ΔE 20.3, loose: different enough that you should pick on purpose. Royal Purple is a little lighter, much more saturated than Paynes Gray.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 20). Royal Purple is a little lighter, much more saturated than Paynes Gray.
The same difference applies the other way round: Paynes Gray is a little darker, much more muted.
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 Paynes Gray on the colour wheel See Royal Purple on the colour wheel
All matches: Paynes Gray equivalents · Royal Purple equivalents