'anti-tartar' is a compound formed from the prefix 'anti-' and the noun 'tartar'. 'anti-' originates from Greek 'anti-' meaning 'against', and 'tartar' originates from Old French 'tartre' (from Medieval Latin 'tartarum').

'tartar' passed into English via Old French 'tartre' and Medieval Latin 'tartarum', originally referring to deposits (such as potassium tartrate) and later used for dental calculus; the prefix 'anti-' from Greek was productive in modern English to form compounds like 'anti-tartar' (20th century usage in product names).

Originally 'tartar' referred to a crusty deposit (chemical or mineral); over time its common sense shifted to dental calculus, and 'anti-tartar' came to mean 'preventing dental calculus' in consumer dental products.