Honestly, I’ve had very little luck to get someone to calm down if they are actually mad at me, but I still try to try.

the only path there is to work out what they’re mad about and productively, empathetically, and concretely work slowly towards a common ground while genuinely apologizing in specific for offense given. it’s much easier when they’re not mad directly at you, though, as it’s more straightforward to establish empathy.