rightness

noun

1. The quality or state of being morally sound: good, goodness, morality, probity, rectitude, righteousness, uprightness, virtue, virtuousness. See right/wrong.
2. The moral quality of a course of action: ethic (used in plural), ethicality, ethicalness, morality, propriety, righteousness, rightfulness. See right/wrong.
3. Freedom from error: accuracy, accurateness, correctness, exactitude, exactness, preciseness, precision. See correct/incorrect.

The noun has 4 meanings:

Meaning #1: according with conscience or morality
  Antonym: wrongness (meaning #2)

Meaning #2: appropriate conduct; doing the right thing
  Synonym: appropriateness

Meaning #3: conformity to fact or truth
  Synonym: correctness
  Antonym: wrongness (meaning #3)

Meaning #4: conformity with some esthetic standard of correctness or propriety
  Synonyms: justness, nicety