Chain Length Calculator
Enter your front sprocket teeth, rear sprocket teeth, center distance in inches, and chain pitch. The calculator returns the number of links (rounded up to the nearest even integer) and the corresponding chain length in inches. The build-time tables below call the same tested Go function as the calculator: one source of truth.
The chain-length formula, term by term
The standard two-sprocket chain-length formula (found in mechanical engineering references and chain manufacturers' engineering guides) is:
L = 2C/P + (N1+N2)/2 + P·((N2−N1)/(2π))²/C
L is the chain length in pitches (links). C is the center distance between the two sprocket shafts, in inches. P is the chain pitch: the length of one link, in inches. N1 and N2 are the tooth counts of the two sprockets; the formula treats them symmetrically, so argument order does not matter (the difference is squared, so swapping N1 and N2 gives the same result).
The first term, 2C/P, is the wrap-distance contribution: if both sprockets had zero radius the chain would run straight across twice (once on each side of the centerline), and 2C/P gives how many pitches that straight span covers. For 520-series chain (P = 5/8 inch = 0.625 in) at a 23.25-inch center: 2 × 23.25 / 0.625 = 74.4 pitches.
The second term, (N1+N2)/2, is the average-engagement contribution: it accounts for how much chain wraps around both sprockets. The average circumference of the two sprockets in pitches gives an accurate first estimate. For 13/49: (13+49)/2 = 31.
The third term, P·((N2−N1)/(2π))²/C, is the wrap-angle correction term. When the two sprockets differ in size, the chain strands are not perfectly parallel, so the wrap around each sprocket departs from a half-turn. The correction is proportional to the square of the tooth difference and inversely proportional to center distance: a large tooth difference or short center distance makes it significant; nearly equal sprockets far apart make it negligible. For 13/49 at 23.25 inches: (36/(2π))² × 0.625 / 23.25 ≈ 32.83 × 0.02688 ≈ 0.88 links.
Adding all three terms: 74.4 + 31 + 0.88 = 106.28 pitches. That raw float is then rounded up to the nearest even integer: in this case 108 links.
Why chain length must be an even number of links
A roller chain is made of alternating inner links and outer links. An inner link consists of two inner plates connected by two rollers; an outer link consists of two outer plates connecting adjacent inner links with pins. The chain closes when an outer link connects back to the beginning of the loop. That closure requires the total link count to be even: an inner link on one end must meet an outer link on the other.
Adding one more link when the raw rounded-up count is odd (making it even) allows the chain to close with a standard master link (also called a clip link). Chain manufacturers' technical guides advise against half-links (offset links) for performance and racing applications: a half-link is simultaneously inner and outer, creating an asymmetric stress point. Always size to an even count and use a standard master link.
The calculator rounds the raw float up to the next integer, then adds one more if the result is odd. The result is always the smallest even number that does not leave the chain too short.
Worked example: 13/49 sprockets, 23.25-inch center, 520 chain
A common motocross setup: 13-tooth front, 49-tooth rear, 23.25-inch shaft center distance, 520-series chain (5/8-inch pitch = 0.625 inch).
- First term (wrap distance): 2C/P = 2 × 23.25 / 0.625 = 74.4 links.
- Second term (average engagement): (N1+N2)/2 = (13+49)/2 = 31 links.
- Third term (wrap-angle correction): (N2−N1)/(2π) = 36 / 6.2832 = 5.730; squared = 32.83; times P/C = 0.625/23.25 = 0.02688; correction = 32.83 × 0.02688 ≈ 0.88 links.
- Sum: 74.4 + 31 + 0.88 = 106.28 links. Round up to next integer: 107 (odd). Add one to make even: 108 links.
- Chain length: 108 links × 0.625 in/link = 67.50 inches. Order a 108-link 520 chain; install with a standard master link.
What to do after changing sprockets
Changing either sprocket changes the required link count. Reenter the new tooth counts and your measured center distance. Measure center distance (axle centerline to countershaft centerline) with the axle at mid-adjuster range, so you have room to take up stretch later.
If the new count matches your current chain, you may keep it. If it is larger, order the next standard length and remove excess links. If it is smaller, use a shorter chain or remove links if length permits. Verify chain slack per your service manual after installation.
Link-count tables: 520 chain @ 23.25 in center
All values are computed at build time by the same tested Go function the calculator calls: one source of truth for every cell.
Front 13 × rear 44-53
| Rear sprocket | Links | Length (in) |
|---|---|---|
| 44-t rear | 104 | 65.00 |
| 45-t rear | 106 | 66.25 |
| 46-t rear | 106 | 66.25 |
| 47-t rear | 106 | 66.25 |
| 48-t rear | 106 | 66.25 |
| 49-t rear | 108 | 67.50 |
| 50-t rear | 108 | 67.50 |
| 51-t rear | 108 | 67.50 |
| 52-t rear | 108 | 67.50 |
| 53-t rear | 110 | 68.75 |
Fronts 12, 14, 15 × rears 48, 50, 52
| Rear \ Front | 12-t front | 14-t front | 15-t front |
|---|---|---|---|
| 48-t rear | 106 (66.25 in) | 108 (67.50 in) | 108 (67.50 in) |
| 50-t rear | 108 (67.50 in) | 108 (67.50 in) | 108 (67.50 in) |
| 52-t rear | 108 (67.50 in) | 110 (68.75 in) | 110 (68.75 in) |
FAQ
How many links are in a 520 chain?
Standard 520 chains are sold in lengths of 100, 106, 110, 114, and 120 links. The right count for your bike depends on your sprocket combination and center distance; use the calculator above. The 520 designation refers to chain pitch and width (the ANSI-derived motorcycle chain numbering convention used in chain manufacturers' size charts), not the number of links.
Can I use an odd number of links?
Technically yes, with a half-link (offset link), but chain manufacturers' technical guides advise against half-links in performance and off-road applications because the asymmetric geometry creates an uneven stress point. Size to an even count with a standard master link. If the even count is too long, remove two links to stay even; if too short, order the next standard length.
Does it matter which sprocket is N1 and which is N2?
No. The chain-length formula uses (N2−N1)², so swapping the two tooth counts gives the same result: the difference squared is always positive. formulas.ChainLinks(n1, n2, center, pitch) produces the same output as formulas.ChainLinks(n2, n1, center, pitch). Pass front and rear in either order.
How does chain length change after changing sprockets?
Rerun the calculator with the new sprocket teeth and the same center distance. Adding rear teeth or reducing front teeth usually adds one to two links; the reverse usually removes one to two links. Always calculate; the exact delta depends on the combination. The sprocket and gear ratio calculator at /sprocket-gear-ratio-calculator/ shows the corresponding drive-ratio change.
What if the calculator gives an odd number of links?
A roller chain closes cleanly only at an even link count, so round the raw result up to the next even number and close it with a standard master link (clip link). Avoid half-links (offset links) on performance and racing machines: a half-link is both an inner and an outer link at once, which creates an asymmetric stress point that chain manufacturers' technical guides flag as a failure risk.
Where do I measure center distance from?
Measure between the centers of the two sprocket shafts, the countershaft and the rear axle, not to an axle bolt or the chain adjuster. On a machine with an adjustable axle, set the axle at the position it will actually run and measure there, because moving the axle changes the required chain length.
Related calculators
- Sprocket and Gear Ratio Calculator: ratio and speed for your sprocket combination
- Go-Kart Gearing Calculator: direct-drive kart chain gearing
Sources
Chain-length formula: standard two-sprocket center-distance chain formula from mechanical engineering references and chain manufacturers' engineering guides. Variables: C = center distance (in), P = chain pitch (in), N1 and N2 = tooth counts. The formula is implemented and tested in formulas.ChainLinks.
Chain pitch dimensions: per the ANSI-derived motorcycle chain numbering convention used in chain manufacturers' size charts. #415/#420/#428 use 1/2-inch (0.500-inch) pitch; #520/#525/#530 use 5/8-inch (0.625-inch) pitch. The first digit approximates pitch in eighths of an inch. Verify against the chain manufacturer's published specifications for your specific chain grade.