Righteous means morally right, or angry at what is wrong. A righteous man, righteous anger, righteous indignation.
It is a religious word first and carries that weight: the righteous, as a plural noun, means the morally upright. Righteous anger and righteous indignation are fixed phrases and are usually treated as justified. Self-righteous is the opposite in tone and means smugly convinced of your own virtue, which is one of the sharpest insults available. Note righteousness, and that in American slang righteous also means excellent.
1adjectiverighteousMorally right.
“The righteous in that book get about as much trouble as everybody else.”
2adjectiveangryAngry at what is wrong.
“There was righteous anger for about a fortnight and then nothing.”
righteous is a quality of moral rightness.
Old English rihtwis means right-wise, meaning in the manner of what is right. The spelling was reshaped in the sixteenth century to look like other -eous adjectives, which is why the wise inside it disappeared.
Proto-Indo-European
*h₃reǵ-
Old English
rihtwīs — righteous, just
Middle English
rightwise
English, today
righteous
From earlier rightuous, rightwose, rightwos, rightwise, from Middle English rightwise, rightwis, from Old English rihtwīs (“righteous, just”), corresponding to right + wise (with assimilation of second element to -ous), or to right + wise. Cognate with Scots richtwis (“righteous”), Old High German rehtwīsic (“righteous, just”), Icelandic réttvíss (“righteous, just”). Compare also thefteous, mighteous.
Etymology from Wiktionary, CC BY-SA