Minimal is an adjective meaning "smallest," "least possible": "He secured a loan at a minimal rate of interest." Minimum is primarily a noun meaning "the least quantity or amount possible" (Jack expended a minimum of time on studying), but is also used as an adjective with the same meaning as minimal: "This is a minimum risk." Neither minimal nor minimum means "just a little" or "not much"; both mean "the least possible." In adjectival use, careful speakers prefer minimal to minimum.
Dictionary of problem words and expressions. Harry Shaw. 1975.