Probably from the alternate of erchomai; unrestrained (to go at pleasure), i.e. (as a citizen) not a slave (whether freeborn or manumitted), or (genitive case) exempt (from obligation or liability) -- free (man, woman), at liberty.
see GREEK erchomai
1. freeborn; in a civil sense, one who is not a slave: John 8:33; 1 Corinthians 7:22; 1 Corinthians 12:13; Galatians 3:28; Ephesians 6:8; Colossians 3:11; Revelation 6:15; Revelation 13:16; Revelation 19:18; feminine, Galatians 4:22f, 30f. (opposed to ἡ παιδίσκη); of one who ceases to be a slave, freed, manumitted: γίνεσθαι ἐλεύθερον, 1 Corinthians 7:21.
2. free, exempt, unrestrained, not bound by an obligation: 1 Corinthians 9:1; ἐκ πάντων (see ἐκ, I. 6 at the end), 1 Corinthians 9:19; ἀπό τίνος, free from i. e. no longer under obligation to, so that one may now do what was formerly forbidden by the person or thing to which he was bound, Romans 7:3 (cf. Winers Grammar, 196f (185); Buttmann, 157f (138), 269 (231)); followed by an infinitive (Winers Grammar, 319 (299); Buttmann, 260 (224)), ἐλευθέρα ἐστιν ... γαμηθῆναι she is free to be married, has liberty to marry, 1 Corinthians 7:39; exempt from paying tribute or tax, Matthew 17:26.
3. in an ethical sense: free from the yoke of the Mosaic law, Galatians 4:26; 1 Peter 2:16; from the bondage of sin, John 8:36; left to one's own will and pleasure, with the dative of respect, τῇ δικαιοσύνη, so far as relates to righteousness, as respects righteousness, Romans 6:20 (Winers Grammar, § 31, 1 k.; Buttmann, § 133, 12).