Though none of them is particularly formal, from least formal (most casual) to most formal (least casual), they are:
I gotta get going.
I've gotta get going.1
I've got to get going.2
I have to get going.
1Personally, I tend to use this one in ordinary conversation.
2I have got to get going is the more emphatic form of this
one. It would probably be said more slowly, with some stress on
each of the first three syllables.
CJ