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Population and Pupils: what we know or can deduce about the number of students attending Hogwarts, and the size of the wizarding population in general
In interviews, JK Rowling has apparently said, variously, that there were a thousand students at Hogwarts, and then that there were six hundred. These total figures would work out, respectively, to an average number of students per house per year of thirty-five, or twenty-one.
In a special interview with the BBC, JKR showed viewers an original cast-list which she had drawn up when she was first planning the books, showing everybody in Harry's year. See also this analysis of the information displayed in the notebook. Although there are only eight Gryffindor students in Harry's year named in the books, JKR has apparently said that there are two more girls, although she has never given us their names, and that there are ten students per house in Harry's year. The list from her notebook shows forty-one students, who include the eight Gryffindors we know about, and eight students whose house is not visible in the image, two of whom may be the missing Gryffindors.
It would not be at all surprising if Harry's year was unusually small, because they were conceived when Vold War One was reaching fever pitch. There were instances during VWI where whole families were killed and although all the cases we known the details of were families of members of the Order of the Phoenix, and possibly killed as collateral damage rather than directly targeted, the general public might not know that. People tend not to have children if they can avoid it if they fear they are likely to be murdered in their cots. If so, you would expect the year below Harry's (and perhaps the year above) also to be very small.
The year two below Harry's would probably be of about average size, but it would be heavily weighted towards children born in July and August, i.e. conceived during the celebrations just after Voldemort's fall. The year three below Harry would be very large, because it would be full of children whose planned conception had been put off until after the war. That bulge would probably balance out the small year one below Harry so that on average you could say that by the time Harry gets to fourth year the school has on average one small and six normal-sized years (in actual fact two small, one large and four normal).
However, even assuming that Harry's year is abnormally small it seems unlikely that it would be so very small that there were only forty students, when JK's own minimum estimate of students at the school (six hundred) would result in an average year-size of eighty-six. And in fact, the internal evidence within the books suggests that Harry's year is considerably larger than forty students.
Thursday afternoon's lesson proceeded in the usual way. Twenty cauldrons stood steaming between the wooden desks, [CoS ch. #11; p. 140]
The joint Gryffindor/Slytherin Potions and broom-riding classes in Harry's year add up to twenty students. If there are eight Gryffindors then there are twelve Slytherins; if ten Gryffindors, ten Slytherins.
The joint Gryffindor/Hufflepuff class in Harry's year adds up to about nineteen students (there are about twenty pairs of earmuffs, but one pair must be for Professor Sprout). If there are eight Gryffindors then there are "about" eleven Hufflepuffs; if ten Gryffindors, "about" nine Hufflepuffs.
We are not told which other house or houses Gryffindor are paired with for fifth-year Defence Against the Dark Arts, but there appear to be thirty-one students in the class. Assuming that nobody is off sick, the possibilities are as follows: a) The class consists of ten Gryffindors, ten Slytherins and eleven Ravenclaws, and Hufflepuff do a class on their own. b) The class consists of eight Gryffindors, twelve Slytherins and eleven Ravenclaws, and Hufflepuff do a class on their own. c) The class consists of ten Gryffindors, nine Hufflepuffs and twelve Ravenclaws, and Slytherin do a class on their own. d) The class consists of eight Gryffindors, eleven Hufflepuffs and twelve Ravenclaws, and Slytherin do a class on their own. e) The class consists of eight Gryffindors, eleven Hufflepuffs and twelve Slytherins, and Ravenclaw do a class on their own. f) The class consists of ten Gryffindors and twenty-one Ravenclaws. g) The class consists of eight Gryffindors and twenty-three Ravenclaws. h) The class consists of all four houses, but so many people have left school by fifth year that there are only thirty-one left in the year. i) The class consists of all four houses, there are forty or so people in the class, but only thirty of them are interested in what Harry has to say. Option i) seems most unlikely, given the general interest in Harry's experiences. It also seems unlikely that so many students have left or are off sick that there are only thirty-one students left, without JK having commented on this. It's possible that the class is a three-house class and one house gets taught on their own but that seems very odd from a scheduling point of view, when we otherwise see either single-house or two-house classes. So that leaves us with the most likely option being that the DADA class is joint Gryffindor and Ravenclaw. If that's true we have either: 8 Gryffindors, 12 Slytherins, 11 Hufflepuffs and 23 Ravenclaws, making 54 students in all, or 10 Gryffindors, 10 Slytherins, 9 Hufflepuffs and 21 Ravenclaws, making 50 students in all.
Option i) seems most unlikely, given the general interest in Harry's experiences. It also seems unlikely that so many students have left or are off sick that there are only thirty-one students left, without JK having commented on this.
It's possible that the class is a three-house class and one house gets taught on their own but that seems very odd from a scheduling point of view, when we otherwise see either single-house or two-house classes. So that leaves us with the most likely option being that the DADA class is joint Gryffindor and Ravenclaw. If that's true we have either:
8 Gryffindors, 12 Slytherins, 11 Hufflepuffs and 23 Ravenclaws, making 54 students in all, or 10 Gryffindors, 10 Slytherins, 9 Hufflepuffs and 21 Ravenclaws, making 50 students in all.
At the big Quidditch match in the summer of Harry's third year, there are about eight hundred spectators, of whom two hundred support Slytherin.
If there are indeed two hundred students per house, that would give an average of twenty-nine students per house per year, which would make Harry's year really exceptionally small. However, we do not know that all the spectators were current students. Given that it was an important match - important enough for Snape to appear in public wearing green robes! - it seems quite possible that some former students and/or Hogsmeade residents came along to watch. Considering what a popular sport Quidditch is, it seems unlikely that Hogsmeade residents wouldn't turn up to a live Quidditch match on their doorstep.
Once breakfast was over, the fifth- and seventh-years milled around in the Entrance Hall while the other students went off to lessons; then, at half past nine, they were called forwards class by class to re-enter the Great Hall, which had been rearranged exactly as Harry had seen it in the Pensieve when his father, Sirius and Snape had been taking their OWLs; [OotP ch. #31; p. 627]
During the bullying sequence which Harry sees in the Pensieve, we see Snape's year sitting their Defence Against the Dark Arts OWL, and there are more than a hundred students present - and enough more than a hundred that Harry can see at a glance that there are more than a hundred, so probably about a hundred and twenty. These may not all be taking OWLs because in Harry's year we see that an OWL group and a NEWT group sit exams at the same time, so there are probably not a hundred and twenty students just in the Marauders' year.
At the same time, there probably are more than sixty. No class is compulsory at NEWT, so even a popular NEWT subject is going to have significantly fewer students taking it than take a compulsory OWL, assuming the year sizes to be roughly equal - and that's not even to mention the fact that you'd expect quite a lot of students to leave school after OWLs. Despite the doubling-up of the exam timetable at the end of Harry's third year (which was of course done just to draw attention to the fact that Hermione was doing something strange with her time), it seems unlikely that NEWTs in two different subjects would be held at once, unless nobody who was taking Subject A was also taking Subject B - and that would only happen if both classes were unpopular and had few people taking them, or the class for one subject was so tiny - say, two students - that it happened by concidence/statistical drift not to overlap with a more popular class.
So, whether the NEWT students who were present when the Marauders sat their OWLs represented one popular class or two or more very unpopular classes, they would still have made up a significantly smaller number than the entire year's-worth of OWL students who were sitting a compulsory DADA exam, and the OWL students would still have made up a lot more than half of the hundred and twenty or so students who were in the hall. And that means that there were significantly more than sixty students in the Snape/Marauders year: probably about seventy-five. Or more, up to about ninety, if the NEWT which was being sat at the same time was an unpopular one.
Harry, Ron and Hermione followed the rest of the school out onto a rough mud track, where at least a hundred stagecoaches awaited the remaining students, each pulled, Harry could only assume, by an invisible horse, because when they climbed inside and shut the door, the coach set off all by itself, bumping and swaying in procession. [PoA ch. #05; p. 68]
A hundred horseless carriages stood waiting for them outside the station. Harry, Ron, Hermione and Neville climbed gratefully into one of them, the door shut with a snap and a few moments later, with a great lurch, the long procession of carriages was rumbling and splashing its way up the track towards Hogwarts castle. [GoF ch. #11; p. 151]
A short distance away, Draco Malfoy, followed by a small gang of cronies including Crabbe, Goyle and Pansy Parkinson, was pushing some timid-looking second-years out of the way so that he and his friends could get a coach to themselves. [OotP ch. #10; p. 178]
'I was saying, what are those horse things?' Harry said, as he, Ron and Luna made for the carriage in which Hermione and Ginny were already sitting. [OotP ch. #10; p. 179]
All students who travel on the Hogwarts Express, except first years, are taken from the station to Hogwarts in a hundred or so carriages. These carriages are filled with students - they apparently do not have to carry luggage, which is conveyed separately. The trunks might be loaded onto some of the carriages by magic, of course, but it does sound as if we are meant to understand that the carriages are just there to carry students.
At various times we see coaches taken by Harry, Ron and Hermione; by Harry, Ron, Hermione and Neville; by Harry, Ron, Hermione, Ginny and Luna and by Draco, Pansy, Crabbe, Goyle and at least one other. This admittedly not very large sample gives an average of four and a quarter students per carriage, or four hundred and twenty-five students in years two to seven and travelling in by train and thestral-drawn carriage.
If there is an error in this calculation it's probably in the direction of being too low. We know that the carriages are fairly well-filled because Draco and co., a party of five or six, have to dislodge someone else in order to be sure of getting a carriage to themselves and it does say "to themselves", not just getting a carriage which they could all fit into. The implication is both that all the carriages have at least somebody in them and that more than five or six people could fit into them, so that four hundred and twenty-five students is a conservative estimate.
Harry's year is unusually small and probably has around fifty-four students in it. Take those fifty-four away and we have around three hundred and seventy students, maybe a few more, in five years. That gives an average of eighteen and a half students per house per year, except in Harry's year which only averages thirteen and a half. Assuming a normal first year is the same sort of size, this gives us about five hundred students at the school, arriving by train.
[If we assume that for some reason Umbridge is teaching a three-house class, then there may be as few as forty-one students in Harry's year, but that makes hardly any difference - nineteen students per house per year, except Harry's year, and five hundred and two total students instead of four hundred and ninety-eight.]
One thing we do not know is whether the students who come in by train are all the students there are. The whole matter of the Hogwarts Express and Platform 9¾ is problematic: are we to understand that students who live in Glasgow or Durham have to travel all the way to London before they can get on the train, or does the train make stops to pick them up, which we haven't been told about? My theory is that major stations throughout Britain have their own version of the walk-through barrier, and they all lead to King's Cross on the magic side even if the mundane side is in Birmingham or Aberdeen.
However, given that Hogsmeade is a purely wizarding village, and large enough to maintain a substantial shopping centre, there must be a fair number of children at Hogwarts whose families live in Hogsmeade. It seems unlikely that children who live almost on the castle's doorstep would be expected to go all the way to London and then take a ten-hour train-ride back, so there may well be a significant number of Hogsmeade-born students who do not come in by train and by those hundred not-really-horseless-at-all carriages. [I would expect, however, that first-years who live in Hogsmeade do come down to the station to meet the train, so they can be carried across to the castle by boat.]
Although we haven't been told about it, it's also possible that students from Hogsmeade do not board but go home every night. This might explain why JKR says there are five Gryffindor girls in Harry's year and yet we only ever see three; if the other two live out they would not be in Hermione's dormitory and would not be as much part of the social life of Gryffindor as the boarders are.
What is the population of Hogsmeade? Well, as a rough rule of thumb, where I live in south-central Scotland there are two villages very close together, which between them have ten thousand residents and at least seven pubs, or about one pub per fourteen hundred inhabitants. One pub per fourteen-hundred-head of population seems reasonable. Hogsmeade has two pubs, and that might suggest about two thousand eight hundred residents. However, those two pubs serve a substantial tourist trade, as well as the locals, so the resident population of Hogsmeade is probably only around two thousand.
How many Hogswarts students should there be among two thousand wizards and witches? Examination of all witches and wizards for whom an age at death is given on the Harry Potter Lexicon (discounting the Flamels, who are anomalous) suggests that the average lifespan of a witch or wizard is seventy-seven years. The efficiency of wizarding medicine means there probably aren't a lot of childhood deaths, and their efficient medicine and their apparently greatly increased lifespan (as far as ageing goes) means that if they are tending to die at seventy-seven a high proportion of them are dying of things like potions accidents, not age or heart disease, so there shouldn't be much tailing off of population as they get older, so the distribution of individuals across aged zero to seventy-seven should be fairly even.
If their population is stable, that should mean that children in the seven years of Hogwarts-age make up one eleventh of the wizarding population. If that's wrong it will tend towards a higher proportion of children, as is the case with Muggle population demographics, so we can say that Hogwarts'-age children make up at least one eleventh of the population of the village. If Hogsmeade has about two thousand residents that means around one hundred and eighty children of Hogwarts age.
Some of those will be Squibs (and in Hogsmeade there are no compensatory Muggle-borns to make up the numbers), and some will simply choose not to go to Hogwarts, although given how handy it is there probably won't be many of those. So at any given time there should be at least about a hundred and forty students (i.e. about twenty per year) at Hogwarts who come from Hogsmeade and who probably don't come in on the Hogwarts Express.
If there are really eight hundred students then Harry's year seems to be exceptionally small - even more so if there are a thousand.
If, however, we discount JKR's initial estimate of a thousand students as just bad math, and go with her later figure of six hundred, that ties in quite well with an estimate derived from the number of carriages used to transport students from the train, and the population of Hogsmeade. That gives us a student body of around six hundred and forty during Harry's time at Hogwarts, and since Harry's year - conceived when Voldemort was at his most threatening - is clearly unusually small, in other decades the number would be closer to six hundred and sixty. Not all of these, however, have to be accommodated in the dormitories, as there should be around twenty Hogsmeade students per year and these probably live out.
For each house, then, there should be an average of around twenty-three or twenty-four students in a normal year, of whom about five are from Hogsmeade and probably live out. Taking the four houses together, in a normal year there should be about ninety-four students.
Harry's year is probably so unusually small because they are children conceived at the height of Voldemort's power. Witches and wizards presumably have better contraception than Muggles, so they would have the power to choose not to bear a child into a world at war, and probably many would so choose.
It's likely that the year below Harry's (Ginny and Luna's year) is also small. The year below that would be small to normal-sized but heavily weighted towards students born towards the end of the academic year, since there would be a low number of conceptions before Voldemort's fall and sharp rise after it as people celebrated, resulting in a rash of births in late July and August 1982. The year after that would probably be unusually large, thus balancing out the small year just below Harry.
So although the distribution between years would be uneven, by the time Harry reaches fourth year it is possible to work out the numbers as if there was one small year (Harry's) and the rest were fairly average, even though it would really go: 1st year - very large 2nd year - small to average, weighted towards July and August births 3rd year - very small 4th year - very small (Harry's year) 5th year - small to average 6th year - average 7th year - average
During Harry's time at Hogwarts there are probably only about six hundred and forty students, plus about fourteen members of staff (Dumbledore, McGonagall, Snape, Sprout, Flitwick, Vector, Sinistra, Burbage, Trelawney, Hooch, Hagrid, Pince, Filch and the current DADA teacher), so the crowd of around eight hundred who attended the Quidditch match in PoA included over a hundred and thirty extra spectators - and they didn't include the castle's hundred house elves, or Hermione wouldn't have been so surprized to learn about them in GoF. So clearly, former students or Hogsmeade residents or both come to the major matches. Given the popularity of Quidditch, and the apparently paucity of wizarding entertainment, it would certainly not be surprising if the villagers took any opportunity they could get to watch an exciting match which is taking place on their doorstep.
There is also another way of looking at the numbers, and that's by considering the wizarding population at large.
JK Rowling said in an interview somewhere that there were only about three thousand wizards in Britain, but if we believe that it creates all manner of problems. [Unless, of course, you take it extremely literally as three thousand adult males over the age of seventeen and qualified to perform magic, which is close to being feasible.]
The population of Britain is getting on for 59 million, so if there were only 3,000 witches and wizards in Britain, the Muggle population would out-number them nearly 20,000 to one.
The Unites States has not produced as many world-class Quidditch teams as other nations because the game has had to compete with the American broom game Quodpot. [QTtA ch. #08; p. 44]
A hundred thousand wizards turn up at the Quidditch World Cup. The world population is about 66 American billions (thousand millions). If that proportion of nearly 20,000 Muggles to one wizard was preserved worldwide, that would mean that there were less than 340,000 witches and wizards worldwide, and the hundred thousand who turned up at the Quidditch World Cup represented nearly 30% of the entire wizarding world. I know it's a popular sport, but that's ridiculous: especially since a sizeable proportion (4.5%, if it follows the same pattern as Muggles) of the world's wizards must be in the U.S.A. and we are told that U.S. wizards don't tend to follow Quidditch.
[cut] hundreds of witches and wizards [cut] strode towards a set of golden gates at the far end of the hall. [OotP ch. #07; p. 117]
They were in what seemed to be a crowded reception area where rows of witches and wizards sat upon rickety wooden chairs [cut] Witches and wizards in lime-green robes were walking up and down the rows, asking questions and making notes on clipboards [OotP ch. #22; p. 427/428]
'Ward forty-nine, but I'm afraid you're wasting your time,' said the witch dismissively. [OotP ch. #22; p. 430]
[cut] 'come to number ninety-three, Diagon Alley -- Weasleys' Wizarding Wheezes,' he said in a loud voice. 'Our new premises!' [OotP ch. #29; p. 595]
'We must be close, that's number ninety-two … ninety-four …' 'Whoa,' said Ron, stopping in his tracks. Set against the dull, poster-muffled shop fronts around them, Fred and George's windows hit the eye like a firework display. [HBP ch. #06; p. 113]
'Women!' he muttered angrily, sloshing down the rain-washed street with his hands in his pockets.' [cut] He turned right and broke into a splashy run, and within minutes he was turning into the doorway of the Three Broomsticks. [OotP ch. #25; p. 497]
Also, the Ministry, St Mungo's, the Diagon Alley/Knockturn Alley complex and Hogsmeade are each fairly large. The Weasley twins' shop, for example, is no #93 Diagon Alley and there's no indication it's even at the end of the street: Harry's party find it by counting street-numbers, not by just going to the far end of the alley. Indeed, the fact that they have to read the numbers to check that they are getting close strongly suggests that no #93 isn't close to the end of the street.
So we have at least a hundred shops in Diagon Alley, probably more, and probably as many again in Knockturn Alley, and many of those shops are large ones with multiple staff. The Ministry is a large, multi-storey building which is bustling with employees (Harry sees hundreds coming in to work and it's very unlikely that he sees the entire staff all in one go) and also has staff posted elsewhere (such as the Aurors based in Hogsmeade). It can afford to assign five hundred employees for a whole year to work on the setup for the World Cup (human employees, not house-elves, because they were working on Muggle-Repelling Charms), and still have enough staff to keep its other functions going - although some of the five hundred who work on the World Cup may be short-term hires. St Mungo's is also a fair-sized, multi-storey hospital with plenty of staff and at least forty-nine wards.
It's obvious that Hogsmeade also is not tiny, for a village - we're not talking twenty houses here. It takes Harry minutes to get from the turning up to Madam Puddifoot's to the Three Broomsticks, even at a run. For reasons stated above, Hogsmeade probably has a population of around two thousand. Many of the residents have already been counted because they work for St Mungo's or the Ministry, but in addition to the shops we are told about that the students frequent there must be a lot of businesses servicing the village itself - groceries, barbers and so on - all with employees, plus there will be children, elderly people, the unemployed and housewives/husbands who haven't been counted elsewhere. There are also sizeable magical communities in Tinworth, Upper Flagley, Ottery St Catchpole and Godric's Hollow and again, some of their residents will not have been counted elsewhere as workers at the wizarding institutions in London.
Harry looked into the stands. Colin was sitting in one of the highest seats [CoS ch. #07; p. 85]
Five minutes later, the stands had begun to fill; the air was full of excited voices and the rumbling of feet as the hundreds of students filed into their seats. [GoF ch. #31; p. 538]
We can surmise that the population of Hogwarts School is also quite large, quite apart from the calculations of class size etc. given above, from the fact that the Quidditch stadium has seating for over a thousand spectators. We know this because we know from Quidditch Through the Ages that the pitch was established as being five hundred feet long and a hundred and eighty feet wide in the fourteenth century, and although there have been subsequent changes to the goals etc. there's no mention of any change in size. That means the pitch has a perimeter over 1,100ft long - more if there is an offside strip between the pitch and the benches, which there probably is. We know that there are at least three tiers, because the mention of a "highest" tier implies the existence of at least a lowest and a middle tier. If the seating goes all the way around the pitch - which it seems to do, judging from a sketch which JK Rowling drew - that's over 3,300ft of benches. Even if you take a bit off for the entrances and the changing rooms, that's still a lot of seats.
The seating is wooden (we know because feet echo on it), so it's unlikely to be more than a hundred and fifty years old, and there's been no indication that the population of wizarding Britain, or of the school, has dropped enormously in that time. If there was a need for anything like a thousand seats when it was built, there still is.
So we’ve got:
Hogwarts: around six hundred and seventy-five students and staff at any one time.
The Ministry of Magic: probably about a thousand staff, since they were able to spare five hundred workers for a year and still function and there are ten floors at the Ministry building in London, eight of them with large numbers of rooms and presumably staff to fill them.
St Mungo's: probably two or three hundred inpatients in St Mungo's at any one time (given that there are at least forty-nine wards) and around two hundred staff, since they need medical staff on the wards, medical staff to see to outpatients, potion-makers, receptionists, medical researchers, administrators and people to perform the "hotel" functions of preparing food, washing sheets and cleaning wards (although some of these people may be house-elves).
Diagon Alley and Knockturn Alley: at least another five hundred or so, even if the buildings are all just businesses and no residential accommodation. And that's assuming that Diagon Alley has only a hundred shops and Knockturn Alley only fifty and that there are an average of around three workers per shop, all of which is likely to be a severe underestimate.
At least fifteen hundred people who live and/or work in Hogsmeade, Tinworth, Ottery St Catchpole, Upper Flagley and Godric's Hollow and haven't been counted elsewhere.
Even allowing for the fact that most of the patients in St Mungo's double up as residents elsewhere, and that many of the people who live in Hogsmeade will also work at the Ministry or St Mungo's, the staff and residents of Hogsmeade, Diagon Alley, Knockturn Alley, the Ministry, St Mungo's and Hogwarts must between them add up to about four thousand people, minimum, before you even start on the people that live out in the Muggle community or in their own separate houses and business enterprises (as we know the Malfoys, the Blacks, the Lovegoods etc. do). And that's assigning minimum sizes to Diagon and Knockturn Alley which are probably gross underestimates, and assuming that there are no actual residents in these streets.
A friend of mine who's something of a mathematical genius estimated the British wizarding population at around sixty thousand. That's probably going too much the other way: since JK has indicated that the wizarding population is very small (even though it can't possibly be as small as she said) we want to go with the lowest figure we can get away with. I don't see how that could be any less than a minimum of nine to ten thousand.
'Original Order of the Phoenix,' growled Moody. 'Found it last night' [cut] 'There's me,' said Moody, unnecessarily pointing at himself. [cut] 'And there's Dumbledore beside me, Dedalus Diggle on the other side ... that's Marlene McKinnon, she was killed two weeks after this was taken, they got her whole family. That's Frank and Alice Longbottom --' [cut] '-- poor devils,' growled Moody. 'Better dead than what happened to them ... and that's Emmeline Vance, you've met her, and that there's Lupin, obviously ... Benjy Fenwick, he copped it too, we only ever found bits of him ... ' [cut] 'That's Edgar Bones ... brother of Amelia Bones, they got him and his family, too, he was a great wizard ... Sturgis Podmore, blimey, he looks young ... Caradoc Dearborn, vanished six months after this, we never found his body ... Hagrid, of course, looks exactly the same as ever ... Elphias Doge, you've met him, I'd forgotten he used to wear that stupid hat ... Gideon Prewett, it took five Death Eaters to kill him and his brother Fabian, they fought like heroes' [cut] 'That's Dumbledore's brother Aberforth, only time I ever met him, strange bloke ... that's Dorcas Meadowes, Voldemort killed her personally ... Sirius, when he still had short hair ... and ... there you go, thought that would interest you!' Harry's heart turned over. His mother and father were beaming up at him, sitting on either side of a small, watery-eyed man whom Harry recognised at once as Wormtail, the one who had betrayed his parents' whereabouts to Voldemort and so helped to bring about their deaths. [OotP ch. #09; p. 157-159]
'You weren't in the Order then, you don't understand. Last time we were outnumbered twenty to one by the Death Eaters and they were picking us off one by one ...' [OotP ch. #09; p. 161]
There is another factor to consider. Lupin says that towards the end of the first Voldemort war the Death Eaters outnumbered the Order by about twenty to one - although it's possible he is talking about Voldemort's entire forces, not just actual Death Eaters. Sirius confirms that Voldemort's army at that time was very large, although he is definitely including non-humans in that.
When Moody shows Harry the photograph of the original Order he names twenty-one people appearing in the image: Moody himself; Dumbledore; Dedalus Diggle; Marlene McKinnon; Frank and Alice Longbottom; Emmeline Vance; Lupin; Benjy Fenwick; Edgar Bones; Sturgis Podmore; Caradoc Dearborn; Hagrid; Elphias Doge; Gideon Prewett; Dumbledore's brother Aberforth; Dorcas Meadowes; Sirius; James and Lily Potter and Peter Pettigrew. It's not clear whether Fabian Prewett was also an Order member/in the photograph or not, but against this there may have been more Order members who weren't in the photograph, or who were but whose names are simply not mentioned by Moody. According to what Dumbledore said to Sirius, Arabella Figg and Mundungus Fletcher were certainly members. Kingsley Shacklebolt, Ted and Andromeda Tonks and Arthur Weasley may well have been members as well, although we know that Molly was not, and even without them there were at least twenty-three: the twenty-one named by Moody as being in the photograph, plus Arabella and Mundungus..
Five of those twenty-three were dead before the night of Voldemort's fall: Marlene McKinnon; Benjy Fenwick; Edgar Bones; Gideon Prewett and Dorcas Meadowes . But assuming that the people Moody doesn't specify as having died survived, there were at least eighteen Order members left when Voldemort fell, not counting Snape since Lupin didn't know about him at the time, but including the Potters, since they were living Order members until a few minutes before Voldemort's fall.
[Caradoc Dearborn disappeared after Voldemort's downfall. We know this because in a letter written in August 1981, soon after Harry's birthday and only two and a half months before Voldemort's fall, Lily referred to the death of Marlene McKinnon as being a very recent event. We know from what Moody says that Caradoc disappeared five and a half months after Marlene was killed.]
He had reached the largest gap of all, and he stood surveying it with his blank, red eyes, as though he could see people standing there. 'And here we have six missing Death Eaters ... three dead in my service. One, too cowardly to return ... he will pay. One, who I believe has left me for ever ... he will be killed, of course ... and one, who remains my most faithful servant, and who has already re-entered my service.' [GoF ch. #33; p. 565]
[cut] and what use would it be, even if he could, to deprive Voldemort of his wand, when he was surrounded by Death Eaters, outnumbered by at least thirty to one? [GoF ch. #34; p. 572]
[cut] Cornelius Fudge, Minister for Magic, confirmed that ten high-security prisoners escaped in the early hours of yesterday evening [OotP ch. #25; p. 481]
That means that if Lupin is right about being outnumbered twenty to one, and he really did mean that they were thus outnumbered by actual Death Eaters, there were about three hundred and fifty Death Eaters. If Lupin means that they were outnumbered twenty to one when the Order still had at least twenty-three members, there were over four hundred and fifty Death Eaters. However, he probably does mean Voldemort's whole army, rather than Death Eaters as such: even though his statement doesn't sound like that.
In the graveyard scene at the end of GoF, Harry thinks of himself as outnumbered "at least" thirty to one, so there are clearly over thirty Death Eaters present at that point (if there were almost exactly thirty it would look like "about thirty to one", not "at least thirty to one") - say thirty-five, maybe forty.
The circle in the graveyard leaves gaps for the dead - probably for those who died since the last time they met, some time just before Voldemort's original fall (otherwise you'd expect a lot more gaps, from what we've been told about the Ministry's shoot-to-kill policy). There is a six-wide gap, which is the largest gap in the circle, which includes three who are dead. We know that this six-wide gap, and the gap for the Lestranges, aren't the only gaps in the group because there are ten living Death Eaters in Azkaban, who will later escape, so there must be gaps left for eight more prisoners, and an unknown number of gaps left for other Death Eaters who have died, whether in Azkaban or of other causes.
But there probably aren't a huge number of others missing and who haven't been mentioned. If there were enough gaps in the circle to fit thirty people, the remaining thirty-five to forty would look like an untidy rabble rather than an organized ring.
So the number who might have come - the number the circle is arranged for, the number Tom presumably had at the end of the war - is these thirty-five or forty, plus sixteen missing that we definitely know about - the ten who are alive in Azkaban, Barty, Snape, Karkaroff, three specified but unnamed dead - and probably a few more dead whose empty slots are not commented on.
That suggests that at the end of VWI the Death Eaters numbered between about fifty-five and seventy - unless there are many more dead for whom spaces have not been left. But why leave spaces then just for the three Tom mentions? Could they be three of whose deaths the rest of the circle was not aware?
Unless there were well over two hundred Death Eaters killed during the last few months of Vold War One or dead since, and for whom spaces have not been left, Lupin's statement about being outnumbered twenty to one by the Death Eaters must include Sirius's "witches and wizards he'd bullied or bewitched into following him"; and probably the Dark creatures Tom also recruited, if he's using the term "Death Eater" so loosely.
We know that there probably really were a lot of Death Eaters killed by Aurors or dead in Azkaban; but if well over two hundred had been killed, out of a total of around four hundred, you'd think that people wouldn't speak as if Voldemort had still been at the height of his power when he fell. So we must assume that Lupin's three hundred and fifty plus refers to Tom's whole army, or at least the human part of it.
Even so, unless Tom's army was mostly Dark creatures (which it probably wasn't because Sirius lists them in third place, not first), even if that four hundred or so "Death Eaters" included other human followers plus Dark creatures, there must have been around two hundred or more human followers. If the wizarding population was only three thousand, that would mean that one person in fifteen was a Death Eater or Death Eater supporter (whether voluntary or otherwise). This seems ridiculously high when you consider that even in its heyday in the 1920s, the British Fascist Party never managed more than about 50,000 members, out of a target population of 49 million (that is, just over one person in a thousand), and had fallen below 8,000 members (less than one person in every six thousand) by the mid 1930s.
If there are ten thousand wizards then about one person in fifty was a Death Eater or fellow-traveller at the height of Voldemort's power - still very high, but not quite so insanely so.
A population of ten thousand would mean that Muggles outnumbered magic folk in Britain by about 5,566:1. If the same proportions were maintained worldwide it would mean a world wizarding population of a little over a million, and 8.4% of that population turning up at the World Cup. That's feasible, given that it's a popular sport and international travel for wizards seems to be fairly easy and cheap.
All eligible British wizarding children are offered a place at Hogwarts. Of course some wizarding children are Squibs and so not eligible but they will be more or less balanced by Muggle-born children coming in from the outside. However, presumably some families don't want to send their children away to boarding school, and some children will want to specialize in Muggle subjects not taught at Hogwarts, such as maths or music. We can be pretty sure that there are no other sizeable wizarding schools in Britain (see British References in the Harry Potter books) but you would certainly expect at least one in Eire, and there may also be a system of apprenticeship for the less academically-minded.
If we go with the idea that Hogwarts'-age children make up one eleventh of the wizarding population, for the reasons described above, and assume that there are about ninety-four students per year at Hogwarts and that two thirds of all eligible children go there, that also equates to a British wizarding population of just over ten thousand.
We certainly don't want there to be much fewer than ninety-four students per year, since we want to arrive at a wizarding population of at least ten thousand. The only way Hogwarts could be much smaller than that would be if far fewer than two thirds of the eligible children go there: which would certainly suggest the existence of other schools which we know, for the reasons given in British References in the Harry Potter books, is very unlikely.
