Is it illegal to share students' grades with somebody else (e.g their parents) without their consent in the US? What are the most common penalties for such a violation of privacy? Is jail time possible as a punishment?
In the US the Family Educational Rights and Privacy Act (FERPA) protects the privacy of students. This "act" is not a law (on further reading it is a law), but rather a stipulation by the Department of Education that universities must obey in order to receive funding. As such, I do not believe that violations are classed as a criminal offense and hence cannot lead to jail time. Universities which violate the FERPA can lose their funding and likely have grounds to dismiss employees who violate the act. The university might even be able to seek damages against those individuals, but again, not jail time.
I would suggest that you not violate FERPA. If you intend to, or have done so (accidentally or otherwise), I suggest that you seek legal advice.
A number of people have mentioned FERPA. Looking at the text of FERPA and at this University web page suggests what some others have said: violations of FERPA can result, ultimately, in withholding funding from the university but the law does not list criminal sanctions for either individuals or institutions for violation. That is also my understanding.
That said, there other privacy laws or other kinds of laws that might be violated by disclosure of educational records. There are a variety of other state, local, and federal laws — plus plenty of common law tort law, that could take effect. And besides, people sue for all kinds of things including things that aren't even in violation of a law.
To be clear: I am not a lawyer nor a legal expert and this is not legal advice. But, as a non-lawyer that likes to believe that world has certain common-sense limits, it seems insane to suggest that telling a parent a grade could result in jail time. If you're worried and need a "real" answer, you should find a lawyer and ask.
This is not legal advice... If only people giving mathematical or dietary advice without credentials could be sued for failing to make a similar disclaimer! :)
There are two parts to this issue. First, is it ok to tell people students' grades? In the U.S., almost entirely "no", if the student is 18 or older. FERPA. It doesn't matter whether or not the student's parents are paying the tuition, the student's grades are privileged personal information.
It is acceptable use to disclose student grades for (e.g.) intra-math-departmental function, such as advising, admission committee work, and other "privileged" use.
A traditional practice that is no longer ok is posting grades on instructors' doors, for example.
For "old" people, the idea that one is not in fact legally entitled to know the grades of the student whose tuition you're paying will seem strange. Indeed, decades ago, the grades were sent to the parents directly, in paper mail.
But, now, 18-or-over people are essentially legal adults in the U.S., and their school records (and medical records) are not automatically open to their parents.
Thus, despite intuition to the contrary, simply do not give grades to parents, ... without seeking legal advice about extenuating circumstances, such as emergencies.
Edit: but, then, "jail time"? Who knows? But maybe monetary damages if someone sues you for violation of their privacy rights. Apart from the risk of this, if we think it through, maybe kids' grades (if they're "adults") should not be divulged to anyone... So don't do it?