[From Cambridge English]

Have got and have mean the same. Have got is more informal.
I’ve got a terrible pain in my back.
I have a terrible pain in my back. (more formal)
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Question: What about in American English? In American English, 'have got' is more informal? Is 'have' formal?

Yes, that's also true of American English.

It's about the same, although in American English the use of "got" is often considered repetitious. If "I have" and "I have got" mean the same thing, then why use the extra word?

=)

In speaking, I often use "got" when it's not necessary.

Same here!! =)

In American English, the usage of "have got" and "have" follows a similar pattern as in British English. "Have got" is generally considered more informal, while "have" is considered more formal. However, it's important to note that the usage of "have got" is less common in American English compared to British English.

So, in American English, you can say:

- I've got a terrible pain in my back. (more informal)
- I have a terrible pain in my back. (more formal)

The difference in formality is subtle, and both forms are generally understood and accepted in American English. It's important to consider the context and level of formality you want to convey when choosing between "have got" and "have."