ΔE 18.7, loose: different enough that you should pick on purpose. Carmine Red is a little darker, warmer than Purple.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 19). Carmine Red is a little darker, warmer than Purple.
The same difference applies the other way round: Purple is a little lighter, cooler.
ΔE is the colour difference between our two swatch estimates: under about 6 is close, over about 15 is loose. Real paints also differ in finish, coverage and how they thin, so test before you commit.
See Purple on the colour wheel See Carmine Red on the colour wheel
All matches: Purple equivalents · Carmine Red equivalents