This post discusses a family of words that pertain to balance, impartiality, or uniformity.
The root equi-, which forms without the i when it precedes a vowel, ultimately derives from the Latin adjective aequus, meaning “even” (which is not related to equus, meaning “horse” and the source of equestrian). Equal refers to a state of balance, and the noun form is equality; a person or system that favors or promotes equality is an egalitarian. (The consonantal change occurred in French.)
Equity is the quality of fairness, though the word also has senses in finance and in property ownership of rights or value. The adjectival form is equitable, and equitably is the adverbial form. The antonym, with the same variations, is inequity, though iniquity, which means “wickedness,” stems from the same source. (Its adjectival form is iniquitous, and the noun is formed by attaching to that word the suffix -ness.)
To equate is to balance or compare, or to make even or smooth; the act of doing so is equation. (That noun also denotes a logical or mathematical expression.) Equanimity is fairness, and equilibrium is mental or physical balance. The root word of the former term is a form of animus, meaning “mind” or “spirit,” so a literal translation is “even mind,” and the root word of the latter term is derived from libra, meaning “balance” or “scale,” so equilibrium literally means “even balance.” (Equanimity has no adjectival form, but equilibrious, though rare, serves that function for equilibrium.)
Equivalence (equivalency is a variation) is literally “equal worth”; the adjectival form is equivalent. The source of the root of equivocation is also that of vocal and voice; literally “equal voice,” the word has pejorative senses of “avoiding commitment to what one says” or “using language to deceive.” One is described as equivocating or being equivocal.
Equinox derives from the Latin word for “equality of night (and day)”—the root nox is related to the first syllable of nocturnal (and both are cognate with night)—and refers to the two days of the year, six months apart, when day and night are of identical duration.
A word that may not be an apparent relative of those described above is adequate, which means “sufficient.” (Its Latin forebear literally means “make equal.”) Depending on context, the word can be neutral or disparaging. And the rare term equiparation means “equal treatment.” (The root syllable is related to par and per, which pertain to value.)