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Obviously it's not in billions. And magic is rare.

So, how rare might it be?
First I'll address some research arguments I found on link and gave some though to.

They seemed to conclude that there'd be approximately 300.000 to 1.000.000 magical people on the entire planet.
Basing on, for example:

”The room for 100.000 at the World Cup.”
Speculated to give some idea of the total number of magical people in the world...I guess because it's the World Cup and witches and wizards don't have televisions...This stadion room was believed to be for approx. 1/3 または 1/10 of the total world population of magical people.

I don't believe so.
Out of the billions of muggles only a tiny minority can attend a World Cup because a stadion can be only so big. Even with magic because no one would want to sit kilometers awy from the game feald which is already in itself quite large. So I think it's entirely possible that only a tiny minority of the world's wizarding population could attend the World Cup. Of course they don't have TVs but they may have something similar for such events as that - after all it is magic we're talking about.
And why would they hold a World Cup for a 人気 sport if everyone interested didn't have a chance to watch it in some way?
(Like someone once asked Rowling if witches and wizards use internet, she 発言しました they don't need to because they have their own way of keeping up with the world, または something like that. I don't know if she's ever explained that further.)

”The number of shops and stuff on Diagon Alley.”
Do we know what that number is exactly? Well, at least way over 100, that's for sure.
But yes, it's a small number. But also, let's remember that it's not the only magical shopping area in Great-Britain. There's also Hogsmeade and probably others the 本 didn't need to touch upon. They only needed one for ロンドン and one for Scotland near the school. But ロンドン alone is a HUGE city with its own inner countries and inner towns, and then there's the rest of England, the rest of Scotland, and then there's the entity of Wales and Northern-Ireland...And the rest of the world!
I'm sure there are a significantly larger number of all-wizarding shopping areas in UK alone not to mentione the whole world.
Diagon Alley is only 発言しました to be the center of the wizarding London. That doesn't mean much for numbers, in my view anyway.

”There were 40 children starting school in Harry's first year.”
Actually the 40 is only the number of kids Rowling thought up - those are her literal words, well something along that line anyway. So there may have been もっと見る that 年 - and surely the number must vary 年 によって year, especially as they do send an invitation to every single magical child turning 11 that year.
Whiloe not everyone sends their children to Hogwarts. Some may send them to other wizarding schools, または to muggle secondary schools and teach magic at ホーム instead.
So I don't hold Hogwarts starters on a specific 年 as a very reliable guideline for a total population.

My theory:

I don't believe there's any way the total population could be very low.
Because according to Rowling, wizards and witches have much longer life expetency than muggles. Ours is approximately 100 years. So theirs could be approx. 200 years. In fact, Rowling's original plan was that Dumbledore was 150 years old in the '90s. And he didn't seem very frail and aging to me which is why I imagine they could live at least twice as long as muggles.
And if Harry and Neville's parents and Harry, Ginny, Ron, Hermione, Draco and so on are anything to go by, wizards and witches are like us - tend to have their first children at a very young age. And seeing to how long they live, they may very well have もっと見る later, and later again.
I mean, surely there have been magical people in the ancient world just as there has been muggles. Magic in my opinion is something that's always existed.
And surely there are magical people born and raised in a culture where families like to have large numbers of children and don't care about birth control.
I mean, considering all that - 'rare' ought to be a huge number, most likely in at least five digits in all countries, probably in six digits in those that have tens of millions of people over-all.

Let's try it. (I hope I'm doing the math correctly.)

In 2012...
According to link, there was in total aprox. 64 million people in UK.
According to link, 18% of them were children under age 15.

Magic is rare. So let's say there were 400.000 magical people in the entity of UK.
- 64 million devided によって 400.000 = 160.
- 18% devided によって 160 = 0,1125%.
- So 0,1125% of 400.000 magical people were children under age 15.
- 1% would be 4000 children, but as that's some ten times less, it comes to approx. 400 magical children under age 15.
---> If some hundred of them turned 11 that year, it's possible only a few tens chose to start Hogwarts.

Sounds quite plausible, doesn't it?
I think it's entirely possibe that the total number of magical people could be even higher, perhaps..Keeping the total number of 11-years old kids per 年 likely within 200 または so, and again if only a few tens actually accept the invitation. A vision depends on how 人気 one wishes to imagine Hogwarts to be. I think tens our of a hundred might be too 人気 seeing to that the child would be far away from ホーム nine months of a 年 for up to seven years. And I don't think anything keeps あなた from taking courses as an adult, somewhere else.

Rowling's thrown a number too, I know; she's 発言しました there are some 3000 magical people in total, in the UK. Tenth of a percent of that would be 3. Three magical children under age 15 in 2012. And perhaps none of them turned 11. または even if all did. If the numbers were anywhere near that each year...I don't think Hogwarts would be a huge 城 for a number of kids あなた could count with your hands and toes. And even that many only if everyone always accepted the invitation and never quit before graduation. And seriously, no way a magical population of UK could've remained that low with their long age and tendency to have first children so early.
But Rowling has admited to be bad at thinking in numbers, and it's okay. She doesn't have to be good at it, we 愛 her and her brilliant universe and story to bits anyway. <3
And no I either did not just think this up in a heartbeat. I used some time and speculation and Google to come up with those numbers. And this was fun. :D

I believe that the total number of magical people in the UK is in six-digits and has been for many decades, as in also back in the '80s and '90s when the Harry Potter books' events took place. And therefore the case of the entire planet - is in a few millions among the total of billions of human beings.
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