Though recent American usage has moved the word "reckon" into the neighbourhood of "guess", it would be as foolish to remove it from the discourse about calculation as it would be to ban "cool" from the vocabulary of temperature. To ascertain that this hunch (and a few others) were not off the wall, I did some etymological exploring. (K.H.)
The following is from Roots of English by Prof. Eugene Cotter of Seton Hall University (cf. http://pirate.shu.edu/~cottereu/rootsof.htm
Italics and underlines are his, boldface and contents of square brackets were added.
/reas /rati 'to think; calculate'.
L ratio 'calculation; reason'. L reri 'to calculate, count, think, reckon'
The whole group is from
L ratus pp of reri, 'to count, calculate, reckon, (and so) to think'.
reason is from ME resoun <OF raison, <L ratio, 'reason, computation',
and is akin to Gothic rathjo, 'account, advice', L reri, 'to calculate',
and Gk arariskein, 'to fit'.
This last, Gk arariskein, is ultimately akin to L ars, '[art], skill',
L arma, 'weapons', Gk harmos, 'joint', L armus, 'shoulder',
all of which are akin to OE earm, ME-E arm.
/put /pute ' to prune; reckon, think'.
L putare 1. 'to prune', 2. ' to purify, correct (an account), count, calculate'.
Perhaps there were two separate roots, with the second, 'to purify'
(especially, to count) deriving from L putus 'pure'.
count is from ME counten <OF conter [F compter] < L computare
/techn /tect /test 'art, skill, craft'.
Gk tekhne 'a working with the hands, a craft, manual skill'.
akin to Gk tekton 'builder, carpenter, L texere 'to weave',
Skt taksati 'he forms, constructs'.
[Further down the long list of cognates, one finds:]
test [in] ME [a] cup to separate precious metals, a cupel < OF a pot
< L testum 'earthen vessel', akin to L testa 'shell, earthen pot', from texere.
At one point I was tempted to relate reckon to F recompter, but that would have been a mistake. Both my "American Heritage Dictionary" (despite its name an erudite Harvard tome) and my "Wahrig" agree that it and its German cousin rechnen come from the IE root /reg, which has spin-offs like regulate, rectify, real, regal, rich, maharaja, and even anorexia.
The former dictionary (AHD) has reckon meaning: "1. To count or compute. 2. To consider as being; regard as. 3. Informal. To think or assume." These meanings are listed in the reverse order by the "Collins Cobuild" dictionary, with explanations as to their usage. The one concerning us here comes off as follows: "3 If you reckon an amount, you calculate it; an old-fashioned or formal use", with examples like "Scylla reckoned on her fingers".
Formal or not, it seems to be a legitimate verb for calculation. If you look it up in Harrap's French-English dictionary, you find compter, calculer, and in the other direction, calcul gives calculation, reckoning, computation. Was there never a time and place where reckoning was a school subject in English?