p · C
Mistake: Changing units and assuming the entered numbers were converted.
Fix: Numbers stay unchanged. Check the new unit and enter the intended measurement, or select an example for that system.
Archive · Free
Roller-chain length planner
Estimate chain pitches, choose a link count and recalculate the resulting centre distance.
This tool is archived. Recheck its method and dated data before use.
01Enter your values
Runs in your browserRuns offline in your browser. Once the page and required files have loaded, processing needs no internet.
02Roller-chain length planner
Runs in your browser
How it works
Estimate chain pitches, choose a link count and recalculate the resulting centre distance.
Lp = 2C/p + (z₁+z₂)/2 + (z₂−z₁)²/(4π²C/p)
Runs in your browser
Discovery source
Your data stays yours
Inputs are processed on this page and are never sent to a server.
About this tool
Use tool ↑Estimate chain pitches, choose a link count and recalculate the resulting centre distance.
Uses sprocket tooth counts, pitch and nominal centre distance. Even-link mode avoids an offset link; verify allowance, tensioning and manufacturer limits.
- Enter your values
- Unit for every dimension
- z₁
- z₂
- p
- C
- N mod 2
- Calculation method
Lp = 2C/p + (z₁+z₂)/2 + (z₂−z₁)²/(4π²C/p)
- Example scenario · Result
116 Links
Calculation method
- Divide centre distance by chain pitch to obtain x.
- Calculate theoretical pitches as 2x + (z₁ + z₂)/2 + (z₂ − z₁)²/(4π²x).
- Round to the nearest whole link, or nearest even link count in even mode.
- Solve the same length equation for centre distance using its larger root; compare that distance with the entered value.
- The table also shows the adjacent allowed link counts.
Lp = 2C/p + (z₁+z₂)/2 + (z₂−z₁)²/(4π²C/p)
Roller-chain length planner
- Unit for every dimension
- mm
- z₁
- 18
- z₂
- 54
- p
- 12.7
- C
- 500
- N mod 2
- Even links
Result
116 Links
Frequently asked questions
Why can the centre distance change?
A chain has a whole number of pitches, so rounding the link count changes the compatible centre distance.
Where does my data go?
Calculations run on your device. Form inputs are not sent to a server.
Terms and definitions
Enter your values
- Measurement system
The initial choice follows your browser region. Your choice is remembered on this device. Gallons are US gallons. Switching units keeps your numbers unchanged and interprets them in the new unit.
Numbers stay unchanged. Check the new unit and enter the intended measurement, or select an example for that system.
- Unit for every dimension
Choose the mode that matches the data you entered.
Options: mm · in
- z₁
Tooth count of the smaller sprocket
Enter a whole number; fractional counts are not valid.
Minimum: 3 · Maximum: 1000
- z₂
Tooth count of the larger sprocket
Enter a whole number; fractional counts are not valid.
Minimum: 3 · Maximum: 1000
- p
Distance between adjacent chain pin centres
Enter a numerical value for this quantity. Use the unit shown beside this field. mm / in
Minimum: 0.0001 · Maximum: 100000 mm
- C
Distance between the two sprocket axes
Enter a numerical value for this quantity. Use the unit shown beside this field. mm / in
Minimum: 0.0001 · Maximum: 10000000 mm
- N mod 2
Choose the mode that matches the data you entered.
Options: Even links · Any integer
Result
- Result
Uses sprocket tooth counts, pitch and nominal centre distance. Even-link mode avoids an offset link; verify allowance, tensioning and manufacturer limits.
Calculated from your entries using the method below.
- Cactual
Uses sprocket tooth counts, pitch and nominal centre distance. Even-link mode avoids an offset link; verify allowance, tensioning and manufacturer limits.
Calculated from your entries using the method below.
- ΔC
Uses sprocket tooth counts, pitch and nominal centre distance. Even-link mode avoids an offset link; verify allowance, tensioning and manufacturer limits.
Calculated from your entries using the method below.
- Lp
Uses sprocket tooth counts, pitch and nominal centre distance. Even-link mode avoids an offset link; verify allowance, tensioning and manufacturer limits.
Calculated from your entries using the method below.
- Links
Uses sprocket tooth counts, pitch and nominal centre distance. Even-link mode avoids an offset link; verify allowance, tensioning and manufacturer limits.
Calculated from your entries using the method below.
- Cactual (mm)
Uses sprocket tooth counts, pitch and nominal centre distance. Even-link mode avoids an offset link; verify allowance, tensioning and manufacturer limits.
Calculated from your entries using the method below.
- ΔC (mm)
Uses sprocket tooth counts, pitch and nominal centre distance. Even-link mode avoids an offset link; verify allowance, tensioning and manufacturer limits.
Calculated from your entries using the method below.
- Cactual (in)
Uses sprocket tooth counts, pitch and nominal centre distance. Even-link mode avoids an offset link; verify allowance, tensioning and manufacturer limits.
Calculated from your entries using the method below.
- ΔC (in)
Uses sprocket tooth counts, pitch and nominal centre distance. Even-link mode avoids an offset link; verify allowance, tensioning and manufacturer limits.
Calculated from your entries using the method below.
Common mistakes and quick fixes
Why can the centre distance change?
Mistake: Treating a result as valid outside the described scope.
Fix: A chain has a whole number of pitches, so rounding the link count changes the compatible centre distance.
Limits and key assumptions
- A chain has a whole number of pitches, so rounding the link count changes the compatible centre distance.
- Even-link mode avoids an offset link; verify allowance, tensioning and manufacturer limits.
- Displayed results may be rounded; rounding does not add measurement precision.