Science & Engineering
Roller chain length.
Chain length in pitches L = 2C + (N + n) ÷ 2 + [(N − n) ÷ 2π]² ÷ C from the two sprocket tooth counts and the centre distance, rounded up to an even number of links, with the true centre distance and wrap angle. Runs in your browser.
Chain drive
Result
Fill the form and press Calculate.
Worked example
Sprockets of 20 and 40 teeth on 0.5 in pitch chain, shafts 20 in apart: C = 20 ÷ 0.5 = 40 pitches. L = 2 × 40 + (40 + 20) ÷ 2 + [(40 − 20) ÷ (2π)]² ÷ 40 = 80 + 30 + 0.253 = 110.25 pitches. Round up to the next even number: 112 links (56 in). With 112 links the true centre distance works out to 40.88 pitches (20.44 in), and the chain wraps about 171.1° of the small sprocket.
How it works
Roller chain length is counted in pitches (links). With C the centre distance divided by the chain pitch, N the teeth on the large sprocket and n the teeth on the small one, L = 2C + (N + n) ÷ 2 + [(N − n) ÷ 2π]² ÷ C. The result is rounded up to an even whole number, because an odd count needs an offset link, which is weaker and usually avoided; rounding down would leave the chain too tight.
The same formula is then solved the other way, as a quadratic in C, to give the centre distance the whole-link chain actually produces. The wrap angle on the small sprocket uses the same geometry as an open belt, π − 2·arcsin((D − d) ÷ 2C), with each pitch diameter taken as P ÷ sin(180° ÷ teeth). A minimum of 90° of contact is the usual floor, with 180° or more recommended for reliable running.
Not for safety-critical design
Planning and learning aid only. It is not for structural, lifting, pressure-system or other safety-critical design, and it is not professional engineering advice. Have a qualified engineer check anything that carries people or could fail dangerously.
Sources and basis: Engineers Edge: Sprocket centre distance and chain length; gm0 (Game Manual 0): Roller chain; tec-science: Belt drive wrap angle; AMESWeb: Roller chain sprocket diameter (pitch diameter = P ÷ sin(180° ÷ N)). Checked 2026-10-16. Planning aid only; see the note above.
FAQ
What is the roller chain length formula?
In pitches, L = 2C + (N + n) ÷ 2 + [(N − n) ÷ 2π]² ÷ C, where C is the centre distance divided by the pitch, N is the teeth on the large sprocket and n the teeth on the small one.
Why round up to an even number of links?
An even link count closes with a standard connecting link. An odd count needs an offset link, which is weaker. Rounding down would leave the chain too tight, so round up.
How many links are in my chain?
The calculator gives the pitches, which equals the number of links (inner plus outer). It rounds the answer up to the next even number.
Is the formula exact?
No. Engineers Edge describes it as approximate, with error smaller than the normal variation in chain length. Chains also stretch as they wear, so allow adjustment.
What wrap angle is enough on the small sprocket?
At least 90° of contact is the usual minimum, and 180° or more is recommended for reliable running. Use the chain maker's data for the exact limit.