This is my guess:

In the movies, when it shows the students in class, there's about 30 people.

There are seven years in Hogwarts, each year divided into four houses. So that's as follows:

1st year Gryffindor
1st year Slytherin
1st year Ravenclaw
1st year Hufflepuff
2nd year Gryffindor
2nd year Slytherin
2nd year Ravenclaw
2nd year Hufflepuff... etc....... there are 28 in all.

30 students per class times 28 classes

30x28=840

So... there are about 840 students at Hogwarts.


Do you agree?