There are actually about three hundred, it would seem, although there is plenty of debate on the subject. Here’s the evidence from the books themselves:
 There are more or less ten students (depending on the vagarities of the Sorting) in each House per year, five boys and five girls.
 There were twenty broomsticks lying on the ground awaiting the first year Gryffindors and Slytherins for their first flying lesson, which bears that number out (PS9).
 A double class of Potions — Gryffindor and Slytherin — had twenty cauldrons set up.
 For a double class of Herbology — Gryffindor and Hufflepuff — Professor Sprout had twenty pairs of earmuffs ready (CS6).
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 Harry’s class in Gryffindor has the following students in it:

 Brown, Lavender
 Finnigan, Seamus
 Granger, Hermione
 Longbottom, Neville
 Patil, Parvati
 Potter, Harry
 Thomas, Dean
 Weasley, Ron
 possibly two unidentified girls.

 If there are more Gryffindors of that year, isn’t it strange that we haven’t heard about them in six years’ worth of books? Not a one has spoken up in class, has been part of any parties or activities in the common room, or anything like that. Judging by the numbers cited above for Herbology, flying, and Potions, they must not even be in the same classes. If there are any others, where in the world are they? We do have evidence suggesting the existence of two more girls, but if they exist they have been awfully quiet.
.  Assuming the ten students per House per year numbers, that would work out to forty students per year for a total of about 280 students. This meshes with the several times that Harry has seen “hundreds” of people in the Great Hall (in PS7 when Harry was Sorted and GF17 when he was chosen for the Tournament, for example).
.  The number of teachers would also suggest a fairly small number of students. In GF12 Harry looks along the staff table in the Great Hall. He notes teachers by name until he gets to Dumbledore in the middle of the table. He has named Flitwick, Sprout, Sinistra, Snape, and an open chair for McGonagall on that side, which means that there would be the same number on the other side, for a total of eleven, counting Dumbledore. Add Trelawney, who we know doesn’t attend these functions, and we get an even dozen teachers. Twelve teachers would not be able to teach classes to a thousand students, unless they used Time Turners constantly, which doesn’t seem likely.
.  The Sorting in PA5 takes only as long as a fairly quick conversation between Harry, McGonagall, and Madam Pomfrey and a subsequent chat between Hermione and McGonagall. The duration of these chats seems quite short. But if there are a thousand students at Hogwarts, there would be between 150 and 200 students to sort every year. Even at the rate of two per minute, that would mean the sorting would last for over an hour. Would the rest of the students really be willing to sit for that long waiting to eat? I think it would get a bit long. And the sorting we’ve witnessed in the books certainly doesn’t seem to last over an hour.
.  On the other hand, there are about a hundred carriages to take students to the castle from the train station in Hogsmeade (PA5). There were also 1200 seats available around the tables at the Yule Ball (GF23). And during one Quidditch match, there were two hundred Slytherin supporters in the stadium when we know that the Ravenclaws and Hufflepuffs were backing Gryffindor (PA15). So there are some references that support the “thousand student” concept. But by far most of the evidence suggests a much smaller number…
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