The answer is a lot less than you think. I'll focus on grad degrees (though this applies to a lesser extent to an undergrad major). First, in the course of a higher degree, you make an original research contribution to a narrow subfield, so you presumably learn a huge amount about antebellum textile production or Seven Years' War, etc. As far as what you learn more broadly, I'd say two things: (1) some rough sense of the contours of your broad historical subfield, such as 19th century American history or the French revolution and (2) how to think about historical debates and historical themes. I'd say the second is much more important in graduate training. The advantage of this knowledge is also that you might not know a specific piece of information, but you'd know how to figure it out / find it. But as a result of these two things, you do not have an in-depth view of much at all. Now you know a LOT more than the average person, but that doesn't mean as much as you might think. There is just a HUGE amount of historical information.

You do end up being extremely well read, but you're often reading for debates, etc. So you'll get some of the factual information, but that's actually somewhat secondary in history graduate training (since understanding how to think about history is much more productive). One way to think about information vs. being able to think about history is that if you had a huge amount of information about say 18th century America, it might not have much of an ability to make sense of the 20th century. But if you knew how to think about history broadly (point 2 I mention above), you could somewhat easily make sense of the facts and information about either period.

I didn't start learning the really in-depth stuff people imagine the average historian knows until I started lecturing. When you have to give a lecture about something, you really start to learn the facts and information. But even then, the limits of that knowledge are very real. I've taught classes on the Civil War multiple times, and I still could get caught off guard if someone just started asking me really detailed factual and chronological information about the war (particularly if I haven't taught the class in a while). There's just so much to know about everything...our brains can only fit so much!

As far as history at its broadest level, not that much more than the average person (though you probably osmose a little bit). As in, I'm an American historian and I know very little about ancient Rome. I have some friends who are classicists, so I've probably learned a bit through random conversations and seminars, but that doesn't result in that much factual knowledge.

EDIT: my answer reflects grad training in the US (and other places where there is a coursework component).

Honestly it’s not about tests (though those exist for courses, not as an emphasis), but about the quality of research you complete. For undergraduate degree, typically you will take classes on a wide variety of eras and regions, and then focus on one geographic location and topic or period and analyze primary sources to build a full thesis (likely roughly 60 pages)- however all of this might vary depending on the university system you’re in, so take that with a grain of salt.

For masters and doctoral programs, research on a specific subject becomes even more of a focus, as instead of spending say a year on your undergraduate thesis which you may or may not need to defend before a committee, you’re digging even deeper and your graduate thesis should be a demonstration of your cumulative years of study on a topic. You will certainly take other courses and do your best to be well rounded (relatively) in some other topics, but the point of your work is to be a master in one subject rather than a jack of all trades.

Most of the historians you see answering a variety of topics in this sub aren’t necessarily experts on more than a couple subjects, but really just love history so they go out on their own to study new topics. You have to love it to spend so many years in study, but the vast general knowledge is really more of a symptom of that passion than a requirement for obtaining a specific degree.

I don’t know of any historian who would say they’re an expert on all of history (and no one should or could say that honestly), because you’ll realize if you study it just how much history there is. Most historians will know a tiny bit about many other topics outside of their focus, but will not claim by any means to be experts in more than a few of them.

As in all fields, what a degree gives you is not "a dump of all of the knowledge in the field" but exposure to how historians think (the methodologies), some "base" knowledge (e.g., survey courses and a few advanced courses), and the opportunity to apply these things in your own research.

For your amusement I will outline, as best I can remember it, all of my formal education in history.

Here are my undergraduate history courses that I can remember off the top of my head:

• Survey courses (broad overviews): US History after 1865, Modern Latin American History, Modern European History

• Focused topics (lectures but not as broad, smaller classes): History of Modern Physics, History of Modern Biology, History of Modern Germany, Medieval European History, History of Death and Dying

• Seminars (small, reading and discussion based, no lectures): History of Hereditarian Thought in the USA, Historiography, Science Under Totalitarianism

• Thesis work (working on papers under advisement of a professor): History of Compulsory Sterilization in California, History of Nuclear Weapons Laboratory Management

I'm probably missing a few here (it's been awhile), but you get the drift. There are many things in history missing from the above topics, but it's a wide-enough exposure that I can claim to know a few things about a lot of history, mostly modern. This was for a History degree in a large History program. I also had to take lots of non-history classes, too, though some of these overlapped with my historical interests (e.g., my courses in Astronomy had a lot of history of physics in them, and a course I took in Physical Anthropology had a lot to do with the history of heredity).

After this I went on to get a PhD in the History of Science (no masters, which is frequently skipped in the USA), a subfield of history. In grad school I took maybe 14 seminars over several years? They ranged from very chronologically- and geographically-bound topics ("History of Medieval Medicine," "History of Probability," "History of Darwinism," "History of Modern Russia, Ukraine, and Poland") to very thematic topics ("Science in Print, Photography, and Film," "Intellectual Property and Science," "Theories of Race in the History of Science and Medicine"). For many of these classes I wrote extensive research papers, deepening my knowledge in something related to the topic area (e.g., for the probability class, I wrote a paper on the history of random number generation prior to the invention of the digital computer — a very specific topic!). I took a few non-history-related classes in grad school, but very few (mostly language classes).

After taking two years of classes I studied for a "General Exam," which was an oral examination on four sub-fields of my choice (Modern US History, History of Modern Physics, History of Modern Biology, and Science & Technology Studies). In studying for this I read (or skimmed) maybe 300 books. The exam itself was nothing too interesting, but the work of digesting that many books was useful in the long-run — it's an attempt to say, "I know a lot about this field!" Of course, not all of that knowledge is retained when you do it in a 3-books-a-day sort of fashion.

I also, crucially, taught many classes, as a teaching assistant. This gives one a wealth of new knowledge, and often this is knowledge that is deeper retained than what you read for a class you are taking (teaching is an entirely different mental operation than listening).

And for most of the PhD, of course, I was also working on a dissertation, which attempted to show that I could become a master of one subset of the field and extend the knowledge of it.

If you imagine knowledge as a tree, you can see that I've fleshed out some very broad branches, and then gone very deep into a few of them. This is not unlike education in really any subject. I would say this education only gave me an "overview of history" in a few specific areas of history (you will notice a conspicuous lack of anything earlier than the Medieval period — and even that is just a smattering — and anything outside of the American-European sphere). I certainly did not come out with an insanely in-depth view of anything I had not written a research paper on (and even then...).

One nice thing about history, though, is that it is cumulative to a degree, and the more you teach and read, the more you add to it. So after becoming a professor I've taught now several survey courses that try to cover ridiculously long timespans (e.g., a "History of Science and Technology" survey that covers from 10,000 BC to the present, and is global in scope). Learning enough to teach this class, and having taught it several times now, means that I now have a much better sense of, say, what was going on in any given part of the world at certain points in history, including the deep past. I'm not an expert in that, to be sure: my knowledge is relatively superficial, enough to teach a broad survey and discuss it with students. But I've expanded the breadth of my "tree," while at the same time the depth of it has also expanded in the areas in which I have continued to do research (e.g., I did almost no research on the bombings of Hiroshima and Nagasaki in grad school, but I've spent a lot of my research time in the last six years or so diving deep into that, to the degree that I do consider myself an expert in that sub-topic).