Calcolatore Catena Moto

How to work out chain length when you change sprockets

Changing sprockets changes the chain length you need.
The correct calculation takes three steps: derive the real centre distance from the chain fitted today,
compute the ideal length with the new sprockets, and check that the commercial chain you pick leaves the
wheel in a usable position within the adjuster travel. The third step is the one almost everybody skips,
and it is the one that decides whether the bike is rideable.

The two formulas

Chain length in links, given centre distance C, pitch p and sprocket sizes
Z₁ (front) and Z₂ (rear):

L = 2C/p + (Z₁ + Z₂)/2 + (Z₂ − Z₁)² · p / (4π²C)

The inverse — deriving centre distance from a known chain length — comes from solving the same
relation for C as a quadratic:

2C² − [L − (Z₁ + Z₂)/2] · p · C + (Z₂ − Z₁)² · p² / (4π²) = 0

Pitch p is 12.70 mm for 415, 420 and 428 chains; 15.875 mm for 520, 525, 530 and 532;
19.05 mm for 630.

Why the ideal length is not the answer

The ideal length is almost always a non-integer — and chains only exist with an even
number of links, because an odd count would need a special master link. You are therefore forced to
choose between the even number below and the one above, and the two are not equivalent: they put the
wheel at two different points of the adjuster travel.

The two thresholds that make a fitment usable

A chain is only fit to install if, once mounted, two distinct margins remain:

• Slack room — at least 8 mm of forward travel. This is what you need to set correct
  chain free play. Without it the chain stays taut, and a taut chain loads the countershaft bearing and
  the swingarm in extension.
• Wear reserve — at least 8 mm of rearward travel. A chain stretches with use.
  Without reserve, after a few thousand kilometres it can no longer be re-tensioned and has to be
  replaced while still otherwise sound.

These are the two thresholds this tool applies. A fitment that matches the geometric ideal but leaves
the wheel one millimetre from the end of its travel is geometrically right and
mechanically useless.

Worked examples

Every row is computed with the formulas above and the stated thresholds. Stock sprocket sizes and
chain lengths come from PBR fitment data, and every proposed sprocket size stays within the fitment
range for that bike: you will not find advice here that the chassis cannot take. Still check your own
figures, as they change between model years — the MT-10 goes from a 43-tooth to a 42-tooth rear sprocket
with the 2022 restyling, and on the CB500F the 14-tooth front is listed up to 2018 but not after.

Frequently asked questions

If I only change the front sprocket, do I need a new chain?

Not necessarily. One tooth more or less at the front moves the wheel by a few millimetres, and the
adjuster often absorbs the difference. What must be checked is that both the slack room and the wear
reserve survive the move — which is exactly what this calculator does.

Why do chains always have an even number of links?

Because a chain closes by joining an inner and an outer link. An odd count needs a special master
link, which is a weak point, so it is avoided.

Front or rear sprocket — which should I change?

One tooth at the front changes the ratio far more than one tooth at the rear, because the front
sprocket has far fewer teeth. Use the rear for fine adjustment and the front for decisive changes.
A very small front sprocket, however, wraps the chain through a tighter angle and shortens the life of
both chain and sprocket.

Can I buy a longer chain and shorten it?

Yes, and it is often the right call: buy the longer length and remove the excess links with a chain
breaker after checking the wheel position with the chain fitted. The opposite — lengthening a short
chain — is not possible.

Does changing sprockets throw off the speedometer?

It depends where the bike reads speed. If the sensor is on the wheel, the reading is unaffected.
If it reads from the gearbox output shaft, the value is off in proportion to the ratio change.

Calculation method and thresholds by PBR Sprockets, Italian
manufacturer of motorcycle final drive components, published on Roadtrips.it.