Roller Chain Length Calculator (links)

Understanding the roller chain length calculator — concept and principle

Roller chain is sold by the link, and a chain can only be closed with a whole number of links. This calculator turns two sprocket tooth counts, the centre distance and the chain pitch into the exact theoretical number of links, then rounds up to the next even number so the chain can be joined with a standard connecting link.

The exact 109.32 links rounds up to an even 110 so the ends join without an offset link.

How it is calculated

L = 2C/p + (z₁ + z₂)/2 + p(z₂ − z₁)²/(4π²C)

C: centre distance between sprocket shafts (mm).
p: chain pitch (mm); 12.7 mm for ISO 08B and ANSI 40.
z₁, z₂: teeth on the small and large sprocket.

The result is in links (pitches). The ratio is z₂/z₁.

The principle

Each tooth carries exactly one pitch of chain, so the chain wrapped around half of each sprocket accounts for (z₁ + z₂)/2 links. The two straight spans add about 2C/p links. The last term corrects for the tilt of the spans when the sprockets differ in size, using the same geometry as a belt drive; it grows with the tooth difference squared and shrinks as the centre distance increases. An even link count lets inner and outer links alternate all the way round; an odd count needs an offset (cranked) link, which is weaker.

Worked example

Inputs: z₁ = 15, z₂ = 45, C = 500 mm, p = 12.7 mm.
2C/p = 1,000/12.7 = 78.740 links.
(z₁ + z₂)/2 = 30 links.
Correction = 12.7 × 30²/(4π² × 500) = 0.579 links.
Exact links = 78.740 + 30 + 0.579 = 109.32; rounded up to an even number = 110 links.
Ratio = 45/15 = 3.

Each point is the calculator re-run with only “Pitch (mm; 08B/ANSI 40 = 12.7)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Pitch (mm; 08B/ANSI 40 = 12.7)	Links (round up to even)
3.17	346
6.35	188
9.53	136
12.7	110
15.9	94
19.1	84
25.4	72

How to read the result

Rounding up means the real centre distance grows slightly. Solving the formula back for 110 links gives about 504.4 mm, so the drive needs an adjustable mount or idler. A common guideline is a centre distance of about 30 to 50 pitches; 500 mm is about 39 pitches. Small sprockets with fewer than about 17 teeth run rougher because of chordal action, which is why 15 teeth is acceptable for moderate speeds but not ideal at high speed.

Common mistakes

Using the pitch in inches with a centre distance in mm.
Rounding down, which leaves the chain too short.
Not allowing for chain wear elongation and slack-span sag.
Using an odd link count without accepting an offset link.

Keep in mind: This geometric estimate does not size the chain for power, speed or lubrication; use the chain manufacturer's rating tables and have real machinery checked by a qualified person.

Frequently asked questions

Why is 08B the same pitch as ANSI 40?

Both use a 12.7 mm (1/2 inch) pitch, but roller diameter and widths differ slightly, so they are not always interchangeable.

How much slack should a chain have?

Manufacturers commonly suggest a slack-span sag of a few percent of the span length; follow their figure.

When is a chain worn out?

When elongation reaches the manufacturer's limit, often in the 1–3% range, measured over several links.

Sources: ISO 606, Short-pitch transmission precision roller and bush chains, attachments and associated chain sprockets · ASME B29.1, Precision power transmission roller chains, attachments, and sprockets

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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