How does regina derive from rex?
Related question: "Are there feminine and neuter versions of 'professor'"?
How does regina derive from rex?
Related question: "Are there feminine and neuter versions of 'professor'"?
The root of rēx is rēg- (compare the genitive rēgis), which explains the first part. But where does that -īna come from?
One theory is that it comes from a Proto-Indo-European *h₃rēǵ-nih₂ "queen", also seen in Sanskrit rājñī, Gaulish rigani, Welsh rhiain, and so on. If this theory is right, Proto-Italic metathesized *rēgnīā into *rēgīnā, and regularized it into a normal a-stem. Sihler supports this one.
Another theory is that it's the same -īn- suffix that makes adjectives, with rēg-īn-a originally meaning something like "the woman intended for the king" (feminine of rēgīnus). We do see this happening with gallus "rooster" > gallīna "hen", though not with any other nouns I know of. De Vaan agrees with this theory and attributes it to Nowicki 2002.
Either way, it doesn't come from any standard way of making feminine nouns in Latin.