[Jack]

Spencers were made originally in 56-52. The Civil War carbines and rifles were 56-52. After the war,some were produced and used out west in 56-50.
Some Civil War carbines were relined to 56-50 from 56-52.
Clear as mud so far, right?
Ok, the '56' does NOT stand for grains of powder.
Remember that when Christian Spencer designed his rifle, cartridges themselves were just being invented, and there was no 'standard' or 'normal' way to designate cartridges.
The 56 is the outside body diameter of the cartridge case.
To further complicate your life, Spencers are notorious for widely varying barrel diameters. Machining in 1862 was far more primitive than today, there was great pressure to produce them rapidly, and they were at the very forward edge of the technology of the time.
I'd bet that the actual diameter of your barrel is at least .515, if it's a 56-50. If it's a 56-52, larger.
One possible way to tell what you have: the original 56-52 was a 6 groove barrel. The ones relined at the arsenals to 56-50 use a 3 groove barrel.
The 56-52 and 56-50 rimfire cartridges (yes, the originals were rimfire) are long since obsolete and unavailable.
I believe someone makes a conversion breechblock you can put in a Spencer so that it will fire centerfire ammo, and then you could reload for it and shoot it, if it's in good enough condition. Probably some of the Civil War reenactors could tell you more about that than I could.