Why 9mm won
For a century the argument about service pistol cartridges was settled and reopened roughly every twenty years. It is settled now, and the reasons have almost nothing to do with the thing people argue about.
The 9×19mm Parabellum was designed in 1902 because a toggle-locked pistol needed a slightly larger case than the 7.65mm bottleneck round it had been built around. That is the whole of its origin: it exists to make the Luger work. It is now the service cartridge of essentially every army and police force outside the former Soviet sphere, and the dominant handgun round on the commercial market as well.
Nothing about its ballistics explains that. Take the three cartridges it has spent a century displacing and put them side by side.
The .45 ACP throws a 15 g bullet at about 250 m/s. The .40 S&W throws 11.7 g at about 300. The 9×19mm throws 7.45 g at about 360. On muzzle energy the three land within a few per cent of each other, which is the first thing worth noticing, because most of the argument is conducted as though they do not. What differs is how each cartridge arrives at that number, and what the arrival costs.
The case that fits
The 9×19mm case is 19.15 mm long and 9.93 mm across the base. The .45 ACP’s is 22.81 mm long and 12.09 mm across. That difference sounds trivial and is not: a magazine well sized for the smaller case holds more columns of ammunition in the same width of grip, and a grip has to fit a hand.
The consequence shows up on every entry in this catalogue. A CZ 75 holds sixteen rounds in a frame a person with average hands can shoot well. A Glock 17 holds seventeen. An M1911 in .45 ACP holds seven, and the double-stack .45s that came later are noticeably fatter through the grip. That is not a marginal preference; for an institution issuing one pistol to thousands of people of different sizes, it is close to decisive.
The pressure that lets a submachine gun be simple
Look at where the 9×19mm shows up outside pistols. The MP 40, the Uzi, the Sterling, the MP5, the TEC-9: a stamped-steel weapon with no locking mechanism, made in millions, in four countries, over eighty years.
It works because 235 MPa is about the ceiling at which a bolt of sensible weight can hold a breech shut on its own. Below that you can build a submachine gun out of tube and pressings; above it you need a delayed or locked breech and the cost goes up several times. The .45 ACP at 130 MPa is milder still, but its case is bigger and its bullet heavier, so the bolt has to be heavier anyway and the weapon ends up larger for the same capacity, which is why the Thompson weighs nearly five kilograms and the MAC-10 that replaced it in the same chambering had to be made almost unusably light to compete.
The FBI detour
The one serious modern attempt to move away from the 9mm is worth following because of how it ended.
After a 1986 shootout in Miami the FBI concluded its 9mm loads were inadequate and adopted the 10mm Auto. Agents found the full-power round more than most of them could shoot quickly and accurately, so the Bureau began issuing a reduced load. Smith & Wesson and Winchester then observed the obvious: if nobody is using the full-power version, the case does not need to be that long. The .40 S&W is a 10mm Auto shortened to fit a 9mm-sized frame, and for two decades it was the default American police cartridge.
It has since lost most of that ground back. The argument that carried it (that a bigger bullet does more) was answered by expanding-bullet design improving on both sides of the comparison at once, and the .40’s 225 MPa in a small case wears pistols out faster than 9mm does in the same design. The FBI moved back to 9mm in 2015 and most large American departments followed.
What actually decided it
Three things, none of them about the projectile.
Capacity, because a duty pistol is a compromise between rounds carried and hands that can hold it. Cost, because an institution that trains properly fires hundreds of practice rounds for every duty round and 9mm is the cheapest centre-fire pistol ammunition made. And recoil, because the difference between a cartridge a shooter can put five rounds into a target with and one they can put three into is not made up by anything the bullet does on arrival.
This site does not publish a stopping-power figure, and the reason is visible in the shape of this argument: the metric everyone wants would have to compress an unresolved question about physiology into a single number, and every attempt to do so has been withdrawn by its own author or discredited by someone else’s data. What we publish instead is muzzle energy, momentum and retained velocity, computed from a mass and a velocity that each name the source they came from and the barrel length that produced them. Those are facts. What they mean is a different argument, and it is not one a specification table can settle.