Chain Length and Center Distance Calculator

Chain length from a centre distance and centre distance from a chain length, with the even link count applied — so the answer is the centre distance the chain you can actually buy will give you, and the take-up you need to find. ANSI B29.1 sprocket diameters rather than the PD + 0.6p shortcut, the wrap and C/p checks with the maker who publishes each one named, and the exact polygonal chain length printed beside the catalogue series so you can see how far the approximation has drifted.

One relation, read both ways — and the even link count is what makes the answer interesting

ANSI / ASME B29.1 chain sizes — the dimensions this page uses

ISO 606 / DIN 8187 B-series chain sizes, and what five catalogues disagree about

The chain-number rule, and the shortcut that only half works

What the PD + 0.6p shortcut costs, on a 12.70 mm pitch

Every formula this page uses

Whole links, even counts, and a formula with a range

This page answers one question in two directions, and the interesting part is the rounding. Give it a centre distance and it returns the chain length; give it a chain length and it returns the centre distance. But chain comes in whole links and a drive should be closed with an even number of them, so the length you fit is almost never the fractional length the formula produced — and the moment you round up, your centre distance changes. The headline on this page is therefore the centre distance the even link count actually gives, in both modes, with the take-up printed beside it. A nominal 500 mm on the default drive becomes 510.0 mm, or 10.0 mm for the tensioner to find. That is the number that goes on the drawing.

Where the formula comes from, and where it stops working. Every catalogue prints L = 2C/p + (N₁+N₂)/2 + K²p/C with K = (N₂−N₁)/2π, and none of them says it is an approximation. It is. The exact length is easier to state than the approximation: the chain’s rollers sit on the pitch circle and the chain between them is straight, so a wrap of θ radians on an N-tooth sprocket carries θN/2π pitches of chain — a count, not an arc length. Add the two tangent spans and you have the exact polygonal length. Expand that in (R₂ − R₁)/C and the second-order term is exactly the K²p/C the catalogues print. This batch compared the two over 60,000 random drives: under (R₂ − R₁)/C = 0.1 they agree to a thousandth of a link, and past 0.6 they are more than a whole link apart. Both numbers are in the results, along with the parameter itself, so you can see which regime you are in instead of trusting a formula past its range.

Five things on the page this replaces were wrong, and one of them was a factor of two. Its seven metric chain options set the chain NUMBER as the pitch instead of the pitch: ISO 08B was 8 where the pitch is 12.70 mm, which is 37% out and puts every length, centre distance and diameter out with it. Its outside diameter was PD + 0.6p, which exceeds ANSI B29.1’s own p(0.6 + cot 180°/N) by exactly p·tan(90°/N) — 1.18 mm on a 17-tooth chain-40 sprocket. Its structured data said the chain number times 0.317 inches gives the pitch in inches, which is wrong twice over. Its Strands control was read, echoed and never used, beside an FAQ claiming capacity multipliers for a capacity the page never computed. And its centre-distance formula paired M = L − (N₁+N₂)/2 with p/8, where that M pairs with p/4: as written it returns exactly half the right answer, every time, for every drive. The strands control is not reproduced here at all — multi-strand capacity belongs on the chain selection page, where there is a capacity to multiply.

What the guidance figures actually are, and who publishes them. Centres of 30 to 50 pitches: Renold Jeffrey’s drive checklist and Tsubaki’s installation notes, which put it as “about 30 to 50 times the pitch”. Wrap of 120° minimum on the small sprocket: Tsubaki, as a requirement, with 90° allowed only for a hanging drive. Seventeen teeth minimum on the driver: Renold Jeffrey, with Diamond-Drives giving 12 slow, 17 medium and 25 fast. Sag: Tsubaki again, about 4% of the SPAN — not of the centre distance, which is what the old page used — cut to about 2% for a vertical drive, centres over a metre, a heavy start or sudden reversals. Ratio 7:1 optimum and 10:1 practical maximum: Renold Jeffrey. None of those is a rule of thumb picked up secondhand; each one is a sentence in a named maker’s document, and where two makers differ the page says so rather than splitting the difference.

And the sprocket diameters are here because you cannot draw the drive without them. Pitch diameter p / sin(180°/N) is exact and uncontroversial. Outside diameter is B29.1’s p(0.6 + cot 180°/N), which the standard itself calls approximate because the real tip is set by the tooth form drawn in its Figure 6 — copyrighted, not reproduced here, and not needed for a layout. Root diameter is PD minus the roller, which is where the roller column in the tables earns its place. For the caliper diameters, the maximum bore and the whole tooth-by-tooth geometry, the sprocket geometry calculator does it at scale; for which chain to use in the first place, the roller chain selection calculator; for when to throw it away, the chain wear and elongation calculator; and for the service factor that all of them want, the drive service factor calculator.

Frequently asked questions

Related calculators

References

1. ASME B29.1-2011 (R2022), Precision Power Transmission Roller Chains, Attachments, and Sprockets. Cited by clause and figure; the standard itself is copyrighted and was not fetched. Its published preview at webstore.ansi.org confirms the structure this page relies on: section 1 Roller Chain, section 3 Sprockets, Figure 6 Theoretical Tooth Form, Figure 7 Sprocket Diameters, Tables 12/12M and 13/13M (caliper diameter tolerances) and Table 14 (pitch and outside diameter). Every printed dimension used here is attributed to a named catalogue instead, and everything computable is computed.
2. ISO 606:1994, Short-pitch transmission precision roller and bush chains, attachments and associated chain sprockets (second edition, 1994-02-15). Cited by number; only the standard’s preview was reachable, which confirms clause 3.6 (a measuring force applied when a chain’s length is measured) and clause 5 (chain wheels, described in its own foreword as ‘the unification of all the relevant national Standards’). The dimensional figures here are taken from five named catalogues instead — see the breaking-load note.
3. Martin Sprocket & Gear. Sprocket Engineering Data, catalogue section E-152. Prints the B29.1 forms directly: “PD = Pitch / SIN (180/Nt)” and “OD = (Pitch)(.6 + COT [180 / Nt])”, and describes the bottom diameter as “the diameter of a circle tangent to the bottoms of the tooth spaces”. Also the source, with chinatransmissions’ ANSI chart, for the roller diameters and roller widths used here.
4. AmesWeb. Roller Chain Sprocket Diameter Calculator — ASME B29.1. The one source consulted that prints all five diameter relations in one place: pitch diameter P / sin(180/N); bottom diameter PD − Dr; caliper diameter (even teeth) = bottom diameter; caliper diameter (odd teeth) = PD × cos(90/N) − Dr; “approximate outside diameter” = P × (0.6 + cot(180/N)); and maximum hub and groove diameter = P × (cot(180/N) − 1) − 0.030 in. AmesWeb also notes that “Dr is bushing diameter for chain 25 and chain 35 as these chains have no rollers”.
5. chinatransmissions. ANSI Roller Chain Size Chart | Dimension Guide. Second, independent transcription of the ANSI roller diameters and roller widths, agreeing with Martin’s where the two overlap. It is also the source that settles chain 41’s roller diameter at 0.306 in — the page being ported had 6.35 mm, which is 0.250 in, chain 41’s roller WIDTH.
6. iwis / JWIS. Catalogue: precision chains, British Standard roller chain table. The lowest of the five minimum-breaking-load columns compared in this batch, and the one that matches the figures usually quoted as ISO 606’s own minima (16B-1 at 60.0 kN, 20B-1 at 95.0 kN). Used as the default on the selection page.
7. Cross+Morse. British Standard Precision Roller Chain Conforming to ISO 606. Second of the five ISO 606 transcriptions cross-checked here.
8. Mädler. Roller chains DIN ISO 606 (formerly DIN 8187), catalogue 43. Confirms the pitch and roller-diameter columns. Its breaking-load column could not be read reliably through the fetch used here — the extracted values were monotone in small steps, which is the signature of a shifted column — so it is NOT one of the five counted in the breaking-load spread.
9. U.S. Tsubaki. RS Chain Drive Selection (chains.ustsubaki.com). Confirms the same service factor table and the same multiple strand factors cell for cell, from a different maker — which is why those two tables are treated here as settled rather than as one publisher’s opinion. Also prints the chain speed relation S = P·N·n/12 (inches, rpm) and the chain length and centre distance forms.
10. Tsubakimoto Chain. Roller Chain Arrangement and Installation, technical data (en.tt-net.tsubakimoto.co.jp). Sag: move the centre of the slack span perpendicular and the movement should be “about 4% of the span AB”, reduced to “approximately 2%” for a vertical drive, centres over a metre, a heavy starting load or sudden reversals. Wrap: “the winding angle between the small sprocket and the chain must be 120° or more”, 90° minimum for a hanging drive. Centres: “the most desirable center distance … is about 30 to 50 times the pitch”.
11. Tsubakimoto Chain. Strength Differences Between Chain and the Connecting Links and Offset Links, chain-guide.com 2.2.3.3. Reduction against the chain’s maximum allowable load: tap-fit connecting link none; standard connecting link 0 to 20%; two-pitch offset link 0 to 25%; one-pitch offset link 35%. “If you use chain with loads that are almost the same as the maximum allowable load, you should avoid using offset links.”
12. Wikipedia, Roller chain. Quoted here only for the ANSI numbering rule, which it states in the same terms as the catalogues: “the first digits indicate the pitch of the chain in eighths of an inch, with the last digit being 0 for standard chain, 1 for lightweight chain, and 5 for bushed chain with no rollers”. Also “one rule of thumb is to replace a roller chain which has elongated 3% on an adjustable drive or 1.5% on a fixed-center drive”, and, on odd link counts, that such a chain “tends to be not so strong”.
13. R.S. Khurmi and J.K. Gupta, A Textbook of Machine Design, chapter 21 Chain Drives and chapter 20 V-Belt and Rope Drives (the chapters as distributed by Al-Mustansiriyah University and Al-Mustaqbal University). Source for Table 21.2, factor of safety for bush roller chain against the smaller sprocket’s speed; for the service factor as K1 × K2 × K3 (load, lubrication, hours); for the recommended teeth on the smaller sprocket against velocity ratio; for the V-belt tension ratio 2.3 log(T1/T2) = μθ cosec β with β the groove HALF angle and a groove angle of 32° to 38°; for the centrifugal tension Tc = mv²; and for the maximum-power condition Tc = T/3.