Measurements will not help date the round ball very much, they have been used for so long and even made today in many calibers that were used 200 years ago. In general there is no accurate way to date round balls. The white oxide can and will build up at different rates depending on lead and soil composition. Folks were regularly using muzzle loaders in some areas up into the early 1900s and of course the rebirth of muzzle loading hunting that got going fifty years or so back. Musket ball implies military use, round ball is a more encompassing description for an item of which many many more were fired in hunting or target practice than were ever fired from military muskets in our country.
^^ I still hunt and shoot with a smoothbore flintlock that takes a 0.648" round lead ball. After five years in the ground they look just like that (I know, because I collect them in my dirt practice backstop and recast them to reuse).
From my experience, the more white the buildup the older. Also chew marks can indicate it’s been around a while. Of course the location helps as well. And then my favorite detail is whether or not they have the mark from removing the sprue after casting. I have many small round balls with a cut mark from the sprue.
Chances are it's very old, but getting an accurate date is almost impossible.
Round balls were used over so many years.
The best way to get an educated guess is by dating relics found in the general area of the round ball.
Round balls are a great find and shows that there is the possibilaty of some good age to the area you are hunting.
Great find... Congrats