How this calculation works
Roller chain length is counted in pitches rather than measured only as a loose overall length. A whole even pitch count supports a conventional alternating link sequence; this page rounds upward to that count and then estimates the required centre adjustment.
L = 2C/p + (N1 + N2)/2 + ((N2 − N1)/(2π))²/(C/p); round L up to even pitches and invert the same approximationA worked example
With equal twenty-tooth sprockets, 12.7 mm pitch and 508 mm centres, the centre distance is forty pitches. The length formula gives twice forty plus twenty, or exactly one hundred pitches. The nominal chain length is therefore 1270 mm and the inverse returns the original 508 mm centres. Changing to unequal sprockets introduces the squared tooth-difference term, which the equal-sprocket shortcut does not contain.
Good to know
Approximate two-sprocket chain geometry and even-pitch rounding only; no offset-link selection, wear allowance or drive approval. Check the chain manufacturer’s centre-distance, adjustment, tensioning and guarding guidance. The calculated cut length does not prove the transmission can carry a load.
Reference: Rexnord — roller chain catalog and engineering formulas (opens in a new tab) ↗
What this model answers
Roller chain length is counted in pitches rather than measured only as a loose overall length. A whole even pitch count supports a conventional alternating link sequence; this page rounds upward to that count and then estimates the required centre adjustment.
The two-sprocket formula is an approximation. The inverse is solved from the same approximation so the displayed adjustment is internally consistent, rather than pairing a rounded chain count with the unchanged nominal centres.
The Belt pitch length and pulley centres calculator uses tangent spans and circular arcs for a continuous flexible belt. A roller chain follows discrete sprocket pitches, so belt length and chain pitch count should not be substituted for one another.
Measure the right inputs
Use the chain’s nominal pitch and integer tooth counts. Centre distance is the distance between shaft axes, not the gap between sprocket rims. The model rejects overlapping or touching pitch circles.
Pitch diameter for each sprocket uses pitch divided by sin(pi/teeth). That checks the geometry but does not define tooth profile, compatible roller size or a rated chain series. Those remain component specifications.
Read the result in context
The larger quadratic root gives the supported centre-distance solution after rounding. The adjustment is the difference between that solution and the entered centres. A tensioner, sliding mount or alternative stock length is not automatically selected.
An even pitch count is not a strength rating and does not include chain elongation, sag or wear. Actual drive selection also depends on load, speed, lubrication and the manufacturer’s installation requirements.
Work through the numbers
With equal twenty-tooth sprockets, 12.7 mm pitch and 508 mm centres, the centre distance is forty pitches. The length formula gives twice forty plus twenty, or exactly one hundred pitches.
The nominal chain length is therefore 1270 mm and the inverse returns the original 508 mm centres. Changing to unequal sprockets introduces the squared tooth-difference term, which the equal-sprocket shortcut does not contain.
Where the model stops
Approximate two-sprocket chain geometry and even-pitch rounding only; no offset-link selection, wear allowance or drive approval.
Check the chain manufacturer’s centre-distance, adjustment, tensioning and guarding guidance. The calculated cut length does not prove the transmission can carry a load.
A few questions, answered
Why round to an even pitch count?
The model uses a conventional even-length chain sequence and deliberately does not select offset or half links.
Why do the centres change after rounding?
Extra chain pitches need a different geometric path length. The inverse estimates that adjustment within the same approximate formula.