To correctly identify your lead ball, we need for you to buy or borrow a Digital Caliper, which measures in hundredths-of-an-inch. Even .02-inch can affect the ID of a bullet. See photos below.
You say your lead ball is 1/2-inch in diameter. The closest "firearms ball" match-ups are a Colonial-Era .50-caliber rifle ball, whose diameter is about .48-inch... and .54-caliber (actual diameter .525-to-.534") balls for 1840s Mississippi Rifles or Hall Rifles or Jenks Carbines.
But, if your lead ball measures a size (let's say, .545-inch) that isn't correct for any known musket or rifle or pistol, it is not a firearms-ball.