Examples
Examples
Try the starting example
- Chain length in roller pitches
- 100
- Front sprocket teeth
- 20
- Rear sprocket teeth
- 20
- Pitch length (mm)
- 12.7
- Measured current center distance (mm)
- 500
- Larger-root approximate required center distance (mm)
- 508
- Required minus measured current center distance (mm)
- 8
- Modeled pitch count at measured current centers
- 98.740157
- Supplied pitch count minus current modeled pitch count
- 1.259843
Try another scenario
- Chain length in roller pitches
- 102
- Front sprocket teeth
- 20
- Rear sprocket teeth
- 20
- Pitch length (mm)
- 12.7
- Measured current center distance (mm)
- 500
- Larger-root approximate required center distance (mm)
- 520.7
- Required minus measured current center distance (mm)
- 20.7
- Modeled pitch count at measured current centers
- 98.740157
- Supplied pitch count minus current modeled pitch count
- 3.259843
Calculation method
Calculation method
Larger-root approximate required center distance (mm)
Invert stated open-chain approximation L=2x+(front+rear)/2+(front−rear)²/(4 pi² x), x=center/pitch, taking larger physical root.
Required minus measured current center distance (mm)
Signed approximate center-distance difference; not a physical axle-adjustment instruction.
Modeled pitch count at measured current centers
Evaluate the same approximation at measured center/pitch.
Supplied pitch count minus current modeled pitch count
Supplied roller pitches−modeled current pitches, without selecting a chain or link count.
Symbols and units
- a
- Chain length in roller pitches
- b
- Front sprocket teeth
- c
- Rear sprocket teeth
- d
- Pitch length (mm)
- e
- Measured current center distance (mm)
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- An explicitly stated approximate open-chain geometry, not an exact roller/sprocket engagement, chain order, slack setting or installation procedure. Link conventions, axle path, wear, alignment and adjustment limits must be checked separately.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
Renold: chain center-distance background; the approximate equation is stated explicitly here ↗
Background reading; this does not imply endorsement or independent review of SumFizz.