In the workplace, if your boss gets angry at you, how can you tell him to calm down?
How can I politely tell the manager to calm down and discuss things rationally?
You probably shouldn't say it.
When you're cross, there's not much that's more infuriating than someone telling you "calm down". The last thing you want to do is escalate the situation.
At the end of the day, a decent manager will usually realise if they've been unreasonable and apologise for it. While what you've described is not always the best way to behave, we are all human and may slip up.
If this is a recurrent issue, you could theoretically raise it with someone else - a senior member of staff who knows this person could give you advice if you approach the issue tactfully, for example, and explain if this type of behaviour is typical.
As others have noted, you can't say this professionally, and you shouldn't try. Instead, try to figure out what motivated the outburst, and next time be ready to address that instead. Here are two likely areas for examination:
Her perception of you
How has your past work been received? Do you have accomplishments and known-strengths that you can build on? If not, now's the time to start establishing your credentials: no one has any reason to grant you respect until you've earned it.
Consider: as an intern, your responsibilities are limited. It is understood by all that your time with the group is limited, and any repercussions for mistakes you make will be shouldered primarily by others. Many people who find themselves in such a role will tend to take a cavalier, short-sighted attitude towards the work, brushing off criticism and doing little to identify or address problems that might crop up in the long term. Whether or not this is your attitude toward the job, it is a stigma you'll have to overcome.
Make it clear that you're willing to follow through. Use responsive listening to demonstrate your willingness to understand the scope of the problem, and then calmly suggest your plan to correct it. Be open to input - if there's some aspect of the problem that you weren't aware of, admit that willingly and offer gratitude for the education. Don't try to downplay the severity of the problem - even if the problem is being blown out of proportion, such an attitude shows disrespect for the time others' must spend helping you correct it. Which brings me to...
Her perception of herself
What makes someone upset and bitter over small things? In the workplace, fatalism often comes from being overburdened. Your mistake may have been small, but she may see it as one more unwelcome test of her already-strained endurance.
Again, your responsibilities are limited. Hers are a superset of yours and everyone else's on the team. What appears to be a small, easily-corrected problem for you may be holding up others while you're busy correcting it - and even if that's not the case, the time needed to help you identify and correct the problem is time that could have been spent elsewhere.
This should go without saying, but make sure you're stepping up to do whatever is necessary to correct the mistake. Even if it requires someone else's skill to resolve, volunteer to help them.
Then ask if there's anything you can do to help out elsewhere on the team. Don't volunteer time you can't give, but make it clear you're not going to sit there playing 2048 while others clean up the mess.
In closing: diplomacy in the workplace
Don't expect to ever be able to operate in an environment populated solely by well-informed, perfectly-rationale actors. Even on a healthy team, you're much more likely to find yourself paired with distracted, over-worked, myopic and overly-emotional folk. And in most cases, that will all apply to you as well. The essence of diplomacy isn't figuring out how to issue harsh commands dressed up in polite language, but in understanding how to get past breakdowns in communication in order to arrive at a solution acceptable to all parties. Your tools for this task are:
Keep them always ready at hand.
Sometimes when a manager is mad at you, it is because her manager is mad at her. Something bad happened. There is a mud (sic) sandwich floating around and everyone had to take a bite. You may not feel that it is your responsibility to care for your boss, but doing so is actually a great way to help the situation. Try to distance yourself from the emotion and focus on what happened. Here are a few things that might defuse the situation:
In general, a manager will lose their professional demeanor when they are at their limit. They just want the situation to go away. Do your best to make the moment pass and assure them that it won't happen again. Show a willingness to learn and accept their 'notes' with strength. If you appear unaffected by their words, an apology will often follow quickly after.
If this doesn't work, then you may need to seek outside help.
Generally, an angry person gets angrier if told to calm down. This effect is intensified if the person telling is not in a position of authority. On top of "I don't need to calm down!" you get "Who do you think you are, telling me what to do or how to react!"
A useful sentence in this case is "I don't think this is as bad as you are suggesting." A variant is "I think this is something we can handle calmly." These sentences have several advantages:
That said, ironic laughing and anger are not appropriate in the workplace, even for a large mistake. You're always ok to point out you don't like that treatment. Try to separate it from the issue of whether or not this is a big deal. Saying something like, "I'm sorry that I've made an error. Laughing at me is making me feel much worse and I don't think it's fair." For anger, "I'm not your child, and when you yell angrily at me that's how I end up feeling. Can we talk about this calmly please?" Of course, in both these cases you need to speak relatively neutrally. You can't yell "DON'T YELL AT ME LIKE THAT!" to anyone, and especially not someone you wish would stop yelling or being angry.
When dealing with a furious person which can not be reasoned with, the best course of action is usually to let them rage on without responding. Give them no resistance and do not try to justify yourself. It won't work. All you will achieve is that they get even more angry and will rant on even longer. You can acknowledge with one-word responses that you are listening to them to not provoke them any further, but nothing more.
When they ran out of words and have nothing more to say, you can try to make your point. It can often be useful to not reply immediately. Let them leave and wait until they have calmed down while preparing your arguments and fact-checking their accusations. Then approach them and attempt to discuss the matter rationally with them.