How do you calculate roller chain length?

Use L = 2C/p + (N1 + N2)/2 + p·(N2 − N1)²/(4π²·C) and round up to an even number of links. For #40 chain, 18 and 36 teeth at 12 in centers, L = 75.34, so you need 76 links, or 38 in of chain.

Why should a roller chain have an even number of links?

Roller chain alternates inner and outer links, so an even count closes with a standard connecting link. An odd count needs an offset (half) link, which is weaker and wears faster, so it is better to change the center distance or a tooth count.

How do I find the center distance for a chain I already have?

Count the links and use C = (p/4)·[A + √(A² − 2(N2 − N1)²/π²)] with A = L − (N1 + N2)/2. A 76-link #40 chain on 18 and 36-tooth sprockets gives C ≈ 12.166 in; switch the tool to Link count mode to do this directly.

What center distance is best for a chain drive?

Between 30 and 50 chain pitches is the usual target, with about 80 pitches as a practical maximum. For #40 chain that is 15 to 25 in, up to about 40 in.

What is the minimum wrap angle on a sprocket?

Keep at least 120° of wrap on the small sprocket. Wrap shrinks as the ratio grows and the centers get closer; the 18 and 36-tooth example at 12.166 in has about 166.5°.

How many links are in 10 feet of #40 chain?

240 links. Ten feet is 120 in, and 120 ÷ 0.500 in pitch = 240; the same 10 ft is 320 links of #35 or 160 links of #60.

What does the ANSI chain number mean?

The leading digits give the pitch in eighths of an inch, so #40 is 4/8 = 0.500 in and #80 is 1.000 in. A last digit of 0 is standard roller chain, 1 is lightweight (#41), and 5 is rollerless bushing chain (#25, #35).

Is this a bicycle chain length calculator?

Not specifically. A singlespeed bike uses 1/2 in pitch chain, so the two-sprocket formula applies with p = 0.500 in, but derailleur drivetrains are sized by the largest cog, largest chainring, and the derailleur maker’s rules.

How much slack should a roller chain have?

Leave a small amount of sag on the slack side rather than running the chain tight, following the chain maker’s guidance, and provide a way to adjust it. Chain lengthens as it wears, so slotted mounts, an adjustable center, or an idler are worth designing in from the start.

Power transmission calculator

Roller Chain Length Calculator

Calculate ANSI roller chain length in links from sprocket teeth and center distance, or the center distance for a given link count, with wrap angle and ratio checks.

Calculator inputs

Results update as you type. Switch units at any time without changing the physical values.

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Results

Chain links (even): 76
Exact length in pitches: 75.34
Chain length: 38 in
Center distance: 12.1657 in
Center distance in pitches: 24.33
Speed ratio (driven ÷ driver): 2
Wrap on small sprocket: 166.5 °

Chain drive layout

Both sprockets and the chain drawn to scale at the calculated center distance, with every link in place.

Generate these sprockets

Driver pitch diameter: 2.879 in
Driven pitch diameter: 5.737 in
Center distance: 12.166 in

The center distance is 24.3 pitches. About 30 to 50 pitches is ideal for chain life; up to 80 works with a guide or idler.

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Generate laser-cut plate sprockets for this drive with ASME B29.1 teeth, one at a time or as a matched set.

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Fabworks plate material

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

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Driver sprocket
3.136 in × 3.096 in
Driven sprocket
⌀ 5.995 in

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Quick answer

How this chain length calculator works

Roller chain length in pitches is L = 2C/p + (N1 + N2)/2 + p·(N2 − N1)²/(4π²·C), rounded up to an even number of links. This calculator is for industrial ANSI roller chain (#25 to #80 or a custom pitch); bicycle derailleur chains are sized by different rules. Enter both tooth counts and a center distance or a link count to get chain length, actual center distance, ratio, and wrap angle.

How to use the calculator

1Choose an ANSI chain size from #25 to #80, or enter a custom chain pitch.
2Enter the driver sprocket teeth N1 and the driven sprocket teeth N2.
3Choose Center distance to get the link count, or Link count to get the center distance that chain produces.
4Use the even link count the tool rounds to. An odd count needs an offset link, which the tool flags.
5Check the wrap angle on the small sprocket (aim for 120° or more) and keep the center distance between 30 and 80 pitches.
6Open the sprocket generator to make either sprocket as a laser-cut part.

Key formulas

Chain length formulas

Chain length in pitches: L = 2C/p + (N1 + N2)/2 + p·(N2 − N1)² ÷ (4π²·C); L is the number of pitches (links), C the center distance, p the chain pitch, N1 and N2 the small and large sprocket tooth counts. Round L up to an even whole number.
Chain length: Length = L × p; 76 links of #40 chain (p = 0.500 in) is 38.0 in.
Center distance from link count: C = (p/4)·[A + √(A² − 2(N2 − N1)²/π²)], where A = L − (N1 + N2)/2; Gives the center distance that pulls a chain of L links snug with no slack.
Sprocket pitch diameter: PD = p ÷ sin(180°/N); N is the tooth count of that sprocket.
Wrap angle on the small sprocket: θ = 180° − 2·asin((PD2 − PD1) ÷ (2C)); PD1 and PD2 are the small and large pitch diameters. Keep θ at 120° or more.
Speed ratio: i = N2 ÷ N1, n2 = n1·N1 ÷ N2; n1 and n2 are the driver and driven speeds in rpm.
Chain speed: v = N1·p·n1 ÷ 12 (ft/min, p in inches); In metric, v = N1·p·n1 ÷ 1000 gives m/min with p in millimeters.

Step by step

How to lay out a two-sprocket roller chain drive

1Pick the chain size from load and speed, then choose the small sprocket tooth count (17 or more runs smoothest).
2Set the large sprocket from the ratio: N2 = N1 × i.
3Choose a starting center distance between 30 and 50 chain pitches.
4Calculate L with the chain length formula and round up to an even link count.
5Recalculate the actual center distance for that link count.
6Check that wrap on the small sprocket is at least 120°.
7Provide adjustment (slotted mounts or an idler) to take up slack and chain wear.

Worked example

#40 chain, 18 and 36 teeth at 12 in centers

Inputs: ANSI #40 chain (p = 0.500 in), 18-tooth driver, 36-tooth driven, target center distance 12.000 in.
Result: L = 75.34 pitches, rounded up to 76 links (38.0 in of chain). Actual center distance ≈ 12.166 in, ratio 2:1, wrap on the 18-tooth sprocket ≈ 166.5°.

2C/p = 48, (N1 + N2)/2 = 27, and the correction term adds 0.34 pitches. Rounding up to 76 even links moves the centers out about 0.166 in. At about 24 pitches this span is shorter than the usual 30 to 50 pitch range, so the tool notes it.

Common questions

What to know before using the result

How do you calculate roller chain length?: Use L = 2C/p + (N1 + N2)/2 + p·(N2 − N1)²/(4π²·C) and round up to an even number of links. For #40 chain, 18 and 36 teeth at 12 in centers, L = 75.34, so you need 76 links, or 38 in of chain.
Why should a roller chain have an even number of links?: Roller chain alternates inner and outer links, so an even count closes with a standard connecting link. An odd count needs an offset (half) link, which is weaker and wears faster, so it is better to change the center distance or a tooth count.
How do I find the center distance for a chain I already have?: Count the links and use C = (p/4)·[A + √(A² − 2(N2 − N1)²/π²)] with A = L − (N1 + N2)/2. A 76-link #40 chain on 18 and 36-tooth sprockets gives C ≈ 12.166 in; switch the tool to Link count mode to do this directly.
What center distance is best for a chain drive?: Between 30 and 50 chain pitches is the usual target, with about 80 pitches as a practical maximum. For #40 chain that is 15 to 25 in, up to about 40 in.
What is the minimum wrap angle on a sprocket?: Keep at least 120° of wrap on the small sprocket. Wrap shrinks as the ratio grows and the centers get closer; the 18 and 36-tooth example at 12.166 in has about 166.5°.
How many links are in 10 feet of #40 chain?: 240 links. Ten feet is 120 in, and 120 ÷ 0.500 in pitch = 240; the same 10 ft is 320 links of #35 or 160 links of #60.
What does the ANSI chain number mean?: The leading digits give the pitch in eighths of an inch, so #40 is 4/8 = 0.500 in and #80 is 1.000 in. A last digit of 0 is standard roller chain, 1 is lightweight (#41), and 5 is rollerless bushing chain (#25, #35).
Is this a bicycle chain length calculator?: Not specifically. A singlespeed bike uses 1/2 in pitch chain, so the two-sprocket formula applies with p = 0.500 in, but derailleur drivetrains are sized by the largest cog, largest chainring, and the derailleur maker’s rules.
How much slack should a roller chain have?: Leave a small amount of sag on the slack side rather than running the chain tight, following the chain maker’s guidance, and provide a way to adjust it. Chain lengthens as it wears, so slotted mounts, an adjustable center, or an idler are worth designing in from the start.

Reference

ANSI roller chain dimensions and sprocket tooth width

Nominal ASME B29.1 values in inches. #25 and #35 are rollerless bushing chains, so the listed diameter is the bushing. Tooth width is for single-strand sprockets (0.93·W − 0.006 in).

Chain	Pitch	Roller diameter	Inside width W	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

Recommended center distance range by chain size (in)

30 to 50 chain pitches is the usual target; 80 pitches is a practical maximum without a support guide or idler.

Chain	Pitch	30 pitches	50 pitches	80 pitches
#25	0.250	7.50	12.50	20.00
#35	0.375	11.25	18.75	30.00
#40, #41	0.500	15.00	25.00	40.00
#50	0.625	18.75	31.25	50.00
#60	0.750	22.50	37.50	60.00
#80	1.000	30.00	50.00	80.00

Formula

L = 2C/p + (N₁ + N₂)/2 + p·(N₂ − N₁)² ÷ (4π²·C)

Chain length L in pitches comes from center distance C, chain pitch p, and the small and large sprocket tooth counts N₁ and N₂, rounded up to an even link count. Center distance for a given link count is C = (p/4)·[A + √(A² − 2(N₂ − N₁)²/π²)], where A = L − (N₁ + N₂)/2.

Engineering references

Assumptions and limits

Presets use nominal ANSI roller chain pitch values covered by ASME B29.1.
Lengths and center distances are for a taut two-sprocket drive with no slack or idlers.
Odd link counts need an offset link, which is weaker than standard links.
Wrap angle uses pitch diameters and is checked against a 120° minimum on the small sprocket.
Chain wear and tensioning allowance are not included; provide center-distance adjustment.

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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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