The approximate 9/16" diameter indicates that it is a civil war era US Sharps "New Model" bullet whose nose got re-shaped by being hammered down by very hard strokes from a rifle ramrod (which bullet collectors call hard-ramming). Your bullet's nose got compressed into the shape of the ramrod's inverse-cone "mouth." The ramrod mouth's lip is what makes the flat area encircling the cone. Here are photos of three other bullets that got hard-rammed.
Yes, I know that a Sharps Rifle (or Carbine) did not have a ramrod. I would guess that a soldier was monkeying around with that Sharps bullet, or ran out of ammo for his rifle and had to use that bullet. Who knows? All I can say is that the shape-change on your Sharps bullet's nose is very distinctively recognizable as being made by a ramrod's conical mouth.
