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An often repeated meme about Harry Potter is that JK Rowling is 'bad at math'.

I see this all over this site and the saying is probably used elsewhere.

The following is said, in the comments for the selected answer for "How had the Potters 'thrice defied him'?"

Hasn't it been mentioned before that JKR has said she is bad with math? And here she says she counts. Almost scary.

And apparently JK Rowling agrees in another question "What is JK Rowling “bad” at?"

JKR: In the world? Oh, Emerson, my maths is so bad.

Are there any particular examples that drive this meme?

Why is JK Rowling considered so 'bad at math'?

Rand al'Thor
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Mark Rogers
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Dates

From alexwlchan's excellent answer here (emphasis mine):

I know that Harry Potter Wikia isn’t usually considered canon, but they have a list of dating contradictions which looks fairly accurate. To me, most of this list can be written off as JK Rowling's dodgy maths, but I thought I'd pick on one example.

For example, in Goblet of Fire, we have Friday the 30th of October and Tuesday the 22nd of November. If you look at a calendar, you see that 22 Nov falls 23 days after 30 Oct, so the 22nd is a Sunday in the Gregorian calendar. There are many possibilities:

  1. Whoops, JK Rowling messed up.
  2. Their weekdays occur in a different order to ours.
  3. The magical calendar puts extra days at the end of October.
  4. There are some "glue" days between months to make up the difference.
  5. Unclear as to whether to start months from the 0th or the 1st day, they compromised and count November from the (-1)st.
  6. At some point, several days were dropped,1 but nobody thought this was remarkable or unusual.

I think the only plausible explanation is (1).

More details from that HP Wikia page on dating contradictions (emphasis mine):

Often when dates are given, they are given with a day of the week that does not match with that date as it in actual history. One such example occurs in Harry Potter and the Prisoner of Azkaban when Sybill Trelawney refers to 16 October as Friday, although 16 October 1993 was a Saturday. This is usually explained as artistic licence on the author's part.

There are also contradictions within the books in this area. For example, in Harry Potter and the Goblet of Fire, both 1 September and 2 September are given as Mondays and, in Harry Potter and the Prisoner of Azkaban, Buckbeak's trial is set on 20 April, but careful parsing of the text reveals that it could have happened no later than February.

Also, if an anachronism counts as a dating error, then we have How could Dudley have wrecked his PlayStation if the PlayStation didn't exist yet?:

Harry was born in 1980. Therefore, the fourth book should be set in 1994. Yet, Harry mentions in his letter to Sirius that Dudley chucked his new PlayStation out of the window. The only problem is that the PlayStation wasn't on the market in Britain at that time.

Population statistics

From Slytherincess's excellent answer here:

I think we have to take the number of students at Hogwarts with a grain of salt. J.K. Rowling has discrepancies in her numbers, and she admits she is "horrible at maths," but at one point it was put forth that there are approximately 1000 students at Hogwarts, which would break down to approximately 250 students per house. There's a short article on how many students there are at Hogwarts here. The number of students in each house does indeed seem evenly distributed.

However, the answers to During the events of the Harry Potter series what is the total population of Wizards/Witches globally? contradict both this and each other. In particular, one of them mentions two very clearly contradictory statements from JKR:

Also, J. K. Rowling has stated that she imagines the wizarding population of the U.K. to be around 3,000. This estimate, although seemingly small, is understandable; a larger population would be far harder to hide from Muggles. However, she also stated that the number of students attending Hogwarts was around 1,000, which seems inconsistent with the population estimate.

Here are the words of JKR herself in the famous "Oh, Emerson, my maths is so bad" interview:

I sat down and I created 40 kids who enter Harry's year. [...] I never consciously thought, “That's it, that' s all the people in his year,” but that's kind of how it's worked out. Then I've been asked a few times how many people and because numbers are not my strong point, one part of my brain knew 40, and another part of my brain said, “Oh, about 600 sounds right.” Then people started working it out and saying, "Where are the other kids sleeping?" [...] But if you assume that all of the wizarding children are being sent to Hogwarts, then that's very few wizard-to-Muggle population, isn’t it? There will be the odd kid whose parents don't want them to go to Hogwarts, but 600 out of the whole of Britain is tiny.

Let's say three thousand [in Britain], actually, thinking about it, and then think of all the magical creatures, some of which appear human. [...] That's going to bump you up a bit as well, so it's a more sizable, total magical community that needs hiding, concealing, but don't hold me to these figures, because that's not how I think.

The problems with, and contradictions between, these figures have been much more extensively discussed in Shisa's excellent answer to Why is the intake of students for Hogwarts so small compared to the number of witches and wizards in Britain?. (As an amusing side-note, after the above-quoted paragraphs, the subject was quickly changed to lovey-dovey stuff, on which JKR was much happier to expound.)

Miscellaneous

  • How could Hermione have gotten more OWLs than classes? Apparently JKR originally wrote Hermione as having taken twelve OWLs, even though she was only taking ten classes from her fourth year onwards.
  • What age did Dumbledore live to? Slytherincess's answer here highlights contradictions between different JKR statements on Dumbledore's age.
  • Why doesn't Hogwarts have more teachers? The number of teachers and students at Hogwarts doesn't really work out to give every teacher a realistic workload. (Admittedly JKR is far from alone among authors of kids' school novels in making this sort of story-simplifying 'error'.)
  • The Weasleys' ages. (This link was actually mentioned by alexwlchan in the first answer quoted above, but I thought it was worth including as its own example.) JKR once messed up the numbers for the age difference between the Weasley boys, specifically Charlie and Percy.

Hat tip to DVK on meta and Valorum in a comment and alexwlchan in an answer for pointing me in the direction of some of these maths errors.
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Rand al'Thor
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    Interesting on that last one; I would have figured the population was skewed young due to deaths in the first wizarding war. – Izkata Oct 19 '16 at 00:33
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    @Izkata See also this question (I'll try to add some info from there in my next edit). – Rand al'Thor Oct 19 '16 at 00:36
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    @Au101 Oh dear lord, I'm not sure I realised what I was letting myself in for. Being a mathematician myself, I get particularly irritated by these kinds of mistakes. It's going to be a long and depressing slog ... – Rand al'Thor Oct 19 '16 at 00:52
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    So..... I definitely understand the Q and the A... But to me,it's less "bad at math" and more "didn't fully think about the implications of what she writes". Rowling just isn't the kind of writer to do research before starting her work i guess. – Patrice Oct 19 '16 at 13:11
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    I don't know if I would necessarily count calendar mismanagement as bad math. Calculating date ranges is not so much math as it is algorithm. August 15, 2015 to August 15, 2016 is 365 days. August 15, 2015 to March 12, 2016 is ummmmm "30 days has September, April, June and November...." It does point to a mind that is not given to OCD over these kinds of details though. :) – Jim Oct 19 '16 at 13:52
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    @Jim August 15, 2015 to August 15, 2016 is 366 days. :) – 8bittree Oct 19 '16 at 14:06
  • Was that ten classes that Hermoine was taking with the timeturner? Cause that would give her time for a few more classes – Wayne Werner Oct 19 '16 at 19:09
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    I think people should remember that while today it's very easy to work out the time between two dates using a computer, whether by looking up how to do it, or just asking some website, or whatever, in the mid 1990s even people that had the internet didn't immediately think 'I'll look it up on the internet' in response to every thought they might have. She'd have probably had to go to the library to find old calendars. It just wasn't important enough. – mrr Oct 19 '16 at 23:26
  • @WayneWerner No, twelve with the Time-Turner, and then ten from GoF onwards. – Rand al'Thor Oct 20 '16 at 00:11
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    Honestly, these all seem to me more like continuity errors than maths errors. J K Rowling may be bad at maths but these errors seem more likely to result from a lack of concern about detail than a failure to accurately calculate. Ultimately, not a single one of the issues has any serious impact on the story - or is even noticed by most readers - so I don't think she'd have been wrong to conclude it doesn't matter. – Jack Aidley Oct 20 '16 at 05:50
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    @JackAidley The reasoning is that the continuity errors stem from J.K. Rowling having such a bad sense for maths and that if she had a better innate sense for it, she would have made fewer errors with the timelines or at least less glaring ones. Personally I couldn't even imagine writing a work such as the Harry Potter books without first establishing the timeline, but different people are creative in different ways, for her the passage of time is only sometimes a useful construct, if the whole story could take place over the course of 7 days rather than several years she'd have done it. – Cronax Oct 20 '16 at 08:54
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    The world of Harry Potter only becomes possible if conventional logic has broken down, so any attempt to use conventional logic to find inconsistencies is inherently flawed; and realising that is a much higher mathematical insight than any of the commenters on this page demonstrate. – Michael Kay Oct 20 '16 at 22:31
  • Here's another question you can cite, since it addresses indications that Umbridge is really not that much older than Harry: http://scifi.stackexchange.com/q/11083/1693 – Tango Oct 26 '16 at 05:29
  • @Tango Thanks for the link ... but: is there any in-canon source for the "born sometime in the 1970s" bit? If not, it doesn't come under "JKR is bad at maths" so much as "HP Wikia contains nonsense". – Rand al'Thor Oct 26 '16 at 23:45
  • @Randal'Thor: I don't remember what got me thinking about that. Maybe I was just reading the wiki and that made me think about it. It's possible something in the books could have made me wonder or maybe it was just that article. I'm not sure what made me question those numbers - maybe the wiki editors are bad at math, too. – Tango Nov 09 '16 at 02:17
  • 22 November is the same as October 53 (31+22); 22 November minus 30 October is 23 days (53-30), which is three weeks and 2 days(3*7=21, 21+2=23). That is easy for me to do in my head. So the weekday of 22 November must be two weekdays after the weekday of 30 October. It seems to me if J.K. Rowling was interested enough she could have called a reference librarian at a large library to look up the weekdays of various dates for her, or spent a few dollars to buy an almanac with a perpetual calendar. – M. A. Golding Feb 21 '18 at 00:16
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    A perpetual calendar in an almanac works like this. There a seven days of the week a year can start on, and a year can be a leap year or not a leap year, so there are 14 possible arrangements of weekdays in different years. A perpetual calendar would have full calendars for the 14 types of years. It would list tens or hundreds of past and future years with their year types. You look up the year and see which type of year it is, and then look up the calendar for that year type. – M. A. Golding Feb 21 '18 at 02:30
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    The calendar thing is even easier. Even back then, there were spreadsheet programs for PCs. They usually have date functions that can easily do all the "what day of the week is this date" stuff. – JRE Apr 07 '18 at 06:57
  • You might also add Marcus Flint to the list. He was at Hogwarts for 8 years. Canonically that's because he failed a year, but that's because JK Rowling "would rather that he was the one who made the mistake ". – Arcanist Lupus Apr 07 '18 at 16:36
  • @ArcanistLupus I'm sure she would ;-) – Rand al'Thor Apr 07 '18 at 19:29
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    @Randal'Thor: No, that's an actual quote. "Either I made a mistake or he failed his exams and repeated a year. I think I prefer Marcus making the mistake. " – Arcanist Lupus Apr 07 '18 at 20:09
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    In defense of one tiny part of this, in the British system one or two classes can lead to multiple exam passes. English Language and English Language Literature for example. Maybe OWLs work the same. – DJClayworth Apr 09 '18 at 00:05
  • See comments of this answer -- may have found another math error regarding Snape's employment. – tonysdg May 04 '18 at 20:17