'간다' is formal but not polite speech (I don't mean to imply that it's impolite, jus that it's not marked as deferential to the listener). '가요' is polite but not formal speech.
[-polite][-formal] 가
[+polite][-formal] 가요
[-polite][+formal] 간다
[+polite][+formal] 갑니다