Calculation
L = 2·C + (N1+N2)·p/2 + (N2−N1)²·p²/(4·π²·C)
Manufacturer approximation for an open two-sprocket drive; the result X = L/p is rounded up to a whole, preferably even, number of pitches and the center distance is then recalculated.
Hersteller-Näherung: X = 2a/p + (z1+z2)/2 + (z2−z1)²/[4π²(a/p)]
Chain Length Calculator for Roller Chain Drives
Manufacturer approximation for an open two-sprocket drive; the result X = L/p is rounded up to a whole, preferably even, number of pitches and the center distance is then recalculated.
MINTSI
02
Result
Select a target and calculate.
Chain length L versus centre distance C
L grows almost linearly with 2·C; the correction term (N₂ − N₁)²·p²/(4·π²·C) for unequal sprockets matters mainly at short centre distances. In practice L is rounded to a whole, preferably even number of links and C is recalculated from it.
No curve point selected yet.
Understand the inputs
- Chain length L — Theoretical pitch length of the roller chain; the pitch count is X=L/p.
- Center distance C — Distance between driving and driven sprocket centers; 482.6 mm equals 19 inches in the Tsubaki example.
- Chain pitch p — Distance between adjacent pin centers; 25.4 mm is the 1-inch pitch of the RS16B chain in the Tsubaki example.
- Small sprocket teeth N1 — Whole-number tooth count of the smaller sprocket.
- Large sprocket teeth N2 — Whole-number tooth count of the larger sprocket.
Example
Tsubaki selection example: RS16B-2 with 25.4 mm pitch, 17/51 teeth and 482.6 mm center distance gives X = 73.541 pitches; round up to 74 links.
Assumptions and limits
Open two-sprocket chain drive without an idler; the equation is a geometric manufacturer approximation. Sag, wear elongation, chordal action, strength and lubrication are not included.
Understand Chain Length Calculator for Roller Chain Drives
This calculator finds the missing quantity among chain length L, center distance C, chain pitch p and the two sprocket tooth counts N1 and N2 from the other four — for an open roller chain drive between two sprockets. It answers two common practical questions at once: what chain length is needed for a planned center distance, and what center distance suits an already available chain?
What does this quantity describe?
The manufacturer formula is clearest in dimensionless form: X = L/p = 2c + (N1+N2)/2 + (N2−N1)²/(4π²c), with c = C/p. Multiplication by p gives L = 2C + (N1+N2)·p/2 + (N2−N1)²·p²/(4π²C). Martin uses the rounded factor 0.1013/4, Tsubaki uses (N2−N1)²/6.28² and Renold gives the same pitch-count approximation; the calculator evaluates their common factor with π and no intermediate rounding.
The first two terms approximate the two straight chain spans and the half-wraps. The third corrects for unequal sprocket sizes. The result is a theoretical length in pitches, not a directly orderable chain: Tsubaki counts any fraction as another pitch; Renold requires rounding up to a whole even number and advises against odd lengths because they require a cranked link.
Formula and variables
L = 2·C + (N1+N2)·p/2 + (N2−N1)²·p²/(4·π²·C)
L = 2C + (N1+N2)p/2 + (N2−N1)²p²/(4π²C)C = p/4 · [(L/p − (N1+N2)/2) + √((L/p − (N1+N2)/2)² − 2(N2−N1)²/π²)]
| Symbol / input | Meaning |
|---|---|
| Chain length L | Theoretical pitch length of the roller chain; the pitch count is X=L/p. |
| Center distance C | Distance between driving and driven sprocket centers; 482.6 mm equals 19 inches in the Tsubaki example. |
| Chain pitch p | Distance between adjacent pin centers; 25.4 mm is the 1-inch pitch of the RS16B chain in the Tsubaki example. |
| Small sprocket teeth N1 | Whole-number tooth count of the smaller sprocket. |
| Large sprocket teeth N2 | Whole-number tooth count of the larger sprocket. |
Choose the inputs correctly
Enter four of the five quantities to find the fifth. Use the nominal pitch of the selected roller chain for p. In a real design N1 and N2 are positive whole tooth counts; a reverse-calculated decimal is only a theoretical solution and must be replaced by an available integer count and checked again. Driver and driven assignments are interchangeable in this length equation.
How to use the calculator
Select the target and enter four known values with units. Divide the length result by p, round the pitch count upward to a whole even number, then use L = X·p to recalculate the adjustable center distance. Check packaging, wrap, capacity, lubrication and take-up separately.
Worked example
Literature comparison using Tsubaki's selection example: RS16B-2 has p = 1 in = 25.4 mm; N1 = 17, N2 = 51 and C = 19 in = 482.6 mm. Thus c = 19 and X = 2·19 + (17+51)/2 + (51−17)²/(4π²·19) = 73.5411. Tsubaki specifies 74 links for this case. The calculator returns L = X·p = 1,867.945 mm and therefore the same X = 73.5411.
Understand the result and units
A 74-link chain has L = 74·25.4 = 1,879.6 mm. Algebraic inversion of the unrounded π formula gives C = 488.671 mm, or 19.2390 pitches. Tsubaki's inverse with its rounded constant 9.86 gives 488.651 mm; the 0.020 mm difference only reflects rounding of the catalog constants. Both methods select the same practical link count.
Chain length L, center distance C and pitch p are given in the same length unit, usually millimetres. N1 and N2 are dimensionless tooth counts.
Typical applications
The formula is used for new chain-drive designs, changing tooth counts to adjust the drive ratio, and retrofitting conveyors, agricultural machinery and drives with different sprockets.
Assumptions, limits and common mistakes
This is a geometric approximation for an open two-sprocket drive without an idler. Tsubaki calls 30 to 50 pitches the optimum center distance and gives a maximum of 20 pitches for pulsating loads. Those recommendations are not the equation's validity interval, so the published 19-pitch example remains a valid mathematical check. Sprocket teeth must not touch. Sag, wear elongation, chordal action, wrap, strength, lubrication and dynamic loads remain outside this calculator.
Common mistake: Do not confuse L and X: L is a length here, while X = L/p is the number of pitches or links. Do not order the theoretical decimal result or merely round it to the nearest value; the cited manufacturer instructions require rounding upward, and Renold additionally specifies an even count. Then recalculate center distance from the selected real length.
Frequently asked questions
Why should the number of chain links be even?
An even number of links closes using the two matching link types (inner and outer link) with no extra piece; an odd number needs a special offset link, which has lower load capacity than a normal link and should be avoided where possible.
Which tooth count is N1 and which is N2?
It doesn't matter which sprocket drives for the length calculation — only the difference between the two tooth counts enters the formula. N1 is conventionally the smaller sprocket, N2 the larger one.
What center distances are customary?
Tsubaki calls 30 to 50 pitches optimum and gives a maximum of 20 pitches for pulsating loads. Independently of that guidance, the sprocket teeth must not touch. These are design notes, not a guarantee of capacity or life.