How many Inari jinja are there in Japan?
Tl;dr: 3,000 and 30,000 and 300,000 are all possible answers, depending on what you count as an “Inari jinja”.
It is very common to see the claim that there are more Inari jinja than any other single kind, both in English and in Japanese, and there are various specific claims about the number. For example, Fushimi Inari Taisha, the original Inari jinja in Kyoto, says on their website that “There are said to be about 30,000”. You might think that they would know, but in fact the phrasing indicates that they do not. They use the standard way of expressing something that you cannot actually confirm.
I can’t do any better, but I want to explain why, because the reasons are interesting.
First, let’s take the Inari jinja that are easiest to count: the Inari jinja that are legally incorporated as religious corporations. Even this is a bit tricky, because not all Inari jinja have “Inari” in their name. Still, it looks as though most of them do, so it is possible to make a count. About fifteen years ago, Kokugakuin University did, based on Jinja Honchō’s list of affiliated jinja.
They counted 2,970 Inari jinja across Japan.
Now, that is not all Inari jinja — for starters, it doesn’t include Fushimi Inari Taisha, which is not affiliated to Jinja Honchō. However, the government’s Culture Agency website tells us that there are about 85,500 Shinto-related jinja-like religious corporations in Japan. About 79,000 of them are affiliated to Jinja Honchō (which means that there are at least 76,000 that are not Inari jinja), which leaves 6,500. They are not all Inari jinja. Nikkō Tōshōgū is not affiliated to Jinja Honchō either (at least, not last time I checked), and those 6,500 also include the jinja affiliated to all the varieties of sect Shinto and Shinto new religions. The overwhelming majority of those are not connected to Inari. We can probably exclude those by looking at the jinja that aren’t affiliated to any national organisation, which brings us down to about 2,000. Again, I know that those are not all Inari Jinja, but it does let us set a maximum.
There are no more than 5,000 Inari Jinja in Japan that are religious corporations, and almost certainly substantially fewer.
This means that they are certainly outnumbered by incorporated Hachiman jinja (around 8,000), and probably by Tenjin jinja (about 4,000) and those enshrining Amaterasu Ōmikami (about 4,500).
However, this is not the only kind of jinja. There are also smaller jinja, called sessha or massha, in the precincts of a main jinja. Almost all jinja have these (Meiji Jingū in Tokyo is a notable exception), and it is very common for them to be Inari jinja.
The first question is whether these should be counted as jinja. I think the best answer is “yes”. They normally have their own buildings, and their own matsuri, and so the fact that they do not have their own legal corporation is not that important.
The second question is “how many of them are there?”. And this is where I cannot say. In total, covering all varieties, probably over 200,000, but even that is a guess. (Smaller religious corporation jinja do not necessarily have any, but Jingū has 124. An average of about 2.5 per religious corporation does not strike me as unreasonable, but it is only a guess.) I do not think that there are any centralised records of this, and it is the sort of thing that might vary by region, so doing a count around Kawasaki would not help much.
If we focus our attention on Inari jinja in this category, 30,000 is not an unreasonable number. That would mean there were Inari sessha or massha at fewer than half of the incorporated jinja in Japan. I have no idea what the number might actually be, but someone else’s guess for the number of sessha and massha is the most likely source for the “30,000” number.
There is still a problem. Certainly around Tokyo, it is not uncommon for a large house to have a small Inari jinja in the garden. Those jinja are found across the country, although the dedication may be different in different regions — Inari has historically been more popular in eastern Japan, and was notoriously popular in Edo, the old name for Tokyo. And then there are small wayside shrines to Inari, with a couple of fox models and maybe some abura-agë (deep-fried tofu, as an offering).
Do we count those? Are they jinja? I’m not sure exactly where to draw the line here. There is a tradition that would say “no” for the garden jinja (they are not publicly accessible) and “yes” to the wayside ones (because they are), but you could certainly make an argument for different lines. However, if we do include them, I suspect that 30,000 is low. It could even be very, very low. 300,000 is right at the top end of what I would think is possible, but I would not want to rule it out without some evidence. On the other hand, I have no idea how one would even make a start at counting these. (Actually, that’s not true. I do know how one would do it. One would get government funding and graduate students. The graduate students would walk around Japan, counting them one by one. Do a hundred areas across the whole country, and you could get a reasonable estimate without having to actually count every single example.)
Thus, this question is difficult to answer because there is no clear and indisputable definition of what counts as an Inari jinja, and no-one keeping central records on any definition. This is typical of problems in Shinto.