BIZOMAT MAKEOS · Power Transmission
Roller Chain Length and Centre Distance
How many links does this roller chain drive need, and what centre distance results?
Chain length in pitches for two sprockets at a centre distance, rounded to an even number of links, the exact centre distance for that length, and chain speed.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Chain pitch | mm | Chain pitch (e.g. 15.875 mm for 10B or 50/ANSI). |
| Small sprocket teeth | teeth | Teeth on the small sprocket. |
| Large sprocket teeth | teeth | Teeth on the large sprocket. |
| Approximate centre distance | mm | Wanted centre distance (often 30–50 pitches). |
| Small sprocket speed | rpm | Speed of the small sprocket. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Chain pitch
- What it is
- The distance between the centres of adjacent chain rollers, from the chain designation or catalogue.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15.875 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Check the chain standard: ISO and ANSI chains of similar size can differ in pitch.
What this means: Small sprocket teeth
- What it is
- The number of teeth on the smaller sprocket.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 6 teeth to 500 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 17 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Count teeth on the small sprocket, usually the driver.
What this means: Large sprocket teeth
- What it is
- The number of teeth on the larger sprocket.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 6 teeth to 1000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 51 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Count teeth on the large sprocket.
What this means: Approximate centre distance
- What it is
- The centre distance between the two sprocket shafts that you would like. The tool rounds the chain to an even number of links and returns the exact centre distance.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 600 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer centre distance needs more links.
- Get it right
- Allow adjustment in the mounting; the exact centre distance will differ slightly from this value.
What this means: Small sprocket speed
- What it is
- The rotational speed of the small sprocket, used only to work out chain speed.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0 rpm to 100000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Chain speed rises in proportion; chain length is unchanged.
- Get it right
- Use the speed of the small sprocket, not the large one.
Method and formulas
- L (pitches) = 2C/p + (z₁ + z₂)/2 + ((z₂ − z₁)/2π)² ÷ (C/p).
- Round up to an even number of links (avoids an offset link).
- C = (p/4)[L − (z₁ + z₂)/2 + √((L − (z₁ + z₂)/2)² − 8((z₂ − z₁)/2π)²)].
- Example: 17/51 teeth at about 600 mm need 112 links, giving an exact centre distance of 613.11 mm.
Limitations
- Allow adjustment for chain wear and sag; the exact centre distance is for a new, tight chain.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Order the right chain length
- Set the centre distance for a standard chain
- Check chain speed
Who it is for
- Design engineers
- Maintenance engineers
- Automation engineers
What you get
- Chain length in pitches (exact and rounded to even)
- Chain length in mm
- Exact centre distance for the rounded chain
- Chain speed and wrap on the small sprocket
Interpreting the result
- Keep at least about 120° of wrap on the small sprocket.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2537–2560. Topic reference; no source tables or recommended settings are reproduced.
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