Native English speaker here. The only time I've heard reckon used is in old cowboy movies or in the case of "a force to be reckoned with."
Generally, if you were to use reckon in an everyday context in a lot of places in the US, there's a good chance that people would think that you are a from a particular part of the country or time traveled here from the Old West (no offense to those who use it regionally, in other countries, or Old West time travelers).
Because there are sometimes subtle negative connotations depending on location, it might be best to avoid its use if you didn't grow up using it or are familiar with the subtleties of when it's fine to use and when it's not. Just my .02.
Also native English speaker. Reckon can also be used to mean "estimate" or "guess", not so much "calculate" (though some part of my brain is telling me that it may have carried that meaning in the past - hence the term "a reckoning" may have been synonymous with "a summing up" of what you have brought on yourself - sorry for the tangent).
It's pretty common in the Antipodes, though generally as an affirmation - "Yeah, I reckon!" as equal to "I know, right?!" - or to invite/express an opinion - "Whaddya reckon [about this subject]?" "I reckon we're in for a wet week" - but not unheard of in the context of tallying something. Usually not conclusive/definite - "I reckon there must've been about twenty of 'em".