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While there is general agreement about the angle, there is no such agreement about the actual width cut off. There are two main standards in current use:
ISO models include:
J.I.S. spindles are shorter and blunter, they don't taper down to quite as small a square. J.I.S. models include:
Confersely, if you install a J.I.S. crank on an ISO spindle, it will wind up about 4.5 mm farther in than it would on a J.I.S spindle of the same length.
Theoretically, ISO cranks should only be used on ISO spindles, and J.I.S. cranks only on J.I.S. spindles.
In practice, you can very often get away with mixing these sizes, as long as you select a spindle length that gives the desired chainline.
Taper matching was fairly important back in the day of loose-ball cup-and-cone bottom brackets, because these required regular maintenance/overhauls, and this required removal of the cranks. Every time you remove and re-install a square taper crank, the hole in the crank is liable to get very slightly larger.
This was particularly an issue when using J.I.S. cranks on ISO spindles, because over time, as the crank went on farther and farther, you could run out of taper, and the square end of the spindle would become flush with the surface the crank fixing bolt/washer pushed against. At that point, further tightening of the bolt won't make the crank any tighter, since the bolt is bumping onto the end of the spindle.
These days, however, most folks are using sealed cartridge bearing bottom brackets. With these, there is no routine maintenance required, so typically the crank will be installed once, and will stay in place unless/until the bottom bracket needs to be replaced. This greatly reduces problems of wear to the interface.
I generally avoid mixing sizes on customers' bikes, but I have a lot of experience mixing ISO/J.I.S. in both directions on my own personal bikes, and it as never given me a lick of trouble.
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