An average shoe size for a 2-year-old is a U.S. children's size 8. This is equivalent to a Euro size 24 or a U.K. size 7. This shoe size fits a foot that is 5.75 inches long.
To get an estimate of a child's shoe size, measure their feet with a ruler. A 5.5-inch foot is a children's size 7; a 5.63-inch foot is a size 7.5; a 5.75-inch foot is an 8; a 6-inch foot is an 8.5; a 6.13-inch foot is a 9.
For a more accurate measurement, visit a shoe store equipped with devices to measure foot length and width. Keep in mind that different brands of shoes sometimes use slightly different sizing. For this reason, it is best to have a child physically try on shoes before buying them, even after being measured.