Roller chain length calculator
Chain links from the centre distance, or centre distance from the chain you have, for two sprockets on ANSI, ISO 606 B, bicycle and motorcycle chains. Exact whole-link lengths, and the ASME B29.1 checks on centre distance, wrap and tooth counts.
The Sprocket Designer opens with both sprockets and this chain. Add bores, keyways, hubs and spokes there, and download STL, STEP, DXF or SVG.
Two ways to count a chain
The formula in most catalogues (Martin E-168) gives the chain length in pitches, with the centre distance C in pitches and N and n the tooth counts:
L = 2C + (N + n)/2 + (N − n)² / (4π²·C)
It is an approximation. This calculator, like the Sprocket Designer, uses the exact layout: each sprocket's pitch diameter is p ÷ sin(180°/N), the chain's straight spans are tangent to the two pitch circles, and on each sprocket the chain follows the pitch polygon, so a wrap of angle θ holds θ/360 of its teeth in links. For a whole number of links it solves the centre distance from that exactly. Both lengths are shown; on most drives they differ by a few hundredths of a link.
A chain is a whole number of links, usually even so that a standard connecting link joins it. The calculator offers the allowed chain just shorter and just longer than your centre distance needs, each with its exact centre distance. The Sprocket Designer takes the longer one.
The checks are ASME B29.1's: 30 to 50 pitches between centres is most desirable, at least 120° of wrap on the small sprocket, an odd tooth count under 25 teeth, and at most 120 teeth. ISO 606 covers 9 to 150 teeth, and Martin suggests two stages beyond 7:1.
Roller chain questions
How do you calculate roller chain length?
The textbook formula (Martin E-168) gives the length in pitches: L = 2C + (N + n)/2 + (N − n)² / (4π²C), with C the centre distance in pitches and N, n the tooth counts. It is an approximation. This calculator uses the exact model the Sprocket Designer uses: the chain's straight spans are tangent to the pitch circles and on each sprocket it follows the pitch polygon, so a wrap of angle θ holds θ/360 of the sprocket's teeth in links. It shows both.
Why should a chain have an even number of links?
A roller chain alternates inner and outer links, so an even count joins with a standard connecting link. An odd count needs an offset (half) link, which is weaker. Round up to the next even length rather than down: a chain that is too short can't be fitted, and one forced on overloads the shafts and bearings.
What centre distance should a chain drive have?
ASME B29.1 calls 30 to 50 chain pitches between shaft centres the most desirable, and wants the chain to wrap at least 120° round the small sprocket. The calculator warns outside those, as the Sprocket Designer does.
How many teeth should a sprocket have?
ASME B29.1 suggests an odd tooth count under 25, so wear spreads round the teeth, and at most 120 teeth. ISO 606 applies from 9 to 150 teeth. Over a 7:1 ratio, Martin suggests a two-stage reduction.
Can I use it for a bicycle?
Yes, for a two-sprocket drive: single speed, fixed gear, BMX, hub gear, e-bike conversions. For a derailleur bike the chain length also depends on the derailleur's capacity; use your derailleur maker's method. For a frame without chain adjustment, the magic gear calculator finds chainring and cog pairs that fit.
Are motorcycle 420, 428 and 530 chains covered?
Yes. Chain length depends only on the pitch: 420 and 428 are ½″ pitch like ANSI 41 and 40, and 530 is ⅝″ like ANSI 50, with the same roller widths. 520 and 525 are also ⅝″ pitch, so the ANSI 50 lengths apply to them too.
Now make the sprockets
Industrial, motorcycle and bicycle sprockets and chainrings with bores, keyways, splines, hubs and spokes, checked against ASME B29.1 and ISO 606, as STL, STEP, DXF or SVG.