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Why did the AR-15 use a smaller 5.56-millimetre cartridge?

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Semiautomatic pistol — small arm Glock .40-calibre semiautomatic pistol.

The AR-15 was designed to use the smaller 5.56-millimetre (.223-calibre) cartridge primarily to create a more portable, lightweight weapon with manageable recoil.12

Following the Korean War, U.S. military researchers were dissatisfied with the performance of existing high-powered rifle ammunition, which produced extreme recoil that made automatic fire difficult to control. In contrast, the 5.56-mm cartridge propelled a lighter projectile at a significantly higher muzzle velocity of 3,000 feet (910 metres) per second. By chambering the AR-15 for this smaller, high-velocity round, designer Eugene Stoner was able to develop a weapon that was not only lighter and more portable than the 7.62-mm rifles of the era but also capable of producing manageable recoil during automatic fire while remaining lethal at ranges of 300 yards (270 metres) and beyond.21