What is the name of the family that the domestic cat is a member of?

Felidae is the biological family that includes all cats—big and small—so domestic cats are felids just like lions, tigers, leopards, and cheetahs. Felis is the genus of the domestic cat (Felis catus), Felinae is the subfamily of small to medium cats, and “Cat” isn’t a formal taxonomic rank. Hence, Felidae is the correct family. Memory tip: in zoology, family names usually end in “-idae” (Felidae), while subfamilies end in “-inae” (Felinae). Domestic cats likely descend from the Near Eastern wildcat (Felis silvestris lybica) and were domesticated around 9,000–10,000 years ago, which is why their scientific name reflects the genus Felis within the cat family Felidae.