I bought a replacement chain for my BMX – obviously a 1/8” chain. I cut it down to the same number of links as the chain I was replacing. However, when I installed it, it was so long that to get any chain tension I had to have the axle right at the end of the dropout, almost falling out of the dropout. If I remove one link, then the chain is so short that the axle has to be right the way forward in the dropout, and it’s almost impossible to get the chain on the chainring & sprocket. With the old chain, the axle was in the centre of the dropout.

While the obvious solution to this is to get a half link chain, that’s not what I’m interested in – what I want to know is how two almost identical chains can give such a huge discrepancy. Any ideas?

old one is worn out

Yes, I know that, but the old one wasn't worn out when I first bought it.

Chains stretch as they wear, so for a chain with the same number of links, the old one should be longer.

Can you compare the bushings in both chains and see if one is somehow different from the other? Looser, thinner, perhaps? This is a pretty dubious theory though, that would seriously screw up a drivetrain.

Do both chains mesh properly with the teeth? Perhaps the chainring is worn such that the old chain does not sit correctly within the teeth? This would take up more chain. Old chain with newer chainring?

Since the number of links is the same, and I assume the length being pretty close to the same even with wear, it must be the way the chain sits on the chainring and cog, somehow reducing the effective diameter of the circle.

They both seem to sit on the teeth perfectly!

It's confusing the hell out of me.

Something doesn't add up.
Is it possible your old chain has a half link built in and your new one doesn't?
Did you maybe switch sprockets, say by mounting a double sided wheel reversed?
Did you count a half link and master link on one, and a non-half link chain w/o master link on the other?

BTW- typical stretch of a worn chain would equal be about 1/2" over it's length or about a half link difference.

Lay the chains flat next to each other and do a detailed comparison, link by link and see where the difference is.

Regardless of stretch, wear, or any other mystical forces, identical length chains, looped over the same sprockets will locate the rear axle in the same place, so something else is different and you're somehow missing it.

Yep, basic diagnostic logic will win.