Etymology
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off-hand (adv.)

also offhand, 1690s, "at once, straightway," from off (prep.) + hand (n.). Probably originally in reference to shooting "from the hand," without a rest or support. Hence, of speech or action, "without deliberation, unpremeditated" (1719). Related: Off-handed; off-handedly.

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Definitions of off-hand

off-hand (adv.)
without preparation;
I don't know the figures off-hand
Synonyms: ex tempore
From wordnet.princeton.edu