righteous, just: being or doing what is right, in line with God's standard of what people, acts, and God himself ought to be
This is the adjective behind "righteous" and "just" in English Bibles. At its core it describes whatever measures up to what is right: a person who lives as God asks, an act or ruling that is fair, or God himself, whose character and verdicts are right through and through. One word stretches across all of these because the New Testament writers share one yardstick of rightness and apply it now to a person, now to a thing, now to God.
Most often it pictures a person: upright, faithful, the kind of life that does right by God and by others. Joseph is called this, and so are Simeon, Zechariah and Elizabeth, Abel, Lot, and the many "righteous" whom Jesus contrasts with sinners. The same word can be turned ironic, naming people who only count themselves righteous. Pointed at God or Christ, it praises the rightness of his character, his judgments, and his dealings, and it becomes a title for Jesus, "the Righteous One." Pointed at a thing, it means simply fair or fitting: a just wage, a right command, a true verdict.
Paul, and the writers who quote the same Old Testament line he loves, press the word into one further use that is easy to miss. When he says "the righteous will live by faith" or that no one is righteous, he is not only describing good behavior. He is asking who counts as right before God, a standing a person receives by trusting God rather than by earning it. That courtroom note is the heart of his message, and it is the sense where careful readers most need to slow down, because the same plain word can mean upright living in one verse and acquitted before God in the next.