How do you calculate sprocket size?

Pitch diameter is PD = p ÷ sin(180°/N). An 18-tooth #40 sprocket (p = 0.500 in) is 2.879 in on the pitch circle, about 3.136 in outside, and 2.567 in at the root.

How do you calculate sprocket ratio?

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

Is this a motorcycle sprocket calculator?

No. It designs industrial roller chain sprockets and gives their ratio and chain speed; motorcycle gearing calculators add gearbox ratios, tire size, and road speed. The ratio math is the same: rear teeth ÷ front teeth.

How many teeth should a sprocket have?

The generator accepts 7 to 150 teeth, but 17 or more runs smoother at moderate speed. Chordal speed variation is about 1 − cos(180°/N): 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, about 0.93 × chain inside width − 0.006 in. That is 0.284 in for #40, so 1/4 in plate is the usual choice; #41 uses 3/16 in and #60 uses 3/8 in.

What does tooth fit change?

Nominal uses the ASME B29.1 minimum seating curve. Free-running adds clearance so a laser-cut plate engages the chain easily, and custom lets you set seat clearance and tip relief yourself.

Can I add a keyway, hex bore, or bolt circle?

Yes. Bores can be none, round, hex, keyed round with a standard key width, or D-flat, and you can add up to two hole patterns on a circle for a hub bolt circle or lightening holes.

Which file formats can I download?

STEP (a solid built and validated in the browser), DXF in millimeters with lines and arcs, and SVG. Tooth curves stay within 0.005 mm of the true profile.

Can a laser-cut plate sprocket be used at any load and speed?

No. Laser-cut plate sprockets suit low to moderate speed and load; critical or high-speed drives need engineering review of material, thickness, hub and keyway design, alignment, lubrication, wear, and heat treatment.

Is this a timing-belt pulley profile?

No. It is a roller chain sprocket profile with roller seats and working flanks. HTD and other synchronous-belt pulleys use different tooth geometry.

Power transmission calculator

Chain Sprocket Generator

Create a laser-cuttable plate sprocket STEP for common ANSI roller chains, calculate its dimensions and chain speed, then 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

100% in-browser

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.

Quick answer

How this sprocket calculator calculator works

A roller chain sprocket’s pitch diameter is PD = p ÷ sin(180°/N), where p is the chain pitch and N the tooth count, so an 18-tooth #40 sprocket is 2.879 in. This tool designs industrial roller chain sprockets (ANSI #25 to #60 or a custom pitch) with the ASME B29.1 tooth form and gives ratio, output speed, and chain speed for a mating sprocket; it is not a motorcycle gearing calculator, though the ratio math is the same. Files are generated in the browser and download as STEP, DXF, or SVG, or go straight into a Fabworks quote.

How to use the calculator

1Choose ANSI #25, #35, #40, #41, #50, or #60 chain, or enter a custom pitch and roller diameter.
2Enter the tooth count (7 to 150) and pick a tooth fit: nominal, free-running, or custom clearance and tip relief.
3Enter the mating sprocket’s teeth and the input speed to get ratio, output rpm, and chain speed, and open the chain length calculator for the center distance.
4Choose a Fabworks material and a plate thickness that fits inside the chain, then add a bore (round, hex, keyed, or D-flat) and up to two hole patterns such as a bolt circle and lightening holes.
5Fix any narrow-gap, tip-land, or web warnings against the minimum feature size for that material and thickness.
6Download STEP, DXF, or SVG, or select Order to upload the STEP into a new Fabworks quote.

Key formulas

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 for a turned or cut 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 tooth gaps on an odd-tooth sprocket. Even counts measure the root diameter.
Roller seating radius: R = 0.5025·Dr + 0.0015 in; Seating curve centered on the roller position, spanning A = 35° + 60°/N on each side.
Working curve radius: E = 1.3025·Dr + 0.0015 in; Drawn from a center 0.8·Dr from the roller center, through B = 18° − 56°/N.
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.

Step by step

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.

Worked example

#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.

Common questions

What to know before using the result

How do you calculate sprocket size?: Pitch diameter is PD = p ÷ sin(180°/N). An 18-tooth #40 sprocket (p = 0.500 in) is 2.879 in on the pitch circle, about 3.136 in outside, and 2.567 in at the root.
How do you calculate sprocket ratio?: Divide the driven sprocket’s teeth by the driver’s teeth. An 18-tooth sprocket driving 36 teeth is 2:1, so 300 rpm in becomes 150 rpm out.
Is this a motorcycle sprocket calculator?: No. It designs industrial roller chain sprockets and gives their ratio and chain speed; motorcycle gearing calculators add gearbox ratios, tire size, and road speed. The ratio math is the same: rear teeth ÷ front teeth.
How many teeth should a sprocket have?: The generator accepts 7 to 150 teeth, but 17 or more runs smoother at moderate speed. Chordal speed variation is about 1 − cos(180°/N): 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, about 0.93 × chain inside width − 0.006 in. That is 0.284 in for #40, so 1/4 in plate is the usual choice; #41 uses 3/16 in and #60 uses 3/8 in.
What does tooth fit change?: Nominal uses the ASME B29.1 minimum seating curve. Free-running adds clearance so a laser-cut plate engages the chain easily, and custom lets you set seat clearance and tip relief yourself.
Can I add a keyway, hex bore, or bolt circle?: Yes. Bores can be none, round, hex, keyed round with a standard key width, or D-flat, and you can add up to two hole patterns on a circle for a hub bolt circle or lightening holes.
Which file formats can I download?: STEP (a solid built and validated in the browser), DXF in millimeters with lines and arcs, and SVG. Tooth curves stay within 0.005 mm of the true profile.
Can a laser-cut plate sprocket be used at any load and speed?: No. Laser-cut plate sprockets suit low to moderate speed and load; critical or high-speed drives need engineering review of material, thickness, hub and keyway design, alignment, lubrication, wear, and heat treatment.
Is this a timing-belt pulley profile?: No. It is a roller chain sprocket profile with roller seats and working flanks. HTD and other synchronous-belt pulleys use different tooth geometry.

Reference

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 Dₚ is set by chain pitch p and tooth count N. The generated profile follows the ASME B29.1-2011 (R2022) theoretical tooth construction: roller seating curve, working curve, tangent flat, topping curve, and catalog outside-diameter truncation.

Engineering references

Assumptions and limits

Presets use nominal ANSI roller-chain pitch and roller diameter values covered by ASME B29.1.
The browser-generated STEP is a closed, uniform-thickness plate sprocket with a round bore.
Nominal fit uses the standard theoretical minimum seating curve; optional clearance and tip relief are deliberate deviations for prototype tuning.
Hubs, keyways, bore tolerances, material, heat treatment, and high-speed applications require an engineering review.
Chain speed assumes the sprocket rotates at the entered shaft speed without slip.

Educational estimate

Use this result for learning and early design exploration. Verify safety-critical or production decisions with the governing standard, material data, real tooling, and a qualified engineer.

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