Chain Length Calculator

Derailleur | Fixed Wheel | Assumptions | Download

Derailleur Mode

When calculating chain length for a derailleur gears bike the program calculates the shortest possible length of chain that will (theoretically at least) go around the two cogs, then adds a 'derailleur allowance' (usually the length of a single link) to allow for the extra chain to go around the derailleurs jockey wheels. This is unrounded result shown below (55.17784 inches or 1401.57mm).

In practice you can't have fractions of a link - it simply ain't possible! So the program rounds up or down to the nearest whole link (same as nearest inch for 1/2inch pitch bicycle chains). I.e. 55 links, 55 inch or 1397 mm above. In the unlikely event of the unrounded result being exactly mid way (to about 12 places of decimal of an inch!) it rounds upwards. If you can't adjust the chainstay length because your bike has vertical dropouts then uncheck the 'Adjustable chainstay length' check box and the program will always round upwards to the nearest whole link value. See Also: Rounding Of Values, Bicycle Frame Droupouts

If ChainLengthCalc has rounded its result down by close to 1/2" and/or your rear gear change mechanism has unusually large jockey wheels (usually these have 10 teeth), or you simply don't trust me and perhaps your bike has vertical dropouts: Play safe by purchasing a chain that is a link longer than suggested and send me the details (particularly if you do not have to remove the extra link). Alternatively you can calculate an accurate derailleur allownce by clicking on the 'Links' button or selecting Derailleur Allowances from he Tools menu.

After fitting your chain with the correct length for your largest/largest gear cogs, its worth performing an additional check. Shift the chain across so it now runs on your smallest front and smallest rear gear cogs. The chain tensioning arm of your derailleur should be not quite all the way back. I.e. it should have enough movement that it can still keep the chain in tension even when the transmission starts to get a bit worn. (See also: Derailleur Limits, Derailleur Allowances, Fractions To Decimal).

Fixed Wheel Mode

In 'fixed wheel' mode the program gives some extra information to enable the correct tension to be achieved without the need for a chain tensioner

'Desired slop' is the amount you should be able to flex the the lower part of chain up and down to achieve the correct amount of tension. Somewhere around 20mm or 3/4 inch (at the tightest point as the wheel is rotated) is about right for a correctly tensioned bike chain.

In the diagram above: The straight line A-B represents the line of a tightly stretched chain. M (not shown due to insufficient space) is the point that is midway between A and B, and also midway between C and D. C is the lowest point that the chain can be pushed down to with a finger, D is the highest point. If the chain is correctly tensioned then the distance from D to C will be about 0.75 inch or about 20mm.

Too tight will cause excessive wear in the chain and cogs. Too loose causes a kind of clunk when you start pedalling and take up the slack. A lot too loose and the chain is in danger of jumping off the cogs when you ride over a bump in the road.

Correct adjustment to give the desired amount of slop is achieved by moving the rear wheel forwards or backwards as appropriate. Effectively changing the chain stay length. Although you can get away with using a fixed wheel on a bike frame that has horizontal dropouts, track dropouts are preferred (particularly with flip flop hubs) because they permit a greater amount of adjustment. Vertical dropouts are not recommended because they don't permit any horizontal adjustment at all.

Notice also that the program can quote negative as well as positive slop values. Although a negative value is impossible in practice - mathematically its not a problem. A negative value (as shown) simply means that the chain will not be long enough to go around the cogs without re-positioning the wheel to give a slightly shorter chainstay length. This is because a minimum length of 54.177 inch has been rounded down to 54 inches (links).

In the above screenshot: New Chainstay Length (17.156 inch) is the length required to produce the desired tension (i.e. 0.75 inch of slop). Difference is the amount the chanstay length must change to give the correct tension in a 54 inch bicycle chain. Accuracy is the number of decimal places of an inch of accuracy to calculate the new chainstay length to. 3 places of accuracy is nearest thousandth of an inch 0.001, 12 places of accuracy is nearest 0.000000000001 inch! Arguably nearest thou is spurious precision because nearest 1mm is about as close as I can get measuring with a tape measure. However, very small changes to the chainstay length result in relatively large changes to the chain slop/slack measurement. The extra precision ensures you can get back to 0.7500 rather than 0.7450 ;-)
See Also: Rounding Of Values, Flip flop hubs, Bicycle Frame Dropouts, Fractions To Decimal

Assumptions and Rules Of Thumb

1. You are using a brand new chain and sprockets that were manufactured with a high degree of precision. (Worn chain and sprockets require a longer chainstay length. This is not noticeable with derailleur geared bicycles because the chain tensioner part of the rear gear change mechanism automatically takes up the extra slack)
2. Bicycle chain is always 1/2" pitch, so 1 link = 1 inch.
3. Rounding a bicycle chain up or down by 1/2" requires a maximum of adjustment of 1/4" of chainstay length to produce the correct tension in an un-tensioned chain. I.e. exactly 1/4" where the gear cogs are of the same size, a bit less when they are different sizes.
4. 1" is usually slightly more than the minimum amount of extra chain required to wrap around 2 gear cogs when a derailleur is used.