About Roller Chain Length Calculator — ANSI Chain & Sprockets
The roller chain length calculator lays out a two-sprocket ANSI chain drive. Pick the chain number — the pitch falls out of the ASME B29.1 identity, where the tens digits of the number are the pitch in eighths of an inch (#40 is 4/8 = 1/2 in, #100 is 10/8 = 1-1/4 in) — enter the two tooth counts and the desired shaft center distance, and the tool computes the chain length in pitches from the standard handbook formula, rounds it UP to an even number of links, and then back-solves the exact center distance that even chain actually gives you.
Even matters: roller chain closes on alternating inner and outer link plates, so only an even pitch count joins with a standard connecting link — an odd count needs an offset (half) link, which is weaker and best avoided. The calculator also reports the sprocket pitch diameters, the speed ratio, and the chain velocity at your small-sprocket RPM.
How It Works
- Pick the chain size from the ANSI ladder (#25 through #240) or enter a custom pitch for metric and specialty chains. The chain-number identity is definitional in ASME B29.1: pitch = (chain number ÷ 10) × 1/8 inch; the trailing digit flags the construction (0 = standard roller, 5 = rollerless bushing).
- Enter the tooth counts — large and small sprocket — and the center distance you want. The formula L = 2C/P + (N+n)/2 + (N−n)²/(4π²·C/P) counts the two straight strands, half of each sprocket wrap, and the correction for the strand angle when the sprockets differ. With equal sprockets the correction vanishes and L = 2C/P + N exactly.
- The computed length is almost never a whole number, so it rounds UP to the next even link count (up, so the chain fits around the sprockets; even, to avoid an offset link). The rounding is epsilon-guarded — a result that is an exact even integer in decimal arithmetic never gains two phantom links to float noise.
- Because the even chain is slightly longer than the exact requirement, the tool back-solves the center distance for the chosen link count: C = P/4 × [A + √(A² − 2(N−n)²/π²)] with A = L − (N+n)/2. Build the drive at this distance (or use it as the nominal for your tensioner range — a common allowance is to leave room to shorten by two pitches as the chain wears).
- Pitch diameters PD = P/sin(180°/N) locate the theoretical chain line on each sprocket, the ratio N/n gives the speed reduction, and the chain speed P × n × rpm ÷ 12 (ft/min) is the number lubrication regimes and horsepower tables key on.
Worked Example
A #40 chain (P = 0.5 in) drives a 45-tooth sprocket from a 17-tooth at a desired 20 in center distance. C/P = 40 pitches, so L = 2×40 + (45+17)/2 + (45−17)²/(4π²×40) = 80 + 31 + 0.4965 = 111.50 pitches. Round up to 112 links — a 56 in chain. Back-solving for 112 links: A = 112 − 31 = 81, C = 0.5/4 × [81 + √(81² − 2×784/π²)] = 20.13 in — set the shafts 20.13 in apart and the 112-link chain fits without an offset link. Pitch diameters: 7.17 in and 2.72 in; ratio 2.65:1; at 600 rpm on the 17-tooth sprocket the chain runs 0.5 × 17 × 600 / 12 = 425 ft/min.
Formulas
- Chain length in pitches
L = 2·C/P + (N + n)/2 + (N − n)² / (4π² · C/P)- Exact center distance for the even chain
C = P/4 × [ A + √(A² − 2(N − n)²/π²) ], A = L − (N + n)/2- Pitch diameter and chain speed
PD = P / sin(180°/N); v = P × n × rpm / 12
Standards & References
- ASME B29.1 — Precision Power Transmission Roller Chains: the chain-number/pitch identity (tens digits = pitch in 1/8 in) and the standard #25–#240 ladder
- Machinery's Handbook, chains and sprockets section — chain length, center-distance correction, and pitch-diameter relations
Frequently Asked Questions
How do I calculate roller chain length?
L (in pitches) = 2C/P + (N+n)/2 + (N−n)²/(4π²·C/P), where C is the center distance, P the pitch, and N, n the tooth counts. Multiply by the pitch for inches, and round up to an even number of links. Example: #40 chain, 45/17 teeth, 20 in centers → 111.5 pitches → 112 links = 56 inches of chain.
Why must the link count be even?
Roller chain alternates inner (roller) links and outer (pin) links, so a loop only closes inner-to-outer with a standard connecting link when the total count is even. An odd count forces an offset link, which is measurably weaker and a common failure point — practice is to round up to even and adjust the center distance instead.
What pitch is a #40 / #60 / #80 chain?
The tens digits of the ANSI number are the pitch in eighths of an inch: #40 = 4/8 = 1/2 in, #60 = 6/8 = 3/4 in, #80 = 8/8 = 1 in, #25 = 2/8 = 1/4 in, #100 = 10/8 = 1-1/4 in. A trailing 0 means standard roller construction, a trailing 5 (#25, #35) rollerless bushing chain. The identity is definitional in ASME B29.1.
Why does the calculator give back a slightly different center distance?
Because the chain you can buy is the even-rounded length, not the fractional ideal. The back-solved value is the center distance at which the even chain runs with theoretical zero slack — build there, or slightly under with a tensioner. If your shafts are fixed at exactly the entered distance, the chain will have the leftover fraction of a pitch as slack.
How much slack should a chain drive have?
Typical practice for horizontal drives is mid-span movement of about 2% of the center distance (more for shock loads, less for vertical drives). This calculator gives the geometric zero-slack center distance; back one shaft off or fit an idler to set the sag, and leave adjustment room to take up wear elongation, which is commonly allowed to reach 2–3% before replacement.
Are sprocket tooth counts restricted?
The formula accepts 9 to 120 here. Fewer than about 17 teeth on the driver increases chordal speed variation and roller impact (small counts are for low speed); very large counts make wear-elongated chain climb the teeth. Odd tooth counts paired with even link counts distribute wear evenly around the chain — one reason 17/45 style combinations are popular.