In hostage negotiation, we have a mantra: seek to understand before you can be understood. This is true with angry people, too. First, check your own emotion, as it’s the only thing you’re in control of. Don’t take rude or negative comments personally and avoid escalating your tone of voice to match the other person’s.
Allow them to vent, while staying aware of your safety. Being empathetic will often calm them, whereas telling them to relax or calm down will not. Maintain eye contact, to show you’re taking this seriously, and don’t smile. Proactively listen and try to understand what the issue is.
Challenge any threats calmly. Don’t say, “You wouldn’t do that.” You can say things like, “Please don’t do that.” Don’t say that you understand, as you don’t know what else has gone on in their day. Instead, try: “So if I understand this right…” to validate your understanding and their concerns.
When you think you’ve gained some understanding, try to communicate calmly. “I see your point of view,” is a good welcomer, or “That must have been frustrating.” If culturally appropriate, using someone’s name can be a good diffuser because we automatically defer when we hear our names.