“It is widely recognized that 1:16-17 functions as a statement of the major theme that Paul works out in the theological and paraenetic sections of Romans…The discussion of the meaning of the righteousness of God in Romans has generated a vast literature which it is beyond the scope of this book to review. Before attempting to explain what Paul means by saying that the righteousness of God is revealed in the gospel, however, it might be helpful to note the different aspects of the righteousness of God as they emerge in the apostle’s argument in Romans.
First, God’s righteousness as distributive justice is implied in 1:18-32 where Paul says that God recompenses humanity in accordance with its response to his revelation, and also in 2:2-11 where he says that God renders to all people according to their works–those who with patience and well-doing seek immortality will be rewarded with eternal life, while those who are factious and do not obey the truth will be rewarded with wrath and fury. It is implied again in 3:1-20 where Paul defends God’s righteousness by arguing that God acts justly when he judges unfaithful Jews.
Second, God’s righteousness as covenant faithfulness is defended in 3:3-9, where Paul argues that when God judges Israel it is evidence not of failure of covenant loyalty on his part, but of sinfulness on Israel’s part. In 9:1-29 God’s covenant faithfulness is further defended when Paul rejects charges that God’s word has failed (v. 6), that there is injustice on God’s part (v. 14) and that God has no right to find fault with Israel (v. 19). Paul argues that Israel has failed to obtain the blessing, not because God is unfaithful to his covenant with Israel, but because that blessing always depended upon election and mercy, not on any inherent rights based on being born a Jew. God’s covenant faithfulness is further defended in 11:1-10 where Paul argues that God has always maintained a remnant of Israel in whom his covenant promises are being fulfilled.
Third, God’s righteousness as saving action is expounded in 3:21-26. Here God’s righteousness is manifested, apart from the law, by providing redemption through Christ’s death, so making possible a righteousness (a right standing before God) to be received by faith.
Fourth, God’s righteousness as the gift of justification and a right relationship with himself, already foreshadowed in 3:21-26, is expounded in terms of the experience of Abraham in 4:1-25. It is referred to again in 5:17 (‘the free gift of righteousness’ received by believers as a result of Christ’s obedience), and explained further in 9:30-10:4, where the apostle speaks of a righteousness not based on law[-observance by Jews], but which comes from God, and is received by all those who believe.
Fifth, the righteousness of God (as a gift) which leads to righteousness of life in believers is expounded in 6:1-23 (esp. vv. 16-18) where Paul points out that those who are under [the] grace [of justification] are no longer slaves of sin but slaves of righteousness. This aspect of the righteousness of God is also rejected in 8:4, where the purpose of Christ’s death is to condemn sin in the flesh so that the just requirement of the law might be fulfilled in believers.
All these aspects of God’s righteousness can be included under the one umbrella idea of God acting in accordance with his own nature for the sake of his name [he cites Piper here]. Understood in this way, it can include God’s distributive justice, his covenant loyalty, his saving action, and his gift of justification leading to righteousness of life.
The central thrust of Paul’s teaching about the righteousness of God in Romans, however, is to explain the way God’s righteousness is revealed in the gospel. And what he means by this is that God’s power for salvation, by which Gentiles as well as Jews are justified freely by his grace, is revealed in the gospel. This is done without any compromise of his distributive justice (because he has set forth Christ as an atoning sacrifice for sin), of his covenant faithfulness to Israel, or of his demands for righteousness of life in his people.” (Colin G. Kruse, Paul, the Law, and Justification, pp. 169-71)