when does the noun "time" become a countable noun?

I am writing an email to my friend and want to use this sentence: "I am having a great time."

I would like to know whether the above sentence is correct.

Also, I know that time can be an uncountable or a countable noun. I would appreciate if you could provide some examples of the word time in sentences and could explain the usage of the word in each case.

"Time" can mean either the passage of time e.g. "time waits for no man", or an occasion or moment e.g. "we had a great time last night" . The passage of time is not countable, but occasions or moments are countable.

Other languages have different words for these which may be less confusing, e.g. in Portuguese, tempo often refers to time as in the passage of time, and altura means time as in an occasion or moment.

In the sentence "I am having a good time", you are not using time in the sense of time on a clock. This sentence is equivalent to saying something like "This moment in time is great.", So that sentence is clearly correct. Also, time is countable in that sentence, because it is specifically "a time.". In the sentence "I don't have the time.", time is not countable. This is because you don't have a set amount of time. It could be any amount, therefore it is uncountable.