ΔE 25.0, loose: different enough that you should pick on purpose. Royal Purple is a little darker, more muted, warmer than Cerulean Blue Deep.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 25). Royal Purple is a little darker, more muted, warmer than Cerulean Blue Deep.
The same difference applies the other way round: Cerulean Blue Deep is a little lighter, more saturated, 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 Cerulean Blue Deep on the colour wheel See Royal Purple on the colour wheel
All matches: Cerulean Blue Deep equivalents · Royal Purple equivalents