The Hebrew word translated “righteous” (⊡ādîq) and its related nominal and verbal forms has the basic meaning of someone or something proven true, especially in a legal context. It therefore has the meaning “innocent” and is applied in the Bible especially to moral conduct and character. But the scope of righteousness is much wider than judicial procedures and embraces the whole covenanted life of the people under God. The specific meaning depends on circumstances: for a ruler, it means good government and the deliverance of true judgment (Isa. 32.1; Jer. 23.5); for ordinary people, it means treating one's neighbor as a covenant partner, neither oppressing nor being oppressed (Amos 5.6–7, 21–4); and for everyone it means keeping God's will as conveyed in the Torah (Deut. 6.25). Sometimes human righteousness is seen as a response to or reflection of the divine righteousness or graciousness (Isa. 56.1; 58.8), and essentially it is the acknowledgment of God in worship of him alone and in living as he wants (Ezek. 18.5, 9).
God's righteousness means that he is a just and reliable judge (Ps. 9.4) who keeps his side of the covenant and who thus delivers Israel from her enemies, so that they experience that righteousness as punishment, while Israel experiences it as salvation and vindication (Judg. 5.11). Indeed in some places God's righteousness and salvation are virtually synonymous (Isa. 51.1–3), and from the exile onward we find God's righteousness as an object of hope (Jer. 23.5; Dan. 9.24).
In rabbinic literature of the Tannaitic period, righteousness is often specified to mean generosity in general and almsgiving in particular. There is also development of the biblical tendency for righteous to refer to Israel, or a group within Israel, everyone else being at least relatively unrighteous; this may reflect experience of oppression. In the Dead Sea Scrolls we find the Qumran sect regarding themselves as the only truly righteous. Righteousness is still, however, essentially conformity to the divine ordinances, that is, covenantal obedience. In the Septuagint there is very high consistency in rendering the derivatives of the Hebrew root ⊡dq by the Greek dikaiosunē and its cognates, whose semantic field overlaps considerably with that of the Hebrew words.
In the New Testament, righteousness occurs with greatest frequency in the gospel of Matthew and in Paul's letters. In the case of Matthew, there is discussion about whether he uses the word for life under God in the Christian community or reserves it for life under God before Christ came and outside the Christian community, and whether righteousness is not only a divine requirement but also a divine gift, especially in 3.25; 5.6; 6.33.
For Paul, the issues are even more widely debated. It is usually agreed that sometimes he uses righteousness in a broadly biblical fashion but in a Christian context for the life of the people of God (Phil. 4.8; 2 Cor. 5.14; 9.10). It is also usually agreed that “the righteousness of God,” whether or not we can speak of a fixed formula, means God's saving activity (Rom. 1.18), characteristically seen in justification by his grace through faith (Rom. 3.21–6). Indeed one of the reasons why the apostle is often held to be quoting a pre‐Pauline formula in the last passage is that in v. 25 God's righteousness can be held to mean God's justice in a strictly judicial sense and not his saving activity. Under the influence particularly of Galatians 3 and Romans 4 and the terminology of reckoning, there has traditionally been a view that in justification Christ's righteousness is placed to the account of sinners (is “imputed” to them).
The question remains whether in some places righteousness and justification are synonymous in Paul or at least that righteousness can sometimes be a purely forensic or relational word. The best evidence for this is Galatians 2.21, but it is widely held for other passages as well. Nevertheless, it has also been maintained that Paul consistently uses “justify” (dikaioō) for the restoration and maintenance of the relationship with God and “righteousness” (dikaiosunē) for the consequent life as his people, with both justification and righteousness being by faith. But there is disagreement about the exact meaning of most of the relevant passages. Some scholars find the key to the whole matter in the idea of God's righteousness as a power, with the gift of righteousness being inseparable from God, the giver, so that the believer is drawn into the sphere of his power.
In the New Testament apart from Paul and Matthew, righteousness normally means life as God wants it and in relation to him. It is not surprising that righteousness is sometimes found as a particular predicate of Jesus Christ (e.g., 1 John 2.1, 29; 1 Pet. 3.18).