Your particular example seems rather large if the size of a penny, many the balls I find are around a cm to half cm in width for pistols, and the larger again from smooth bore muzzleloaders. They can be identified firstly by having no holes for fishing line, or a split, and they tend to have a ridge around the circumference from the mould, and a clipped sprue on one or both sides (tabs joining the balls together in the mould which are cut off after casting). Sometimes the sprue is clipped off too close to the ball, leaving a flat edge one or both sides.
Here's a few that I regularly come across, both smooth bore pistol/musket balls, and later rifle projectiles. Many of them come out of the ground as mangled lead, whilst most these balls would have been dropped back in the day. Muzzleloader balls generally range in size from 13 - 19mm (0.50 to 0.75), and smaller again for pistol balls.
The site where these were found dates back to the 1840/50's.
Here are some weights and sizes of smooth bore projectiles.
Lead Round Ball Bullet, Weights:
0.350" Diameter Lead Round Ball Weight = 64 Grains.
0.375" Diameter Lead Round Ball Weight = 79 Grains.
0.433" Diameter Lead Round Ball Weight = 122 Grains.
0.440" Diameter Lead Round Ball Weight = 128 Grains.
0.445" Diameter Lead Round Ball Weight = 132 Grains.
0.451" Diameter Lead Round Ball Weight = 138 Grains.
0.454" Diameter Lead Round Ball Weight = 141 Grains.
0.457" Diameter Lead Round Ball Weight = 143 Grains.
0.490" Diameter Lead Round Ball Weight = 177 Grains.
0.495" Diameter Lead Round Ball Weight = 182 Grains.
0.530" Diameter Lead Round Ball Weight = 224 Grains.
0.535" Diameter Lead Round Ball Weight = 230 Grains.
0.570" Diameter Lead Round Ball Weight = 278 Grains.