6 + cot(180°/N)). For an 18-tooth #40 sprocket that is 3.136 in.

Roller Chain Sprocket Dimensions

Calculate pitch, outside, root, and caliper diameters for an ANSI roller chain sprocket, with tooth width, plate fit, and a live profile.

Build a laser-cut plate sprocket

Select a roller chain and tooth count, then set the bore, holes, and plate.

Units

Roller chain

Sprocket teeth

Shaft speed

rpm

Chain pitch

Roller diameter

Tooth fit

Mating sprocket

Add the driven sprocket to see the ratio and output speed, and generate both parts.

Hub, holes, and plate

Bore

Bore diameter

Mounting holes

Lightening holes

Fabworks plate material

Plate thickness for chain fitMin. feature 0.050 in · 1.27 mm

Generated dimensions

Recommended chain fit

Pitch diameter: 2.8794 in
Outside diameter: 3.1356 in
Root diameter: 2.5628 in
Roller seat radius: 0.1583 in
Chain speed At 300 rpm: 225 ft/min
Plate: Steel 1008 · 0.187 in
Chain side clearance: 0.0628 in per side

ANSI roller chain dimensions

Recommended plate thickness leaves side clearance inside the chain.

ANSI #40 selected

Chain	Pitch	Roller diameter	Inside width	Ideal plate
ANSI #25	0.250 in · 6.35 mm	0.130 in · 3.302 mm	0.125 in · 3.175 mm	0.098 in · 2.5 mm
ANSI #35	0.375 in · 9.525 mm	0.200 in · 5.08 mm	0.188 in · 4.763 mm	0.118 in · 3 mm
ANSI #40	0.500 in · 12.7 mm	0.312 in · 7.925 mm	0.313 in · 7.938 mm	0.250 in · 6.35 mm
ANSI #41	0.500 in · 12.7 mm	0.306 in · 7.772 mm	0.250 in · 6.35 mm	0.188 in · 4.763 mm
ANSI #50	0.625 in · 15.875 mm	0.400 in · 10.16 mm	0.375 in · 9.525 mm	0.313 in · 7.938 mm
ANSI #60	0.750 in · 19.05 mm	0.469 in · 11.913 mm	0.500 in · 12.7 mm	0.375 in · 9.525 mm

Laser-cut profile preview

The B29.1 profile uses a roller seating curve, working curve, tangent flat, and topping curve. The dashed circle is the pitch circle and the filled circle is a seated roller.

ASME B29.1 profile

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Sprocket
3.136 in × 3.096 in

Laser cut it at Fabworks

We generate the STEP files, add them to a new quote, and open it in a new tab where you can review material, finish, and quantity.

The STEP uses the ASME B29.1 theoretical tooth form and catalog outside-diameter truncation. Manufacturing tolerances, material, heat treatment, alignment, lubrication, and application loads still require engineering review.

How it works

Pitch diameter is the chain pitch divided by sin(180° ÷ teeth). Outside diameter is about pitch × (0.6 + cot(180° ÷ teeth)), and root diameter is the pitch diameter minus the roller diameter. On odd tooth counts no two gaps face each other, so a caliper reads less than the root diameter. Use the caliper diameter to check a part.

How to use the calculator

1Pick the ANSI chain size, or enter pitch and roller diameter. #40 and #41 share a pitch but have different rollers.
2Enter the tooth count and read the pitch, outside, and root diameters. For an odd count, check a finished part against the caliper diameter.
3Keep the plate at or under the tooth width, 0.284 in for #40.
4Keep the bore, bolt circle, and lightening holes inside the root diameter.

Sprocket dimensions formulas

Pitch diameter: PD = p ÷ sin(180°/N)
Outside diameter: OD = p·(0.6 + cot(180°/N))
Root diameter: Db = PD − Dr
Caliper diameter, odd tooth counts: Dc = PD·cos(90°/N) − Dr
Tooth width, single strand: t = 0.93·W − 0.006 in; W is the chain’s inside width.

#40 chain, 18-tooth sprocket

Inputs: ANSI #40 chain with 0.500 in pitch, 0.312 in rollers, and 18 teeth.
Result: Pitch diameter ≈ 2.879 in, outside diameter ≈ 3.136 in, root diameter ≈ 2.567 in.

PD = 0.500 ÷ sin(10°) = 2.879 in. OD = 0.500 × (0.6 + cot 10°) = 3.136 in. Root = 2.879 − 0.312 = 2.567 in.

What to know before using the result

How do I tell which ANSI chain I have?: Measure the pitch from one pin center to the next, then the roller diameter and the inside width between the inner plates. The first digits of the ANSI number are the pitch in eighths of an inch, so #40 is 4/8 = 0.500 in. A last digit of 0 is standard chain, 1 is lightweight, and 5 is bushed chain with no rollers.
How do I measure an odd-tooth sprocket?: Measure the caliper diameter across the gaps that are most nearly opposite: Dc = PD·cos(90°/N) − Dr. A 15-tooth #40 sprocket measures 2.080 in instead of its 2.093 in root diameter.
Which plate thickness should I use?: No thicker than the tooth width, 0.93·W − 0.006 in, where W is the chain’s inside width. That is 0.284 in for #40. The thickness list stops there.
Does a #41 sprocket have the same diameter as a #40?: The pitch and outside diameters match because both chains have a 0.500 in pitch. The root diameter differs slightly with the 0.306 in roller, and the tooth is narrower (0.227 in) for #41’s 0.250 in inside width.
How do you calculate sprocket outside diameter?: ASME B29.1 gives OD ≈ p·(0.6 + cot(180°/N)). For an 18-tooth #40 sprocket that is 3.136 in.

18-tooth sprocket dimensions by chain size (in)

Chain	Pitch	Pitch dia	Outside dia	Root dia
#25	0.250	1.440	1.568	1.310
#35	0.375	2.160	2.352	1.960
#40	0.500	2.879	3.136	2.567
#41	0.500	2.879	3.136	2.573
#50	0.625	3.599	3.920	3.199
#60	0.750	4.319	4.703	3.850
#80	1.000	5.759	6.271	5.134

#40 sprocket dimensions by tooth count (in)

p = 0.500 in, roller 0.312 in.

Teeth	Pitch dia	Outside dia	Root dia	Caliper dia
9	1.462	1.674	1.150	1.128
12	1.932	2.166	1.620	1.620
15	2.405	2.652	2.093	2.080
18	2.879	3.136	2.567	2.567
24	3.831	4.098	3.519	3.519
30	4.783	5.057	4.471	4.471
36	5.737	6.015	5.425	5.425
48	7.645	7.929	7.333	7.333
60	9.554	9.841	9.242	9.242

Formula

Dₚ = p ÷ sin(180° ÷ N)

Pitch diameter is the chain pitch divided by sin(180° ÷ teeth). The teeth follow the ASME B29.1 construction: a roller seating curve, a working curve, a short straight, and a topping curve, trimmed at the catalog outside diameter.

Engineering references

Assumptions and limits

Chain sizes use nominal ASME B29.1 pitch and roller diameter. Free-running fit and tip relief depart from the standard tooth form on purpose.
The STEP is a flat plate of one thickness with the bore and holes you set. It has no hub or set screw.
The plate is as hard as the sheet it is cut from. Chain makers recommend hardened teeth on sprockets of 25 teeth or fewer.
Chain speed assumes the sprocket turns at the entered shaft speed with no slip.

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Fabworks resources

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