The word ʿadil is not in the Quran, but justice is constantly commanded there: “Be just: that is nearer to piety” (5:8); “Allah commands justice and good conduct” (16:90). The first of the seven whom Allah will shade on the Day when there is no shade but His is “the just ruler (al-imam al-ʿadil)” (al-Bukhari 660).
Meaning of the name Adil
ʿAdil is the active participle of ʿadala, “to be just, fair” (root ʿ-d-l of justice, ʿadl, and of balance): one who judges rightly, leaning to neither side. Al-ʿAdl, “the Just”, appears in the list of the 99 names of Allah transmitted by al-Tirmidhi. The name is Adel in the Maghreb and the Middle East, Adil in Turkey and South Asia.
O you who have believed, be persistently standing firm for Allāh, witnesses in justice, and do not let the hatred of a people prevent you from being just. Be just; that is nearer to righteousness. And fear Allāh; indeed, Allāh is [fully] Aware of what you do.
Indeed, Allāh orders justice and good conduct and giving [help] to relatives and forbids immorality and bad conduct and oppression. He admonishes you that perhaps you will be reminded.
Indeed, Allāh commands you to render trusts to whom they are due and when you judge between people to judge with justice. Excellent is that which Allāh instructs you. Indeed, Allāh is ever Hearing and Seeing.