Calculating Roller Chain Length

Given two sprockets, a known distance apart.
The number of teeth on each sprocket is known.
The pitch of the chain is also known.

This page calculates the length of the chain required
to wrap both sprockets, and the number of links of chain
to do so.

The distance between sprockets can be adjusted to make an
integer number of links. Better still, make the number of
links an even integer so that an offset link is not required.

This program does not take into account chain stretch or
wear of chain or sprockets, or link tolerances.
Roller Chain Length Calculator
Note: All dimensional units must be the same.

  Pitch: / or
  Number of Teeth: and for each sprocket
  Distance between Sprocket Centers:
  Chain length:
  links:
  Integer Links: Slop : or :
Intermediate Results

Sprocket Pin Circle Diameters:
  and

Chain dimension breakdown:
  Unsupported Chain Length
  Small sprocket contact Links
  Large sprocket contact Links 
This form uses a "pin position" model. The number of supported
links is calculated for each sprocket, based on the pin circle
diameters and distance between sprockets. The coordinates of the
last pins in the last supported links is determined. Then the
distance between these pins is calculated.

In reality, the number of links contacting a sprocket alternates
between odd and even as the drive rotates. Because this model
equalizes the amount of chain wrapped around each side of each
sprocket, the number of contacting links will always be even.

You can also use the old formula.


Note: If there is a large size difference between the
two sprockets, you may want to avoid minimum spacing
between them as this will decrease the wrap length
around the smaller sprocket, increasing the tendancy
of the chain to jump teeth or slip.