Depends on caliber or diameter and whether it is a solid shot or a shell which is hollow and potentially filled with powder. People can still be killed by shells as the black powder can still be explosive for hundreds of years.
Cannon were designated both with reference to the caliber and the weight of the solid shot they fired and since rifles pieces fired elongated shot these references soon became very confusing.
A common field piece early in the war was called a six pounder, which are references to the approximate weight of the solid shot they fired. A spherical case shell for this cannon weighed less and contained black powder, a fuse hole, and some musket balls for added shrapnel. The diameter of a six pounder's bore was 3.58 inches.
Are you trying to determine if the projectile you have is from the war era? The same artillery pieces that were used in the 1860's stayed in use for many decades afterward.
Unless the projectiles you have were found in a known WBTS battle site there may not be a way to authenticate them as being from that period.