miscalculation n.

prefix of Germanic origin affixed to nouns and verbs and meaning "bad, wrong," from Old English mis-, from Proto-Germanic *missa- "divergent, astray" (source also of Old Frisian and Old Saxon mis-, Middle Dutch misse-, Old High German missa-, German miß-, Old Norse mis-, Gothic missa-), perhaps literally "in a changed manner," and with a root sense of "difference, change" (compare Gothic misso "mutually"), and thus possibly from PIE *mit-to-, from root *mei- (1) "to change."

Productive as word-forming element in Old English (as in mislæran "to give bad advice, teach amiss"). In 14c.-16c. in a few verbs its sense began to be felt as "unfavorably," and it came to be used as an intensive prefix with words already expressing negative feeling (as in misdoubt). Practically a separate word in Old and early Middle English (and often written as such). Old English also had an adjective (mislic "diverse, unlike, various") and an adverb (mislice "in various directions, wrongly, astray") derived from it, corresponding to German misslich (adj.). It has become confused with mis- (2).

late 14c., calculacioun, "art, manner, or practice of computing by numbers," also "the process of making a horoscope," from Late Latin calculationem (nominative calculatio) "a computation, calculation, reckoning," noun of action from past-participle stem of calculare "to reckon, compute," from Latin calculus "reckoning, account," originally "pebble used in counting," diminutive of calx (genitive calcis) "limestone" (see chalk (n.)). It is attested from early 15c. as "the result of reckoning, the solution for a problem."