God's Attributes
Righteousness / Just
2 Thessalonians 1:6
since it is a righteous thing with God to repay
with tribulation those who trouble you,
NKJV
If holiness may be stated as the separation of God from evil, sin, and darkness, righteousness is that attribute of God that leads to pure justice and morality. This is God's attribute which leads Him to always think and do what is right or to act in perfect goodness towards His creation.
2 Corinthians 5:21
For He made Him who knew no sin to be sin for us, that we might become the righteousness of God in Him. NKJV
Another translation for righteous is justice. Justice is the attribute which vindicates the righteousness of God, not as vengeance, but in holiness. Justice refers to the judgment which God, as a righteous God, must exercise against anything which falls short of His holy standards. This may include laws and principles.
Romans 3:21-26
21 But now the righteousness of God apart from the law is revealed, being witnessed by the Law and the Prophets, 22 even the righteousness of God, through faith in Jesus Christ, to all and on all who believe. For there is no difference; 23 for all have sinned and fall short of the glory of God, 24 being justified freely by His grace through the redemption that is in Christ Jesus, 25 whom God set forth as a propitiation by His blood, through faith, to demonstrate His righteousness, because in His forbearance God had passed over the sins that were previously committed, 26 to demonstrate at the present time His righteousness, that He might be just and the justifier of the one who has faith in Jesus.NKJV
God's justice, in what we view as a negative sense, is His wrath. This is a direct punishment or application of justice to His creation for violation of His righteousness and holiness. Justice is a rendering to everything of that actually due it. Man is saved from this justice only by God's grace and mercy.
Isaiah 30:18
Therefore the Lord will wait, that He may be gracious to you; And therefore He will be exalted, that He may have mercy on you. For the Lord is a God of justice; Blessed are all those who wait for Him.NKJV
In righteousness we have the manifestation of Gods love of holiness, of what is right and good. In justice, we have the manifestation of Gods hatred of sin.
Habakkuk 1:13
You are of purer eyes than to behold evil, And cannot look on wickedness. Why do You look on those who deal treacherously, And hold Your tongue when the wicked devours A person more righteous than he?NKJV