ΔE 13.8, fair: the same colour family, but not a straight swap. Royal Blue is noticeably darker, more muted, cooler than Purple Rain.
Only where an exact match doesn’t matter, such as a new unit or a highlight. Fair match (ΔE 14). Royal Blue is noticeably darker, more muted, cooler than Purple Rain.
The same difference applies the other way round: Purple Rain is noticeably lighter, more saturated, warmer.
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 Rain on the colour wheel See Royal Blue on the colour wheel
All matches: Purple Rain equivalents · Royal Blue equivalents