Emperor Gold vs Fire Opal

How close are they?

ΔE 27.6, loose: different enough that you should pick on purpose. Fire Opal is noticeably lighter, much more saturated than Emperor Gold.

Can I use Fire Opal instead of Emperor Gold?

Not as a straight swap; see the closer alternatives below. Loose match (ΔE 28). Fire Opal is noticeably lighter, much more saturated than Emperor Gold.

Can I use Emperor Gold instead of Fire Opal?

The same difference applies the other way round: Emperor Gold is noticeably 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.