What to enter
- Front and rear teeth: stamped on each sprocket.
- Countershaft to rear axle: centre of the front sprocket to centre of the rear axle. Measure with the axle where you want it in the adjusters, usually near the front of the range on a new chain.
- Chain size: the first digit gives the pitch in eighths of an inch. 415, 420 and 428 have a 1/2 inch (12.7 mm) pitch, 520, 525 and 530 have 5/8 inch (15.875 mm), and 630 has 3/4 inch (19.05 mm).
The formula
With C the centre distance divided by the pitch, N1 the front teeth and N2 the rear teeth:
links = 2 × C + (N1 + N2) ÷ 2 + (N2 − N1)² ÷ (4 × π² × C)This is the standard roller chain length approximation used in chain design handbooks. The calculator also runs it backwards to find the centre distance for a whole even number of links.
Worked example
15 front, 45 rear, 520 chain, 23 in between the countershaft and the axle. The pitch is 15.875 mm, so C = 584.2 ÷ 15.875 = 36.8 pitches. Links = 73.6 + 30 + 0.62 = 104.22. Rounded up to an even count that is 106 links, which puts the axle at 23.56 in, 0.56 in further back. With 104 links the axle sits at 22.93 in, 0.07 in forward. Whichever count keeps the axle inside your adjusters with room for wear is the one to use.
Even links and master links
A chain alternates inner and outer links, so a chain joined with a standard master link needs an even count. Chains are sold in lengths like 120 links and cut to size. Changing the sprockets by a total of 2 teeth changes the length by about 1 link, so small sprocket changes often fit the old chain inside the adjuster range.
Questions
How do I calculate motorcycle chain length?
Divide the countershaft to axle distance by the chain pitch (C), then links = 2C + (front + rear) ÷ 2 + (rear − front)² ÷ (4π²C). For 15/45 at 23 in on a 520 chain that is 104.22 links.
Why does a chain need an even number of links?
A roller chain alternates inner and outer links, so both ends only match with an even count. An odd count needs an offset (half) link.
How many links do I add for a bigger rear sprocket?
About half a link per extra tooth. Going from 43 to 45 teeth at the rear with a 16 front on a 520 chain at 23 in adds 1.08 links, so you would move the axle back or add 2 links.
What is the pitch of a 520 chain?
5/8 inch, which is 15.875 mm. 415, 420 and 428 chains are 1/2 inch (12.7 mm) and 630 is 3/4 inch (19.05 mm).