Where the length formula comes from
A chain wraps two sprockets and spans the distance between them twice. The standard approximation, with everything in inches, is:
L = 2C + (F + R)/4 + 0.25
C is the chainstay length from bottom bracket centre to rear axle centre, F is the tooth count of the largest chainring and R the largest rear cog. The 2C is the two straight runs. The (F + R)/4 is the chain wrapped around the two sprockets: each tooth accounts for half an inch of chain, roughly half the teeth are engaged, and the result is expressed in inches, which is where the division by four comes from. The trailing quarter inch is a small correction for the fact that the two sprockets are different sizes, so the straight runs are not quite parallel.
Worked through: a 419 mm chainstay is 16.5 inches, and with a 50 tooth ring and a 28 tooth cog the result is 33 + 19.5 + 0.25, which is 52.75 inches. Chain pitch is half an inch, so that is 105.5 pitches, rounded up to 106 because a chain must have an even number of pitches to close. A rear derailleur then needs a couple more so its cage is not fully extended in the largest combination, which is where the 108 that most road bikes actually run comes from.
The exact geometric formula, with a term that accounts for the sprocket size difference properly rather than as a constant, gives 52.686 inches for the same case. The difference is a sixteenth of an inch, well inside the rounding, which is why the simple version has survived.
Links, pitches and the counting confusion
Almost every disagreement about chain length is a units disagreement. In the sense the chain industry uses on the box, a 116 link chain has 116 half-inch pitches and is 58 inches long. In the sense a mechanic uses when saying "take out two links", the same unit is meant. But a chain is physically built of alternating inner and outer plate pairs, and some people call one inner-plus-outer combination a link, which halves every number.
| Term | Length | Where you meet it |
|---|---|---|
| Pitch | 0.5 in | The engineering unit, pin centre to pin centre |
| Link, as chains are sold | 0.5 in | The number on the box: 114, 116, 126 |
| Full link or inner-outer pair | 1.0 in | Some tool instructions and older references |
| Twelve inch span | 24 pitches | The classic wear measurement |
This page uses pitches throughout and calls them links, matching the number printed on a chain box. If a source gives you a figure that is exactly half or double what you expect, this is why.
Measuring wear honestly
A chain does not stretch. The pins and the bushing surfaces wear, each joint gains a little play, and the accumulated play across many joints shows up as a longer chain. Measuring one joint is hopeless, so wear is measured across a span: put a steel rule on a pin centre with the chain on the large ring under light tension, and read where the rule lands twelve inches later. A new chain puts a pin centre exactly on the twelve inch mark. A worn one puts it past.
Over twenty-four pitches, a sixteenth of an inch of elongation is 0.52 percent and three thirty-seconds is 0.78 percent. Those are the two figures behind the numbers everyone quotes, which is a useful thing to know because it means a plain rule resolves the decision perfectly well without a dedicated tool. Do the measurement in two or three places along the chain and take the worst, since wear is rarely even.
Dedicated chain checkers are faster and mostly agree with a rule, with one caveat worth knowing: some designs measure across a span that includes roller clearance as well as pin wear, so they read high compared with a rule. If a tool and a rule disagree by a couple of tenths of a percent, that is usually why, and the rule is measuring the thing the threshold was defined against.
Why the thresholds differ, and why they are inputs here
The figure quoted for replacement is not a physical constant. It is the point at which the chain pitch has grown enough that it no longer sits properly in the cog teeth, and how much growth that takes depends on how wide the chain and cassette are. Narrower chains with more sprockets packed into the same space have less tolerance for the mismatch, which is the reason the commonly quoted figure for modern drivetrains is lower than the one quoted for older eight speed setups.
Beyond the point where a chain is worn, the cost stops being the chain. A worn chain drives the cassette teeth into a matching worn profile, and once that has happened a new chain skips under load on the cogs it used most. Replace the chain in time and it is an inexpensive consumable; leave it and it takes a cassette and eventually the chainrings with it. That asymmetry is the entire argument for measuring rather than waiting for a symptom, and it is why running two or three chains in rotation appeals to people who like arithmetic.
Because the correct threshold depends on the parts, this calculator makes it a selection rather than deciding for you. If the manufacturer of your chain or cassette publishes a figure, that figure wins over anything here.
What the formula cannot see
It does not know your rear derailleur, and derailleurs differ in how much chain their cage takes up and how much slack they can absorb. It does not know whether the bike has a suspension design where the effective chainstay length changes through the travel, which needs the length measured at the position that demands the most chain. It does not know about chain guides, idler pulleys or unusual routing, all of which add length that no tooth count predicts.
So use the number as the order quantity and the bike as the authority. Wrap the chain around the largest ring and largest cog with the rear derailleur bypassed, bring the ends to meet, add whatever allowance the derailleur asks for, and check the result shifts cleanly at both extremes before you consider it settled. The rest of the periodic drivetrain routine is covered in the bike maintenance guide; if you are changing gear ratios at the same time, work out the tooth counts first in the gear ratio calculator, since the largest cog is an input here and changing it changes the chain.
Questions people ask
How many links does a bike chain need?
It follows from the chainstay length and the two largest sprockets rather than from the type of bike, though the types cluster. A road bike with a 405 to 415 mm chainstay and a 50 tooth ring with a 28 tooth cassette typically lands on 106 to 108 links once the derailleur allowance is added. A mountain bike with a 435 mm chainstay, a 32 tooth ring and a 52 tooth cog usually lands near 116. Wide range single ring drivetrains and long chainstays push the number up, and small wheels with short stays pull it down. Chains are supplied at 114, 116 or 126 links precisely so there is something to remove.
How do I measure chain wear without a chain checker?
A steel rule is enough and arguably better. With the chain on the bike, on the large chainring, under light tension, align the end of the rule with the centre of one pin and look at the twelve inch mark. On a new chain a pin centre sits exactly on it. A sixteenth of an inch past is about 0.52 percent wear and three thirty-seconds past is about 0.78 percent, which brackets the two thresholds people quote. Measure in two or three places around the chain and take the worst reading, because wear concentrates on the links that spend most time on the cogs you use most.
What happens if I ride a chain past the threshold?
The chain pitch grows so that it no longer sits correctly in the cog teeth, and the load concentrates on fewer teeth than it should. Those teeth wear into a hooked profile that matches the elongated chain, at which point the cassette and the chain are a matched worn pair that works acceptably together and rejects any new chain, which skips under load. In practice that means the cost of ignoring the measurement is a cassette rather than a chain, and eventually the chainrings too. Wear is not linear in consequence: the first half a percent costs nothing and the following half costs a drivetrain.
Should the derailleur allowance be two links or four?
It depends on the derailleur and on how much slack the drivetrain has to absorb, and the manufacturer instruction for your rear derailleur is the authority. Two links is a common figure for a road drivetrain with a moderate cassette range. Four is more usual for a long cage derailleur, a very wide range cassette, or a full suspension frame where the chainstay length grows through the travel and the chain must be long enough for the worst case. The failure modes are asymmetric: a chain slightly too long shifts slightly worse in the smallest combination, while a chain too short can wreck a derailleur the first time it is shifted into the largest one.
Does chain length change when the chain wears?
It grows, which is the whole basis of the measurement, but not by enough to change how many links you fit. A one percent elongation on a 108 link chain is about half an inch across the whole chain, which the rear derailleur absorbs without difficulty. What matters is the pitch mismatch against the cog teeth rather than the total length. When you replace the chain you cut the new one to the same link count as the old one, assuming the old one was right, which is why counting the links you take off the old chain before you throw it away is a habit worth having.