What diameter is the sprocket blank?

The outside diameter, about p·(0.6 + cot(180° ÷ N)), which is 3.136 in for an 18-tooth #40. Keep the bore, bolt circle, and lightening holes inside the root diameter (2.567 in here).

How do you calculate sprocket ratio?

Divide the driven sprocket’s teeth by the driver’s. An 18-tooth sprocket driving 36 teeth is 2:1, so 300 rpm in becomes 150 rpm out, with about twice the torque before losses.

How many teeth should the small sprocket have?

Diamond Chain suggests 12 teeth for slow drives, 17 for medium speed, and 25 for high speed. Fewer teeth means more chordal action: chain speed varies by 1 − cos(180° ÷ N), which is 6.0% at 9 teeth, 1.5% at 18, and 0.8% at 25.

What plate thickness should a sprocket be?

No thicker than the tooth width, 0.93 × the chain’s inside width − 0.006 in. That is 0.284 in for #40, so 1/4 in plate works. #41 allows 0.227 in (3/16 in plate) and #60 allows 0.459 in (3/8 in plate).

Will a laser-cut plate sprocket wear out quickly?

It can. The teeth are only as hard as the sheet, and chain makers recommend hardened teeth on sprockets of 25 teeth or fewer. Plate sprockets suit robots, prototypes, and light low-speed drives.

Chain Sprocket Generator

Size an ANSI roller chain sprocket, check chain speed, and download a laser-cut plate version as STEP, DXF, or SVG or order it from Fabworks.

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

Download the manufacturing files

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STEP solids are built and checked in your browser. DXF and SVG drawings use lines and true arcs at full scale. Nothing is uploaded until you order.

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), so an 18-tooth #40 sprocket is 2.879 in across the pitch circle. Pitch alone does not identify the chain: #40 and #41 are both 1/2 in, but #41 is narrower. Check the roller diameter and inside width before you pick a plate thickness.

How to use the calculator

1Match the chain, not just the pitch. #40 and #41 share a 1/2 in pitch but have different rollers and widths. Pick the ANSI size, or enter pitch and roller diameter for chain that is not listed.
2Choose the small sprocket’s tooth count for your speed. Chain makers suggest 12 teeth for slow drives, 17 for medium speed, and 25 for fast ones. The tool warns below 12.
3Pick a plate thickness. The list only offers plates at or under the chain’s tooth width, 0.284 in for #40.
4Leave the tooth fit on nominal unless the chain binds on a test part. Free-running adds 0.0015 in to the roller seat radius, which gives a laser-cut tooth some room.
5Add the bore and holes. The tool flags gaps and webs thinner than our minimum feature size for that thickness. Then download STEP, DXF, or SVG, or order it.

Sprocket calculator formulas

Pitch diameter: PD = p ÷ sin(180°/N); p is the chain pitch and N the number of teeth.
Outside diameter: OD = p·(0.6 + cot(180°/N)); The ASME B29.1 approximate outside diameter of the blank.
Root (bottom) diameter: Db = PD − Dr; Dr is the roller diameter.
Caliper diameter, odd tooth counts: Dc = PD·cos(90°/N) − Dr; What you measure across the gaps of an odd-tooth sprocket. On even counts you measure the root diameter.
Sprocket ratio and output speed: i = N2 ÷ N1, n2 = n1·N1 ÷ N2; N1 and n1 are the driver teeth and rpm; N2 and n2 the driven teeth and rpm.
Chain speed: v = N·p·n ÷ 12 (ft/min, p in inches); In metric, v = N·p·n ÷ 1000 gives m/min with p in millimeters.
Tooth width, single strand: t = 0.93·W − 0.006 in; W is the chain’s inside width. The plate must be no thicker than t.

How to draw a roller chain sprocket (ASME B29.1)

Dimensions are in inches; p is chain pitch, Dr roller diameter, and N the tooth count.

1Draw the pitch circle PD = p ÷ sin(180°/N) and mark N roller centers 360°/N apart.
2At each roller center, draw the seating curve of radius R = 0.5025·Dr + 0.0015, spanning A = 35° + 60°/N either side of the gap centerline.
3Locate the working curve center 0.8·Dr from the roller center on the opposite side of the gap, offset M = 0.8·Dr·cos A along the pitch line and T = 0.8·Dr·sin A outward.
4Draw the working curve of radius E = 1.3025·Dr + 0.0015 from the end of the seating curve through B = 18° − 56°/N.
5Continue with a straight tangent of length Dr·[1.4·sin(17° − 64°/N) − 0.8·sin(18° − 56°/N)].
6Finish the flank with the topping curve of radius F = Dr·[0.8·cos(18° − 56°/N) + 1.4·cos(17° − 64°/N) − 1.3025] − 0.0015.
7Trim the tooth tips at OD = p·(0.6 + cot(180°/N)), mirror the flank about the gap centerline, and pattern it N times.
8Add the bore, keyway, and bolt holes, and choose a plate no thicker than the tooth width 0.93·W − 0.006.

#40 chain, 18 teeth driving 36 teeth at 300 rpm

Inputs: ANSI #40 chain (p = 0.500 in, roller 0.312 in), 18-tooth sprocket at 300 rpm driving a 36-tooth sprocket.
Result: Pitch diameter ≈ 2.879 in, outside diameter ≈ 3.136 in, root diameter ≈ 2.567 in. Ratio 2:1, output 150 rpm, chain speed 225 ft/min (68.6 m/min).

PD = 0.500 ÷ sin(10°). OD = p·(0.6 + cot(180°/N)) and root = PD − roller diameter. Chain speed = 18 × 0.500 in × 300 rpm ÷ 12 = 225 ft/min.

What to know before using the result

What diameter is the sprocket blank?: The outside diameter, about p·(0.6 + cot(180° ÷ N)), which is 3.136 in for an 18-tooth #40. Keep the bore, bolt circle, and lightening holes inside the root diameter (2.567 in here).
How do you calculate sprocket ratio?: Divide the driven sprocket’s teeth by the driver’s. An 18-tooth sprocket driving 36 teeth is 2:1, so 300 rpm in becomes 150 rpm out, with about twice the torque before losses.
How many teeth should the small sprocket have?: Diamond Chain suggests 12 teeth for slow drives, 17 for medium speed, and 25 for high speed. Fewer teeth means more chordal action: chain speed varies by 1 − cos(180° ÷ N), which is 6.0% at 9 teeth, 1.5% at 18, and 0.8% at 25.
What plate thickness should a sprocket be?: No thicker than the tooth width, 0.93 × the chain’s inside width − 0.006 in. That is 0.284 in for #40, so 1/4 in plate works. #41 allows 0.227 in (3/16 in plate) and #60 allows 0.459 in (3/8 in plate).
Will a laser-cut plate sprocket wear out quickly?: It can. The teeth are only as hard as the sheet, and chain makers recommend hardened teeth on sprockets of 25 teeth or fewer. Plate sprockets suit robots, prototypes, and light low-speed drives.

ANSI roller chain dimensions and sprocket tooth width (in)

Nominal ASME B29.1 values. #25 and #35 are rollerless bushing chains, so the listed diameter is the bushing.

Chain	Pitch	Roller diameter	Inside width	Sprocket tooth width
#25	0.250	0.130	0.125	0.110
#35	0.375	0.200	0.188	0.168
#40	0.500	0.312	0.312	0.284
#41	0.500	0.306	0.250	0.227
#50	0.625	0.400	0.375	0.343
#60	0.750	0.469	0.500	0.459
#80	1.000	0.625	0.625	0.575

#40 sprocket dimensions by tooth count (in)

p = 0.500 in, roller 0.312 in. Caliper diameter applies to odd tooth counts.

Teeth	Pitch dia	Outside dia	Root dia	Caliper dia
9	1.462	1.674	1.150	1.128
10	1.618	1.839	1.306	1.306
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
20	3.196	3.457	2.884	2.884
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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