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From Pottermore:

Witches and wizards are not averse to laborious calculations, which they can, after all, do magically, so they do not find it inconvenient to weigh in ounces, pounds and stones; measure in inches, feet and miles; or pay for goods in Knuts, Sickles, and Galleons.
(Pottermore, "Measurements").

It seems that witches and wizards can use magic to perform "laborious calculations" if they so choose.

But I don't recall an incident where we actually see this in the books. Do we ever see a witch or wizard perform any sort of mathematical calculation using magic?

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    No I don't think we do, but we do get this when Ron and Harry were trying to do their Divination homework "An hour later, they had made very little progress, though their table was littered with bits of parchment bearing sums and symbols, and Harry's brain was as fogged as though it had been filled with the fumes from Professor Trelawney's fire. 'I haven't got a clue what this lot's supposed to mean,' he said, staring down at a long list of calculations." We have no idea, unfortunately, how the actual calculations were done, but given this is astrology – Au101 Jun 20 '17 at 21:08
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    I know nothing about astrology, but astronomy certainly involves pretty tricky trigonometry, so it's possible the actual computations were done by magic in the way that we when doing our maths homework might write out the sum, reach for the calculator, plug in the numbers, write down the result, move on to the next step. But its equally possible it was all quill and parchment since we only ever see quill and parchment on screen – Au101 Jun 20 '17 at 21:10
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We don't actually see it, no.

But there is a numbers-related subject that Hermione claims is better than divination: Arithmancy.

On Pottermore it's defined as "a magical discipline that studies the magical properties of numbers, including predicting the future with numbers and numerology" and "homework assignments of which included writing essays that required the consultation and/or composition of complex number charts."

You can find mention of it in Chapter 12 of the Prisoner of Azkaban

While there is some math in Divination, Arithmancy is more math intensive.

Despite the fact that Hermione claims that it's a better class (she might like it because there's math and clear answers) when they go searching for the Horcruxes the textbook is specifically mentioned as something she leaves behind because "it was useless for what they were about to set out and do."

Therefore the predictive powers of the discipline might not be that great and akin to Divination in the end.

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    I know that Pottermore is no longer the reliable site that it once was, but it still isn't HP wiki. Please try quoting from the original sources if you can find them. – ibid Jun 21 '17 at 3:54
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    Arithmancy may be relevant/related but I don't see any evidence that the mathematical part of it was actually done by magic. I'm looking for magical calculations, not the study of numbers. – The Dark Lord Jun 21 '17 at 12:45
  • @TheDarkLord I don't recall seeing it in the books at any point. It's difficult to prove the absence of something. Basically, this is the closest mentioned thing. – Erin Thursby Jul 4 '17 at 18:31
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I'm not sure about calculations but in Hogwarts they measure using their hands.

Potions class uses scales to measure the ingredients. There is a quote where someone from the trio balances the scales and the other writes it down. If someone finds it please edit.

Outside of Hogwarts we see people use magic to measure things. When Ollivander measures the length of Harry's arm, a meter just flies around and measure the parts. We also don't recall the meter saying the measurement out loud so we can infer that it is bonded to the magician somehow or he basically reads the meter afterwards. The second example is when students buy robes. There we also see a magical meter measuring students and then communicates with the tailor ( Don't remember her name) non-verbally.

The closest thing we see about mathematical calculations is Quidditch and Wood tries to make sure that Harry understands when to catch snitch so either wood does not trust on Harry's magic to do the calculations correctly as he has a wand with him in the game or he doesn't trust Harry's intelligence to calculate and remember correctly.

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While we don't ever see a specific person perform this calculation with magic, I would assume that the House points are calculated by magic. Consider that the House points are displayed in hourglasses in the entrance hall using colored gems to represent points. We never find anyone taking out the gems to count them to see how many points a house has, yet no one seems to have difficulty knowing how many points a house has. In Philosopher's Stone, for example, people seem to be able to tell that 150 rubies were removed from the Gryffindor hourglass, despite nobody performing a count:

At first, Gryffindors passing the giant hourglasses that recorded the House points the next day thought there'd been a mistake. How could they suddenly have a hundred and fifty points fewer than yesterday.

Apparently, there is some magical automated system that counts the gems in each hourglass, in which case it is performing calculations (addition and subtraction).

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