Bicycle Chain Length Calculator (Links)

How it works

L (inches) = 2C + F/4 + R/4 + (F − R)² ÷ (4π²C), C = chainstay in inches, F/R = teeth; derailleur: + 2 pins (+4 for 50–52 t 1×); round up to an even number of pins (1 pin = ½″)

Chain length is geometry: the chain wraps half of each sprocket (a quarter of the teeth each, since one tooth is half an inch) and runs two chainstay lengths between them, plus a small correction for the fact that the two runs are not parallel when the sprockets differ in size — the rigorous equation of Sheldon Brown and Park Tool. Derailleur drivetrains add two pins so that the largest-to-largest combination can be shifted into without tearing the cage, four for the enormous cogs of modern 1× systems; single-speeds need the exact even count and set tension with the dropouts. Full-suspension frames measure the chainstay at full compression because the rear axle moves away from the crank as the shock compresses.

Worked example

With 425 mm chainstays, a 50-tooth ring and a 34-tooth cog the rigorous length is 2 × 16.73 + 12.5 + 8.5 + 256 ÷ (39.5 × 16.73) = 54.85″; adding 2 pins for the derailleur and rounding up to an even count gives 112 pins (56″), so 4 links come off a 116-link chain. The simple big-big-plus-two method lands on the same 112.

Frequently asked questions