Both cannot and can not are correct spellings, but they are not quite the same. Cannot is the usual form and the one to use in formal writing. Can not is right in a few special cases, for example when not belongs to the phrase not only.
Several English words confuse native speakers and learners alike when it comes to their spelling. Sometimes there is not even a final answer to the question of how to spell a word. For cannot and can not, though, there is a fairly simple answer: in most sentences, they mean the same thing.
Both ways of negating can appear in literature and in informal writing, but cannot is by far the more common and the preferred spelling.
Some distinctions
Still, there are a few cases in which can not, written as two words, says something different.
When there is another option
Cannot means that something is impossible or not allowed. Can not, with the stress on not, can mean that you are free not to do something:
You cannot attend the meeting. (You are not allowed to, or you are not able to.)
You can not attend the meeting if you are busy. (You may skip it: attending is optional.)
In the second sentence, cannot would change the meaning completely.
When not belongs to another part of the sentence
Write two words when not is part of another phrase, such as not only and but also:
She can not only play the guitar but also sing like an angel.
Here, not belongs to not only, not to can, so cannot would be wrong.
For emphasis
Some writers use can not to put special emphasis on the negation:
Can he fix the car? No, he can not fix the car!
In formal writing, though, it is better to write cannot and to stress it in another way, for example with italics.
What about can't?
Can't is the short form of cannot. Like don't and didn't, it is a contraction, and it means exactly the same as the full form. It is the usual form in speech and in informal writing.
So which one should you use?
In most sentences, it does not matter much. If you want to be on the safe side, here is an easy rule of thumb:
- In informal writing, all three forms are fine, and can't sounds the most natural.
- In formal writing, use cannot.
- Write can not only when not belongs to another phrase, such as not only, or when you mean that someone is free not to do something.
Other words raise the same question of one word or two, such as everyday and every day and a while and awhile.