Chain length for a 415 mm chainstay with a 50t ring and 18t sprocket

Chain length

102links

50.7″ for a 415 mm chainstay with a 50t ring and a 18t sprocket

Links (round up to even)	102links
Length1,287 mm	50.7in
FormulaPark Tool / Shimano method	2 × 16.34 + 50/4 + 18/4 + 1
Chainstay16.34″ — bottom bracket centre to rear axle	415mm
Absolute minimumbig ring to big sprocket, with no slack left at all	100links
From a 116-link chainlinks to take out of a new chain	remove 14
Total teeth50t ring + 18t sprocket	68

Notes

Round up to an even number, always. A link is one inner plate plus one outer plate; there is no such thing as an odd link on a derailleur chain. 101.4 rounds to 102.
Too long beats too short, and it is not close. A chain that cannot reach big ring to big sprocket will tear the derailleur into the wheel and take the hanger — sometimes the frame — with it. A chain a couple of links too long just hangs slightly slack in the small–small combination you should not be using anyway.
Measure the chainstay to the axle centre, not to the dropout face. On a bike with sliding dropouts or an eccentric bottom bracket, measure it in the position you actually ride.
This formula gives a slightly longer chain than wrapping it around the big ring and big sprocket and adding two links. That is deliberate: the wrap method has no allowance for the derailleur cage taking up slack, and it comes out short on long-cage rear derailleurs.
A new chain on a worn cassette will skip under load. If you are replacing a chain that has been on the bike a long time, check cassette wear at the same time — a chain checker under 0.75% means you probably got away with it.

The formula

L = 2C + (F/4) + (R/4) + 1

with C the chainstay in inches, F the largest chainring and R the largest sprocket. For a 415 mm (16.34″) chainstay with a 50t ring and 18t sprocket that gives 50.7″ — 102 links.

Round up, and round to even

A link is one inner plate plus one outer plate. There is no such thing as an odd link on a derailleur chain, so the answer always lands on an even number. From a new 116-link chain, take out 14 links.

Too long beats too short, and it is not close

The absolute floor here is 100 links — big ring to big sprocket with no slack whatsoever. A chain that cannot reach that combination will pull the derailleur into the wheel and take the hanger, sometimes the frame, with it.

A chain a couple of links longer than ideal just hangs slightly slack in the small–small combination you should not be riding anyway.

Measure to the axle centre

Not to the dropout face. On a bike with sliding dropouts or an eccentric bottom bracket, measure in the position you actually ride.

Why this comes out longer than wrapping

Wrapping the chain around the big ring and big sprocket and adding two links has no allowance for the derailleur cage taking up slack, and it comes out short on long-cage rear derailleurs. That is the failure mode this formula is built to avoid.

Nearby sizes

Sizing a Chain — Big-Big Plus Two, and When That Rule FailsA chain two links too long shifts badly and slaps. Two links too short destroys a derailleur the first time someone cross-chains by accident.
Disc Pads and Rotors — The Numbers That Say ReplaceA pad worn to the backing plate gouges the rotor in one descent, and a rotor is several times the price of a set of pads.
Hub Bearings — Play, Drag, and the Difference Between ThemTwo seconds with the wheel in the frame tells you whether a hub needs attention. Most people never do it, and hubs fail quietly.
Gear Inches and Development — Two Ways to Compare Any Two BikesA 34/28 on one bike and a 30/25 on another are almost the same gear. Ratios alone will not tell you that; gear inches will.