I have heard that the .380 is the minimum for self defense. That is what I use for my carry pistol, using corbon HP bullets that boost the speed up to 1100fps. I also have a .25 auto. I have a very informal ballistics test that I have used. I get shipping drums from work to use as burn barrels for trash. Here are the results. A .22lr will penetrate the barrel, and sometimes exit the back side, always leaving a big dent if it doesn't pass thru. A .22 mag in a Davis derringer will penetrate both sides of the barrel, and also penetrate the barrel behind it. A .25 auto will only dent the entrance hole, and not pass thru. A .38 special in a Davis Derringer will put a large dent in the barrel, usually leaving a crack, but, no complete penetration. The .380 hp Corbon ammo will penetrate both sides of the barrel and put a large dent in the barrel behind it. The .45 auto will penetrate three drums. The .44 mag.........I don't have enough drums.
I realize that this data doesn't have any scientific background, but for an ol' country boy, it tells me how much power those rounds have, relative to each other.