# Doing the Math

Posted on Saturday, 19th of November, 2011 @ 4:11am by Seventh Year Prefect (G) Evan Grant

## Doing the Math: How many kids are at Hogwarts

by David Haber

On October 16, 2000, J.K. Rowling gave a live interview on Scholastic.com with classrooms across America, which were allowed to ask her questions about the books up until then (at the time, Goblet of Fire), one of the earliest of these kinds of interviews with J.K.

When a student asked, "How many students attend Hogwarts, and how many students per year per house?" she replied, simply, "There are about a thousand students at Hogwarts."

And because she said it, this has persisted as the proper answer accepted by most fans. But I don't see how that could be correct.

So, let's do the math. There are four houses at Hogwarts, so if there are 1000 students, that means each house has 250 students in it (1000 divided by 4). There are 7 years at Hogwarts. So, if there are 250 students in each house, that means there are approximately 36 students in each year in each house (250 divided by 7 equals 35.7).

That means, if we assume there are approximately the same number of boys and girls in each year, that there are approximately 18 boys in Harry's year. But besides Harry, throughout all seven books, we've only ever seen four others (Ron, Neville, Seamus and Dean).

Another thing, we don't see a lot of actual classes at Hogwarts, but we see some in the course of Harry's adventures, and others are mentioned. On page 135 of Harry Potter and the Sorcerer's Stone (page 100 of Philosopher's Stone), Harry asks what class they have next, and Ron replies, "Double potions". We can't tell for sure from the books, but I've always assumed that "double potions" meant two houses together, as well as a double class time period. In any event, we can be sure from the books that a double class means the students of two houses together.

But that means, if we use the counts from above, that there would be about 72 kids in double potions class. That sounds like way more kids than would fit or could be handled in one classroom, even by Snape.

And, we've seen McGonagall call all her students into the Gryffindor common room for important announcements. I can see 70 kids stuffed into that room, but 250?

I know the movies are not cannon, but they also disagree with the above numbers.

This is an image from Sorcerer's Stone, from the sorting feast, the second before food appears on the table, and on some of the rows you can quite clearly count the number of empty plates on the tables (click on the image above to see the full-size image). As you can see, in the rows that can be completely counted, there are 33 plates on each side of the table, which would make 66 students per table. Even if that shot is not of the complete dining hall floor, it is certainly most of it, and even if there are few plates in the foreground that we cannot see, it still places the number of students per table in the 66-70 range.

I believe there are, indeed, 70 students at each table. Here is how I calculate the Hogwarts math:

We know that there are, including Harry, five Gryffindor boys in Harry's year at Hogwarts. Assuming that there are the same number of girls as boys, that means there are 10 students in Harry's year in Gryffindor at Hogwarts. Since there are 7 years, that means there are 70 Gryffindor students total at Hogwarts, and since there are 4 houses, that means there are only 280 students all together at Hogwarts. Quite a different number than J.K.'s thousand.

The number of students in our double potions class now makes a lot more sense, 10 Gyrffindors and 10 Slytherins makes 20 students, a very normal student class size, especially for a "lab" kind of course.

Another scene in the movie kind of agrees with my Hogwarts math.

This is the scene where the first years are following Percy up the stairs to Gryffindor Tower for the first time. If you look closely, not counting Percy who is right-most in the picture, there are 13 students. A few more than the 10 in my math, but a lot closer to my number than the 36 in J.K.'s count.

Do you think this count of 280 makes sense, or do you think there is evidence in the books that, as J.K. said, there are more students at Hogwarts?

And, if there are only 280 students at Hogwarts, how does that speak to the general population count of Wizards to Muggles? If there are only 280 kids in Hogwarts, how many wizarding families could there be in Britain? Or is it possible there are other wizarding schools besides Hogwarts?

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I tend to agree with this math, more or less. When you also consider that you only ever hear of 13 - 14 teachers at hogwarts each year.

Minerva McGonagall - Transfiguration
Pemona Sprout - Herbology
Severus Snape - Potions
Filius Flitwick - Charms
Various - Defence Against the Dark Arts.
Cuthbert Binns - History Of Magic
Aurora Sinistra - Astronomy
Charity Burbage - Muggle Studies
Bathsheda Babbling - Ancient Runes
Rubeus Hagrid - Care of Magical Creatures
Septima Vector - Arithmancy
Sybill Trelawney / Firenze - Divination
Rolanda Hooch - Flying

And the Following
Argus Filch - Caretaker
Rubeus Hagrid - Gamekeeper, Keeper of Keys and Grounds.
Irma Pince - Librarian
Poppy Pomfrey - Matron / Nurse

If indeed there are more pupils the school is seriously under staffed..

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