How big was a military unit during the civil war?

Because the Confederacy was limited in their manpower, artillery, ammunition, and resources in general (even their prized CSA Virginia was actually the captured USS Merrimac) they had a smaller number to their US counterparts, such as 6 guns to a US Battery...which stayed that way up to the Vietnam War. While the Southern Army had a 4 gun battery (and most of the Confederate guns were captured US field pieces).

Therefore, discounting the CSA (Confederate States of America), since the US Artillery stayed the same up thru the Vietnam War (almost exactly a hundred years later), US units in the US Civil War most likely ran along the same lines as they did in Vietnam: US Infantry platoon 40 plus men; US Infantry company about 200 men; battalion 600 plus men; two or more battalions=brigade; two or more brigades=division. A regiment=brigade in size. A squadron=battalion.

Australian & ARVN armored cav units were different in Vietnam: An Australian/ARVN regiment=US battalion; and their Squadron=US Company.