How to use the motorcycle chain length and sprocket calculator
- Choose the chain size: 420 and 428 chains have a 12.7 mm pitch, 520, 525 and 530 have 15.875 mm and 630 has 19.05 mm.
- Enter the number of teeth on the front and rear sprockets and the distance between the axles in millimeters.
- Optionally enter another sprocket pair in the advanced options to compare final drive ratios.
- Read the chain links to buy, the center distance that fits that number of links and the final drive ratio.
Formula
links = 2C / p + (N + n) / 2 + ((N - n) / (2 pi))^2 x p / C
links to buy = the next even whole number
final drive ratio = N / n
C is the center distance and p the chain pitch in the same unit, N the rear teeth and n the front teeth. The center distance for a given even number of links L comes from solving the same formula: C = p / 8 x ((2L - N - n) + sqrt((2L - N - n)^2 - 8 / pi^2 x (N - n)^2)).
A 520 chain with 15 and 45 teeth
With a 15.875 mm pitch, 15 front teeth, 45 rear teeth and a center distance of 455 mm, the formula gives 57.32 + 30 + 0.80 = 88.12 links. The chain is bought in pairs of links, so 90 links.
A 90 link chain fits a center distance of 470.1 mm, so the axle must move about 15.1 mm back to take up the extra length; an 88 link chain fits 454.0 mm. The final drive ratio is 45 / 15 = 3.000. Changing to 16 and 44 teeth gives 2.750, 8.33% lower, which raises road speed at the same engine speed by about 9.09%.
How the formula was checked
The formula is a standard approximation that treats the chain as wrapped around the sprocket pitch circles. The tests compare it with the exact length of the chain wrapped around two circles with straight tangent runs, and the two agree within half a link across 80 setups. In practice a chain is rarely used at its exact length, since it stretches and the swingarm has a range of adjustment.
To see the effect of a gearing change on engine speed, use the Gear Ratio Calculator. A new sprocket pair also changes what the speedometer shows, which the Speedometer Error Calculator can work out. For power, see the Horsepower from Torque Calculator.
Before you cut or buy a chain
Check that the sprockets and the chain are the same size and type, that your swingarm adjusters can reach the center distance, and what the maker recommends for the slack to leave. Measure the center distance with the wheel in the middle of its range. When in doubt, a shop or the maker's guide has the final word.
Assumptions and limits
- Sprockets are on a straight line with the axles at the center distance given.
- Chain pitches are 12.7 mm for 420 and 428, 15.875 mm for 520, 525 and 530, and 19.05 mm for 630.
- Teeth counts are whole numbers from 6 upward, and the rear sprocket has at least as many teeth as the front.
- The links are an even number, as for a chain without an offset link.
- The formula ignores chain stretch, slack and the sag of the lower run.
Frequently asked questions
Why is the number of links always even?
A chain made of inner and outer links in pairs joins into a loop only with an even count. An odd count needs a special offset link.
What does a higher final drive ratio do?
It gives stronger acceleration and a lower top speed at the same engine speed, since the engine turns more times for each turn of the rear wheel.
Why does the page show a center distance that fits?
Rounding the links up makes the chain longer than your measurement, and that distance is where the rear axle would sit with the longer chain pulled tight.
Is 520 the same pitch as 530?
Yes, 15.875 mm. The last digit refers to the width between the inner plates, which affects which sprockets fit.