An Etymological Dictionary of the German Language/rechnen
rechnen, vb., ‘to reckon, estimate, deem,’ from MidHG. rëchennen, OHG. rëhhanôn, ‘to count, reckon, render an account’ (ë is proved by modern dials.). The assumed Goth. *rikanôn, which is also implied by AS. rëconian, E. to reckon, and likewise the equiv. LG. and Du. rekenen, is abnormally represented by the strange word rahnjan. The West Teut. *rëkanôn is connected, probably in the sense of ‘to compute, collect’ (comp. the meanings of lesen), with the root rak, ‘to collect’ (see Rechen), to which AS. ręččan (from rakjan), ‘to count up, compute, arrange,’ and AS. racu, OSax. raka, OIc. rahha, f., ‘speech, account, affair,’ also belong; so too geruhen.