Chain Length Calculator
How many links a chain run needs, and more usefully, what center distance a whole number of links actually gives you.
Inputs
A sprocket only fits the chain it was made for, and the two sizes are not interchangeable. Picking the type sets both the pitch and the sprockets you can choose.
Distance between the two shafts.
Read the warning below before trusting this default. To measure your own: lay out 20 links, measure end to end, divide by 20.
Results
Links needed
—
Rounded up to a whole link.
Exact figure
—links
Nearest even link count
—
Even avoids a weak offset link.
Center distance at that whole link count
—in
Difference from what you asked for
—in
Chain length
—in
How this is calculated
Chain length is not simply twice the center distance. The chain also wraps around both sprockets, and when the two sprockets differ in size the run between them sits at a slight angle, which adds a little more:
links = 2C/p + (N₁ + N₂)/2 + p·((N₂ − N₁)/2π)² / C C = center distance p = chain pitch N₁ = teeth on first sprocket N₂ = teeth on secondWith your numbers
The first term is the two straight runs, the second is the wrap around both sprockets, and the third is the small correction for unequal sprockets. That third term vanishes when both sprockets are the same size.
The part that actually matters
Chain comes in whole links. You almost never get the center distance you asked for. You get the one the nearest whole link count gives you. So this calculator runs the formula backwards too:
C = (p/8) · [ 2L − N₁ − N₂ + √( (2L − N₁ − N₂)² − (8/π²)(N₂ − N₁)² ) ]Design your mounting holes around that number, not the one you first thought of. A chain cut to the right length and mounted at the wrong distance is either too slack to stay on or too tight to turn.
Odd links
An odd number of links needs an offset link to close the loop, and an offset link is the weakest part of the chain. Where you have the freedom, take the even count. Where you do not, tension it properly and expect it to be the first thing that fails.
Leave room to tension
Chain stretches with use. A run mounted at exactly the calculated distance with no adjustment will go slack and start skipping teeth. Either mount one shaft in a slot, or plan on an idler sprocket taking up the slack.
Sources & assumptions
Sprocket tooth counts are the confirmed contents of the VEX High Strength Sprocket & Chain Kit (276-2252). Sprocket pitch diameter is computed as pitch ÷ sin(180°/teeth), the standard roller chain geometry, rather than from the kit's approximate outer diameters.
The chain pitch default is derived from that kit listing (140 links, 54 inches) and is the weakest number on this page. Every result scales directly with it. Measure your own chain and override it.
- VEX High Strength Sprocket & Chain Kit (276-2252) — kit contents — checked 2026-08-17
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Keeps what is on screen so you can change something and see both sides of the change. Saved in this browser only, never uploaded.
Save this as evidence
Collects what you entered, what came out, how it was worked out, and anything the tool flagged, with a timestamp and a version so someone else can reproduce it.
This is evidence, not a notebook entry. It deliberately does not write your problem statement, your reasoning, or your conclusion, because under RECF rules an Engineering Notebook has to be the students' own work and no tool may generate or organise its content. Take the numbers, decide what matters, and write it yourself.