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c.1200, recenen, from Old English gerecenian "to explain, relate, recount," from West Germanic *(ga)rekenojanan (cf. Old Frisian rekenia, Middle Dutch and Dutch rekenen, Old High German rehhanon, German rechnen, Gothic rahnjan "to count, reckon"), from Proto-Germanic *rakinaz "ready, straightforward," from PIE *reg- "to move in a straight line," with derivatives meaning "direct in a straight line, rule" (see regal).
Intransitive sense "make a computation" is from c.1300. In I reckon, the sense is "hold an impression or opinion," and the expression, used parenthetically, dates from c.1600 and formerly was in literary use (Richardson, etc.), but came to be associated with U.S. Southern dialect and was regarded as provincial or vulgar. Related: Reckoned; reckoning.