How it works
The roller-chain length is solved in pitches (link count): L = 2C/p + (N₁ + N₂)/2 + ((N₂ − N₁)/2π)² · (p/C) where C is the centre distance, p the chain pitch, and N₁, N₂ the small and large tooth counts. The first term is the two straight spans, the middle term is the chain wrapped around the two sprockets, and the last term corrects for the size difference between them.
That theoretical value is then rounded up to the next even number of
links, because a roller chain closes with a standard connecting link
only when the pitch count is even. The chain length is finally
length = links × pitch.
Worked example
A 15-tooth and a 45-tooth sprocket on a 500 mm centre distance with ANSI 40
chain (12.7 mm pitch) gives
L = 2·500/12.7 + (15+45)/2 + ((45−15)/2π)²·(12.7/500) ≈ 109.3 pitches.
Rounded up to an even count that is 110 links, so the chain
length is 110 × 12.7 = 1,397 mm. The calculator returns exactly
these values.
Frequently asked questions
- How do I calculate roller chain length?
- Solve the chain length in pitches: L = 2C/p + (N₁ + N₂)/2 + ((N₂ − N₁)/2π)²·(p/C), where C is the centre distance, p the chain pitch, and N₁, N₂ the tooth counts. Round that up to the next even number of links, then the length is links × pitch. Enter the four values above and the calculator does it.
- Why does a roller chain need an even number of links?
- A standard connecting (master) link joins an inner link to an outer link, which only works when the pitch count is even. An odd number of links has to be closed with an offset (cranked) link, which is weaker and cuts the chain rating — so chain length is always rounded up to an even number.
- How do I find chain length in inches or mm?
- Multiply the number of links by the chain pitch: length = links × pitch. With ANSI 40 chain (1/2 in = 12.7 mm pitch), 110 links is 110 × 0.5 = 55 in, or 110 × 12.7 = 1,397 mm. Toggle SI/Imperial in the header to read either.
- What is chain pitch?
- Chain pitch is the distance between adjacent roller (pin) centres — the basic size of the chain. ANSI 40 (#40) is 12.7 mm (1/2 in), the most common general-purpose size; ANSI 35 is 9.525 mm (3/8 in), ANSI 50 is 15.875 mm (5/8 in), ANSI 60 is 19.05 mm (3/4 in), and ANSI 80 is 25.4 mm (1 in).
- Do I need to adjust the centre distance after rounding up?
- Slightly. Rounding the link count up makes the chain a touch longer than the exact geometry, so the chain runs with a little extra slack. Take it up by reducing the centre distance a small amount, or — better on a fixed-centre drive — fit a chain tensioner or idler.
- Does this work in metric and imperial?
- Yes — enter the centre distance and chain pitch in mm or inches; the link count is the same either way and the length is shown in mm or inches. Toggle SI/Imperial in the header.
Method & assumptions
- The link count is rounded up to the next even number so the chain closes with a standard connecting link (an odd count needs a weaker offset/cranked link).
- Rounding up leaves a little slack — recut the centre distance slightly or fit a tensioner/idler to take it up.
- Standard roller chain on a two-sprocket drive; chain length = links × pitch.
Related calculators
- Pulley Calculator — Pulley ratio, driven RPM and belt speed from pulley diameters.
- Sprocket Calculator — Sprocket ratio, RPM, chain speed and pitch diameters for a chain drive.
- Belt Length Calculator — Two-pulley belt length and wrap angle from center distance and diameters.
- Bearing Life (L10) Calculator — Basic L10 rating life in revolutions and hours from load, speed and rating.