what is the politically correct term currently for black person?

What country do you live in?

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Someone whose ancestors have lived in a non-African country for 100 years is unlikely to appreciate being called 'African'.

Here are a couple of possibilities.

African American Obviously, this only works in America. That's why I asked where the person lives.

a person of colour I hear this phrase a lot these days.

You probably realize that this is a sensitive and touchy subject, about which you need to be careful. Different terms come into fashion and go out of fashion.

The first question you need to ask yourself is 'Why do I need to speak of this at all? Is it important in some way to say, eg 'Tom is an African American'.

Best wishes, Clive