Chain length
-Exact center distance
-Speed ratio
-Chain speed
-All results
| Chain length before rounding | - |
| Chain length, rounded up to an even number of pitches | - |
| Output speed | - |
| Small sprocket pitch diameter | - |
| Large sprocket pitch diameter | - |
| Wrap angle, small sprocket | - |
| Teeth engaged on the small sprocket (approx.) | - |
| Chordal speed variation, small sprocket | - |
| Center distance in chain pitches | - |
| Chain pull from the power | - |
Method and formulas
Standard roller chain geometry on two sprockets, so every figure can be checked by hand. The chain wraps each sprocket as a polygon whose side is the pitch p.
| Quantity | Formula |
|---|---|
| Chain length in pitches | L = 2 C / p + (N1 + N2) / 2 + [(N2 − N1) / (2π)]² · p / C, rounded up to an even whole number |
| Exact center distance for L | C = (p / 4) [K + √(K² − 8 ((N2 − N1) / (2π))²)], K = L − (N1 + N2) / 2 |
| Pitch diameter | PD = p / sin(180° / N) |
| Wrap angle, small sprocket | θ = 180° − 2 asin[(PD2 − PD1) / (2 C)] |
| Speed ratio and output speed | i = N2 / N1, n2 = n1 / i |
| Chain speed | v = N1 p n1 / 60 (p in m, v in m/s) |
| Chordal speed variation | 1 − cos(180° / N1) |
| Chain pull | F = P / v |
The sprockets are in the same plane with parallel shafts and the drive is a simple two-sprocket layout with no idler. The length formula is the standard approximation for chain over two sprockets, the exact center distance is its inversion. The rounded length is a nominal figure: allow for adjustment of the center distance or a tensioner to take up wear elongation.
Worked example: 19 and 57 teeth, 12.7 mm pitch, about 500 mm center distance, 1450 rpm
L = 2 × 500 / 12.7 + (19 + 57) / 2 + [(57 − 19) / (2π)]² × 12.7 / 500 = 117.67 pitches, rounded up to 118. K = 118 − 38 = 80, so C = (12.7 / 4) [80 + √(80² − 8 × 6.048²)] = 502.1 mm. PD1 = 12.7 / sin(180°/19) = 77.16 mm, PD2 = 230.54 mm. Wrap angle = 162.4°. Ratio = 57 / 19 = 3; output speed = 1450 / 3 = 483 rpm. Chain speed = 19 × 0.0127 × 1450 / 60 = 5.83 m/s.
Questions
How do you calculate roller chain length?
Chain length in pitches is L = 2 C / p + (N1 + N2) / 2 + ((N2 - N1) / (2 pi))^2 x p / C, where C is the center distance, p the chain pitch and N1, N2 the tooth counts. Round the result up to the next whole number, and to an even number so the chain closes without an offset link. An offset link is weaker and is best avoided.
How do I find the center distance for a given number of links?
Solve the length equation for C: with K = L - (N1 + N2) / 2 the exact center distance is C = (p / 4) x [K + sqrt(K^2 - 8 ((N2 - N1) / (2 pi))^2)]. This calculator rounds L up to an even number of pitches and then reports the exact center distance that the chain will give, which is slightly different from the one you typed in. Allow for adjustment or a tensioner.
What center distance is best for a roller chain drive?
Common guidance is about 30 to 50 chain pitches, and not more than about 80 pitches without a support for the slack side. Below roughly 30 pitches the wrap on the small sprocket is small and the chain flexes often. The minimum center distance is set by the sprockets clearing each other and by keeping about 120 degrees of wrap on the small sprocket. Follow your chain maker's recommendations.
How many teeth should the small sprocket have?
More teeth give smoother, quieter running and less wear: very small sprockets (under about 17 teeth) cause strong chordal action and are normally kept for slow drives. Around 19 to 25 teeth is a common choice for general drives. Keep the speed ratio to about 7:1 or less in one stage, and prefer an odd tooth count on the large sprocket with an even number of links so wear spreads over all teeth.
What is chordal action or polygonal effect?
A chain wraps a sprocket as a polygon, so the chain speed pulses as each link engages. The speed variation of the chain is 1 - cos(180 / N) for N teeth, which is about 1.2 percent at 17 teeth and 0.7 percent at 22 teeth. It matters at high speed and for positioning drives and is one reason to use more teeth on the small sprocket.
How do I calculate chain speed and chain pull?
Mean chain speed is v = N1 x p x n1 / 60, with the pitch in meters for m/s. The tight-side pull from the power transmitted is F = P / v. Rated chain pull, working load limits, service factors and lubrication limits depend on the chain maker's data and are not included here.
What does this calculator not cover?
It covers sprocket and chain geometry, ratio, speed and the pull implied by the power. It does not select a chain size or strand count, check power rating, shock and inertia loads, shaft loads, lubrication regime, wear elongation allowance, chain tensioners or multi-sprocket layouts. Use the chain maker's selection method for power rating. Verify critical designs.
Engineering aid for guidance. It covers two-sprocket roller chain geometry, speed and pull and does not cover chain selection, power rating, service factors, shock loads, lubrication, tensioners, idlers or multi-sprocket layouts. Verify critical designs.