Chainline is a position, deflection is an angle
Chainline is a single distance: how far the chain sits from the frame centreline when it leaves the chainring. The cassette has its own, measured to the middle of the block. When those two numbers match, the middle sprocket runs the chain dead straight and the deflection grows evenly toward both ends.
Each sprocket sits half a spacing further out than its neighbour, so its distance from the centreline is the cassette chainline plus or minus a multiple of the spacing. Subtract the ring position and you have the sideways offset for that gear, in millimetres. Divide by the chainstay length, take the arctangent, and you have the angle the chain is actually running at.
Working an example through: a cassette chainline of 43.5 mm with eleven sprockets at 3.95 mm spacing puts the smallest sprocket 19.75 mm outboard of the middle, at 63.25 mm from the centreline, and the largest 19.75 mm inboard at 23.75 mm. Against a single ring at 45 mm the offsets are 18.25 mm one way and 21.25 mm the other, and on a 415 mm chainstay those are 2.5 and 2.9 degrees.
The chainstay is the term nobody adjusts for
Every angle on this page has the chainstay length in the denominator. Move the same crank and cassette from a 405 mm chainstay to a 445 mm one and every offset is unchanged while every angle drops by roughly a tenth. That is a real difference in how hard the chain is working at the ends of the cassette, and it is invisible if you think of cross-chaining as a rule about gear combinations rather than as geometry.
It explains a pattern people notice without being able to name: touring and cargo frames, which have long rear ends for heel clearance and stability, tolerate wide cassettes and single rings comfortably. Short-stay road and criterium frames run the same parts at visibly worse angles. Neither drivetrain changed.
One ring or two
| Setup | Where the chain runs straight | Consequence |
|---|---|---|
| Single ring, centred on the cassette | Middle of the block | Deflection shared between both ends; nowhere worse than about half the cassette width |
| Single ring, offset outboard | Toward the small cogs | The climbing gears run at the worst angles, which is the wrong way round for a loaded bike |
| Two rings | Outer near the small cogs, inner near the large | Each ring covers half the cassette well, and the bad cells usually have a duplicate elsewhere |
The reason chainline is discussed far more in the single-ring era than it was before is straightforward: there is no second ring to escape to. On a double, the combinations with the worst angles are also the ones that duplicate a ratio available on the other ring, so avoiding them costs nothing. On a single ring every gear is the only way to get that ratio, and the position of the ring decides which gears pay for it.
What the angle actually costs
A deflected chain does not sit squarely on the teeth. Its side plates bear against the tooth flanks on entry and exit, so material is removed from the sides of the teeth and from the inside faces of the plates, and the chain articulates laterally with every link that engages. The results are faster wear on all three of chain, ring and sprocket, a rising level of noise as the surfaces roughen, and on a single ring with retention teeth a slightly greater chance of the chain letting go under a heavy shock.
What it is not, in ordinary use, is a failure mode. Riders run badly deflected gears constantly and the drivetrain wears out sooner rather than breaking. Where the angle should stop being acceptable is a judgement, and different drivetrain makers publish different guidance for their own systems, which is why the limit on this page is a field you fill in rather than a number supplied for you.
Measuring the inputs
Chainring chainline can be measured from the seat tube: take the distance from the flat face of the seat tube to the ring, and add half the seat tube diameter to get back to the centreline. Cassette chainline can be derived from the hub over-locknut dimension and the position of the cassette on the freehub, or measured the same way against the seat tube with the wheel in the frame.
Sprocket spacing is best measured across the whole cassette rather than one gap. Put a caliper across from the outboard face of the smallest sprocket to the inboard face of the largest, work out the centre-to-centre span, and divide by one less than the number of sprockets. A single gap measurement carries too much error into every position down the block.
Questions people ask
What is a cross-chain angle?
The angle the chain runs at when the chainring and the sprocket sit at different distances from the frame centreline. Take the difference between the two positions in millimetres, divide by the chainstay length, and take the arctangent. On a typical road setup the extremes land somewhere between three and four and a half degrees.
What angle is too much?
That is a judgement rather than a physical threshold, and drivetrain makers publish different guidance for their own systems, which is why the limit here is a field. What the geometry can tell you is exactly which gears sit either side of whatever line you draw, and how much moving the ring or changing frames would shift them.
Does the chainstay length really change the angle?
Yes, and it is the only term in the calculation that has nothing to do with the drivetrain. The offsets in millimetres are fixed by the parts; the angle is that offset divided by the chainstay length. Moving the same crank and cassette from a short road rear end to a long touring one drops every angle by around ten percent.
Why does chainline matter more on a 1x?
Because there is no alternative ring. On a double, a badly deflected combination almost always duplicates a ratio you can reach on the other ring at a far better angle, so avoiding it costs nothing. With one ring, every gear is the only way to get that ratio, and the ring position decides which end of the cassette carries the worst deflection.
How do I measure chainline at home?
Against the seat tube. Measure from its flat side to the chainring, then add half the seat tube diameter to bring the reading back to the frame centreline. Do the same with the wheel in the frame to find the cassette centre. For sprocket spacing, measure across the whole block and divide by one less than the number of sprockets rather than trusting a single gap.