Used to introduce an interrogative content clause (indirect question) that consists of multiple alternative possibilities, and indicate uncertainty between them; if.
He chose the correct answer, but whether by luck or by skill I don't know.
Used to introduce a yes-or-no interrogative content clause (indirect question) that consists of a single possibility, and indicate uncertainty over it; if, whether or not.
Do you know whether he's coming?
Used to introduce multiple alternative possibilities, and indicate the irrelevance of which is the case; regardless of whether, no matter whether.
He's coming, whether you like it or not.
There is some overlap in usage between the first two senses, in that a yes-or-no interrogative content clause can list the two possibilities explicitly in a number of ways:
Do you know whether he's coming or staying?
Do you know whether he's coming or not?
Do you know whether or not he's coming?
Further, in the first two of these examples, the "or staying" and "or not" may be added as an afterthought (sometimes indicated in writing with a comma before), such that the whether may be uttered in sense 2 and then corrected to sense 1.
Unlike sense 1, sense 3 does not have a counterpart that introduces only a single possibility; *"He's coming, whether you like it" is ungrammatical.
In traditional grammar, the clauses headed by whether in senses 1 and 2 are classified as noun clauses, and those headed by whether in sense 3 are classified as adverb clauses.
