Roller Chain Length & Sprocket Center Distance Calculator

How it works

L (pitches) = 2C ÷ p + (z₁ + z₂) ÷ 2 + p (z₂ − z₁)² ÷ (4π² C), rounded UP to an even number · exact C = p ÷ 4 × [ A + √(A² − 8 ((z₂ − z₁) ÷ 2π)²) ], A = L − (z₁ + z₂) ÷ 2 · sprocket PD = p ÷ sin(180° ÷ z) · chain speed = z₁ p n ÷ 60,000 m/s

A chain wraps half of each sprocket plus two straight runs, and because the straight runs are tangents that lean when the sprockets differ in size, the length picks up a small correction proportional to the square of the tooth difference — the same formula as a belt, expressed in pitches so it can be rounded to whole links. An even count matters because roller chain alternates inner and outer links; an odd count needs an offset link, which is weaker. Once the count is fixed, the centre distance is recomputed exactly so the tensioner range is known, and the geometry also yields the wrap angle on the small sprocket, which must keep enough teeth engaged, and the chordal speed variation that makes small sprockets run roughly.

Worked example

A #40 (12.7 mm pitch) chain over 17- and 45-tooth sprockets at a nominal 500 mm centre distance calculates to 110.2 pitches, so use 112 links (1,422 mm). The exact centre distance for 112 pitches is 511.2 mm, so the mount needs about 11 mm of adjustment; pitch diameters are 69.1 and 182.1 mm, the 17-tooth sprocket has 167° of wrap, and at 300 rpm the chain runs at 1.08 m/s — drip lubrication is enough.

Frequently asked questions