There’s a story behind every round.
.30 Caliber rifle rounds were standard for many years. In metric, that’s 7.62mm. Quite simply, it’s a standard sized round that’s converted to a different unit.
5.56x45mm NATO was created to meet the CONARC parameters. They built a round to meet parameters and it just so happened to come out that size.
Remington was making the .222, Springfield made the .224 based on their design. Remington’s .222 underperformed, so they made a “.222 special” with a bigger case. It’s common in the ammunition world to give hotter loads a bigger number, so they re-named it a .223 (despite it actually being a .224 projectile). Converting the .223cal to metric, we get 5.56mm.
There’s plenty of “round number” bullet sizes, 9mm is one of the most popular in the world for instance. .30 cal, .40 cal, .50 cal, 10mm, and 13mm are pretty common as well.
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