From The Collaborative International Dictionary of English v.0.48:

Reckon \Reck"on\ (r[e^]k"'n), v. t. [imp. & p. p. Reckoned
   (r[e^]k"'nd); p. pr. & vb. n. Reckoning.] [OE. rekenen, AS.
   gerecenian to explain; akin to D. rekenen to reckon, G.
   rechnen, OHG. rehhan[=o]n (cf. Goth. rahnjan), and to E.
   reck, rake an implement; the original sense probably being,
   to bring together, count together. See Reck, v. t.]
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   1. To count; to enumerate; to number; also, to compute; to
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            The priest shall reckon to him the money according
            to the years that remain.             --Lev. xxvii.
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            I reckoned above two hundred and fifty on the
            outside of the church.                --Addison.
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   2. To count as in a number, rank, or series; to estimate by
      rank or quality; to place by estimation; to account; to
      esteem; to repute.
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            He was reckoned among the transgressors. --Luke
                                                  xxii. 37.
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            For him I reckon not in high estate.  --Milton.
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   3. To charge, attribute, or adjudge to one, as having a
      certain quality or value.
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            Faith was reckoned to Abraham for righteousness.
                                                  --Rom. iv. 9.
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            Without her eccentricities being reckoned to her for
            a crime.                              --Hawthorne.
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   4. To conclude, as by an enumeration and balancing of
      chances; hence, to think; to suppose; -- followed by an
      objective clause; as, I reckon he won't try that again.
      [Prov. Eng. & Colloq. U. S.]
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   Syn: To number; enumerate; compute; calculate; estimate;
        value; esteem; account; repute. See Calculate,
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From The Collaborative International Dictionary of English v.0.48:

Reckon \Reck"on\, v. i.
   1. To make an enumeration or computation; to engage in
      numbering or computing. --Shak.
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   2. To come to an accounting; to make up accounts; to settle;
      to examine and strike the balance of debt and credit; to
      adjust relations of desert or penalty.
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            "Parfay," sayst thou, "sometime he reckon shall."
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   To reckon for, to answer for; to pay the account for. "If
      they fail in their bounden duty, they shall reckon for it
      one day." --Bp. Sanderson.

   To reckon on To reckon upon, to count or depend on; to
      include as a factor within one's considerations.

   To reckon with,
      (a) to settle accounts or claims with; -- used literally
          or figuratively.
      (b) to include as a factor in one's plans or calculations;
          to anticipate.
      (c) to deal with; to handle; as, I have to reckon with
          raising three children as well as doing my job.
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                After a long time the lord of those servants
                cometh, and reckoneth with them.  --Matt. xxv.
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   To reckon without one's host, to ignore in a calculation or
      arrangement the person whose assent is essential; hence,
      to reckon erroneously.
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