Generally these numbers are roughly the bullet diameter either in metric or in hundreths of an inch. But they are nominal numbers, which are not always the actual dimension.
In NATO metric designation the numbers are *nominal* *bullet diameter x case length.* So 9×19 is a 9mm thick round stuck in a 19mm long case, 5.56×45 is a 5.56 milimeter thick round stuck in a 45mm long case. American round tend to be named by the bullet diameter in hundreths of an inch, so .40 is not 40mm as some journalists seem to think, it’s 0.40 inch which is roughly 10mm. Older black powder rounds tend to have a dash in their designation, like 45-70. In that case the first number is caliber in hundreths of an inch and the second number is how much black powder in grains the cartridge holds
The problem is that the number is very rarely exact because there is no universally accepted naming convention and different ways to measure plus marketing considerations come into play. So is the number you are looking at the diameter of the unfired bullet? Is it actually the caliber (barrels have lands and grooves in them, caliber is the barrel diameter measured land to land). Is it the barrel diameter groove to groove? Is it an arbitrary number selected to make the round stand out? For example 38 Special is the same diamter as 357 Magnum. You can even fire 38 Special out of 357 magnum revolvers. 44 magnum is actually .43 inch in diameter. 300 Winchester Magnum is the same diameter as 308 Winchester. 9mm Luger and 9mm Browning which is also called 380 ACP are also the same diameter, but it’s not 0.380 inch, it’s 0.355 inch and to make it even worse, 9mm Makarov is not actually 9mm, it’s 9.27mm.
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