Power transmission calculator
Chain Center Distance Calculator
Find the sprocket center distance for a roller chain with a given number of links, pitch, and tooth counts, with wrap angle and ratio checks.
Calculator inputs
Results update as you type. Switch units at any time without changing the physical values.
Results
- Chain links (even)
- 76
- 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.
- Driver pitch diameter
- 2.879 in
- Driven pitch diameter
- 5.737 in
- Center distance
- 12.166 in
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3.136 in × 3.096 in
⌀ 5.995 in
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Quick answer
How this chain center distance calculator works
For a two-sprocket roller chain drive, center distance is C = (p/4)·[A + √(A² − 2(N2 − N1)²/π²)], where A = L − (N1 + N2)/2 and L is the link count. Enter the chain size, both tooth counts, and the number of links to get the center distance, wrap angle, and ratio, with warnings for odd links and short or long spans.
How to use the calculator
- 1Choose the ANSI chain size or a custom pitch.
- 2Enter the driver and driven sprocket tooth counts.
- 3Enter the number of links in the chain, preferably even.
- 4Read the center distance, wrap angle, and ratio, and adjust the link count if the span falls outside 30 to 80 pitches.
Key formulas
Chain center distance formulas
- Center distance from link count
- C = (p/4)·[A + √(A² − 2(N2 − N1)²/π²)]
- A = L − (N1 + N2)/2; L links, pitch p, tooth counts N1 and N2.
- Equal sprockets
- C = p·(L − N)/2
- When N1 = N2 = N the correction term vanishes.
- Wrap angle
- θ = 180° − 2·asin((PD2 − PD1) ÷ (2C))
- Keep at least 120° on the small sprocket.
Worked example
76 links of #40 chain on 18 and 36 teeth
- Inputs
- ANSI #40 chain (p = 0.500 in), 18-tooth and 36-tooth sprockets, 76 links.
- Result
- Center distance ≈ 12.166 in, wrap on the small sprocket ≈ 166.5°, ratio 2:1.
A = 76 − 27 = 49. C = 0.125 × [49 + √(49² − 2 × 18²/π²)] = 0.125 × (49 + 48.33) ≈ 12.166 in.
Common questions
What to know before using the result
- How do you calculate sprocket center distance from chain length?
- Use C = (p/4)·[A + √(A² − 2(N2 − N1)²/π²)] with A = L − (N1 + N2)/2. For 76 links of #40 chain on 18 and 36 teeth, C ≈ 12.166 in.
- What if both sprockets are the same size?
- Then C = p·(L − N)/2. Two 20-tooth #40 sprockets with 80 links sit 0.5 × 60 ÷ 2 = 15 in apart.
- Why does the calculated distance leave no slack?
- The formula gives the distance at which the chain is just taut. Provide adjustment so you can set a small sag on the slack side and take up wear.
- What center distance range is recommended?
- 30 to 50 chain pitches is typical and about 80 pitches is a practical maximum. For #40 that is 15 to 25 in, up to about 40 in.
- Can I use an odd number of links?
- Only with an offset link, which is weaker. Changing the link count by one moves the center distance by roughly half a pitch, so pick the even count that fits your adjustment range.
Reference
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.
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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