Basic arithmetic terms in Japanese

I’m currently trying to create a list of basic math terms in Japanese with the intention of eventually making a deck in Kitsun for them. Right now I’m trying to decide which terms to include for the four arithmetic operations. There are three sets of words.

First set:

  • 足し算
  • 引き算
  • 掛け算
  • 割り算

Second set:

  • 加法
  • 減法
  • 乗法
  • 除法

Third set:

  • 加算
  • 減算
  • 乗算
  • 除算

I’m definitely going to include the first set, since that’s the simplest version. I also want to include one, but not both, of the other two sets so some more formal terms are included. Does anyone know from experience or have access to some elementary school Japanese math books to say with certainty which is more useful or more correct? I’m leaning towards the 法 group, simply because that’s the primary one used in all the Wikipedia pages. Of course, now I see that the 算 group are all する verbs, so it seems like they all have their usages…


I don’t have actual experience, but I have spent a bit of time sifting through and whatnot, adding math-, computer-, and logic-related vocab to my lists. In particular, I spent a while trying to figure out which versions of Linear Algebra-related terms would be most relevant/useful to add.

One strategy I used which seemed to help provide extra context was to do ‘wildcard’ searches using the ‘glob’ patterns with asterisks. For example, just searching for ‘加算’ gives you 4 matches (since it only searches for terms starting with 加算), but searching for ‘*加算*’ (加算 with any prefix or suffix) gives 19 results, which can often help ‘suss out’ the more subtle distinctions between similar words. For instance, it appears that ‘加算’ is more about the ‘mechanics’ of addition whereas ‘加法’ seems more about the mathematical concept or ‘method’ of solving problems via ‘addition’ (with the exception that 加算 is also used for ‘additional tax’ – which perhaps makes sense as that’s kind of an accounting-type of term, and perhaps accountants are more concerned with the ‘mechanics’ of addition than the ‘method’ or ‘mathematics’ of addition).

It seems to me that, as you say, they do have their own uses, just as English has a distinction between ‘addition’ the abstract mathematical operation/method for posing and solving problems and ‘addition’ the actual algorithm (“four plus seven, carry the three…”) of producing a new number as the sum of other numbers.

I guess picking which set will depend on what your main interests in learning math-related terms is about. Personally, I’d just include them all, but that’s just me. :nerd_face::sweat_smile:

P.S. there’s a drop-down box on the left side of the search textbox on Jisho (usually it says “All▾”) which contains a link to their advanced search options documentation. It’s not the most sophisticated search, but knowing the options can help produce more useful searches. Also, there’s a list of tags you can use, some of which are useful. There’s even a tag for #math related terms.


Thanks, I’ll be sure to search jisho for related terms. The monolingual definitions were enlightening as well. Most interestingly, 足し算 specifically mentions adding two numbers, while 加法 mentions adding two numbers or formulas/equations. It was the same for the other operations. Unfortunately, 加算 (and the other 算 on’yomi ones) just referenced back to the other words without any clarification on nuance.

I’d be open to including all three versions, but this is a deck I’m considering publishing for other users to use as well. As such, I’d feel a little weird adding three versions of the same word if I’m unable to clarify the nuance somehow in the cards. Of course, if all three are in use, you could argue that leaving one set out would also be weird.

One Hi Native answer says that in elementary school they say 足し算, then starting in middle school they say 加算, and they personally don’t use 加法 but that others might.

I think it might take me longer than I originally thought to make this deck. I’d hate to share bad information with other people.

By the way, if you can easily share the list of math words you learned, that would be helpful to see. I’m looking not just for arithmetic and other basic math terms, but also basic algebra and geometry terms as well. I already have a list of over 60 words (not all simple arithmetic) just from a few hours of searching for terms I know in English and finding related terms. (I’m embarrassed to say I forgot the word “quotient” in English until I read the Japanese Wikipedia page on division!)


Houston, we have a problem :eyes:.


Ah, yes, that’s a very different use case. More of a curation than a gotta-catch-em-all collection.

Hmm, that seems to go along with the ‘additional tax’ usage. 加算 is probably the more common of the two. Perhaps 加法 is more like what a mathematician or university maths student would use? I’m just speculating now, though.

Perhaps your best bet is to either do a broader search, like maybe finding English Wikipedia pages on the topic that best matches what you want to include, and then see what the Japanese Wikipedia equivalent page is titled and also the words used within it.

Or, maybe even better, find some more native speakers and get a kind of consensus from them. Maybe ask someone who actually has some university-level math background (not necessarily math degree, just that they’ve taken a uni-level math course); they would surely be able to help with these subtle distinctions.

It’s in KameSame, and I just did a quick check and couldn’t find an obvious way to find all the words I’ve added. Unfortunately my ADHD has gotten the better of me once again, and I have like 19,000+ entries (something like half that being distinct items), which is far more than I could ever really learn via SRS, I imagine. I just find some interesting (that day, at least) topic, search up all sorts of words related to it on Jisho, then add them to KameSame. It’s … almost… too easy… :thinking::face_with_raised_eyebrow::open_mouth:

If you know of a way to extract word/item lists from KameSame, let me know and I’ll try to extract them for ya.

I’ve forgotten the specific meaning of the word ‘quotient’ so many times… At least ‘remainder’ gives you a clue of what it might be. Are we ‘quoting’ something? Don’t know the etymology. Probably French <grumble>.

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That’s basically where I started. The article was titled 加法 and then said it was also called 足し算 and 加算. So still unclear from that.

I don’t know any native speakers. :cry:

I don’t unfortunately. Thanks anyway.

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Heh! Turns out we are ‘quoting’ something. At least, in the original meaning of ‘quote’. Turns out both ‘quotient’ and ‘quote’ come from Latin ‘quot’ meaning ‘how many’. The original meaning of ‘quote’ was to give a chapter/page/verse number as a reference (like a bible reference like Mark 13:20 (1990 cyberpunk movie reference)). The idea of ‘quoting’ words verbatim arose later.

To quote the Wiktionary entry for ‘quote’, an HTML blockquote (quote-ception!):

From Middle English quoten, coten (“to mark (a book) with chapter numbers or marginal references”), from Old French coter, from Medieval Latin quotāre (“to distinguish by numbers, number chapters”), itself from Latin quotus (“which, what number (in sequence)”), from quot (“how many”) and related to quis (“who”). The sense developed via “to give as a reference, to cite as an authority” to “to copy out exact words” (since 1680); the business sense “to state the price of a commodity” (1866) revives the etymological meaning. The noun, in the sense of “quotation,” is attested from 1885; see also usage note, below.

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I see you’ve already found the answer on HiNative that I was about to link to. Something else you might want to consider is this page:

The introductory paragraph might suggest that the versions with 法 might be more appropriate when it’s a question of how a calculation is done. However, in this article

the two versions seem to be used as synonyms.

Personally, I think it’s not so much a question of which is used more as it is of what each emphasises: the version with 算 is about calculations themselves, I think, whereas 法 is about the way in which the calculations are carried out (e.g. in what order, using what ideas etc.). If you’re looking for words that are closer to 足し算 and so on, I’d take the 算 versions just because they refer to the simple act of calculating, in my opinion.

EDIT: OK, so…

I think this is possible. Take a look at this article on summation:

Under the definition, we have:

So yeah, it seems like 加法 is what you’d use to refer to addition as an ‘operation’ rather than a simple calculation.


Did you see this video in the math club thread? Basic arithmetic/四則演算 [Maths 1.1] - YouTube

The first set definitely seems to be most used in speech.

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I guess that makes sense. The Wikipedia article titled 加法 does go through various aspects of how one might do addition.

Any suggestion for how to differentiate them in English for a one word / short phrase flash card situation?

Yep, I’ve watched it twice now. And yeah, I know the first set is the most used in speech. I’m just deciding which of the other two to add as well.


This is a little vague, but maybe ‘adding’ vs ‘addition’ might do the trick? Alternatively, maybe ‘addition (operation)’ vs ‘addition (calculation)’ might work?


Hmm, I’ll have to think on it a bit. By the way, I did ask someone on the Kitsun discord as well (not a Japanese native, but very knowledgeable), and their answer was similar to yours.

加法 and 減法 are the concepts themselves (the rules on how to do them). 加算 and 減算 are the process of actually doing it.
As a result, 加法 and 減法 are true nouns while 加算 and 減算 can be する verbs


You might go with some convention where you more-emphasize the verb aspect of the suru-verb version and the noun aspect of the noun version, like: Add vs. Addition, Multiply vs. Multiplication, Divide vs. Division, Subtract vs. Subtraction. (But that may not actually be how the Japanese works – I’m just brainstorming here.)

Or, similarly, and perhaps more in line with the actual Japanese (but again, I’m just guessing), you could frame the verb-ish kind as a gerund, like Adding vs. Addition, Multiplying vs. Multiplication, etc. This might be a bit harder for users of the SRS cards to distinguish, but then again, it does seem like a very subtle distinction.

Further out on the limb, you could try to distinguish, say, Addition vs. Summation, (but what’s the alternative for Multiplication?). Or, Addition, Sum, Multiplication, Product, but I think that video pokes holes in this idea (again, just brainstorming, not every idea’s gonna be a keeper! :sweat_smile:).

Personally, I’m leaning towards the gerund version, as it’s like, Q: “What are you doing?” A: “I’m adding” or “I’m doing adding” or “I’m doing addition (as a verb),” versus, Q: “What is that method called?” A: “It’s called addition.”

ETA: Also, the ‘wildcard’ Jisho search I mentioned earlier gave things like “Adder” and “Half-Adder” which are computer/electronics terms for ‘a machine/circuit that performs addition’, and this was for the 算 versions, so it makes sense that those would be more ‘verb-like’ than the 法 versions, even if there wasn’t the suru-verb distinction.

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The Youtube series “Math in Japanese” was already mentioned, I think. They also cover some basic terms in geometry, statistics, and algebra.

Another series that might be interesting for you was mentioned by @FlamySerpent senpai :

I started looking into the videos and I like them as they introduce terms and concepts in context. They also do some quizzes to apply the terms that had been introduced before.

They also have a series about

I haven’t watched it yet but maybe it is helpful for your project. :four_leaf_clover:


I don’t think this would work, as summation is a different concept. A summation is the operation signified by capital sigma. I know you use capital pi for the product version, but I don’t actually know what it’s called. :thinking:

This is probably the best idea so far. Though 加算 and 足し算 are basically the same thing, and it would be a shame to have to change 足し算 to “adding” as well. I suppose I could put both “addition” and “adding” for 足し算 and 加算, but only put “addition” for 加法. Maybe I could do that in combination with @Jonapedia’s parenthetical idea actually, so that “addition” itself is still distinguished a bit. If I understood all the suggestions correctly, I think this would make it:

  • 足し算・加算: addition (operation), adding
  • 加法: addition (calculation)

From what I’ve seen, 足し算 and those variants seem to be universally referred to as ‘-tion’ type nouns, almost like “Today we’re going to have a lesson on addition.” Or, “Did you do your addition homework?” Like a school subject. The idea for this distinction was sparked by that video’s naming the whole field as 算術さんじゅつ , like it’s a martial art or something, and how they name various techniques in martial arts, so this would be the 足し算 technique of the 算術 school you send your kids to. (Like, literally, actually!)

So, what I’m saying is that maybe you could keep 足し算 as Addition (the technique/exercises practiced at the 算術 dojo), and 加算 as Adding (like performing the 足し算 technique on an ‘opponent’ in a spar), and 加法 would also be Addition (but more like the title of a chapter in a book about Zen and the Art of 算術, where the senseis all muse about the deeper meanings of 加 and 法 (or something :wink:)).

Parentheses is definitely a good idea, IMHO.

Actually, I personally find the distinction be ‘operation’ and ‘calculation’ weak. Calculation seems clear to me, and it seems to be more closely associated with 算. Again, I’m going back to how the 加算 Jisho search turned up things like ‘adding machine’, ‘adder’, ‘half adder’, etc. The mechanical aspect of addition that even a machine can perform.

Then, that would just leave the question of how to characterize the 法 version. The kanji is associated with things like ‘law’, ‘method’, ‘principle’, ‘system’, ‘rules’ etc. Even ‘grammar’, which I think is actually a pretty good analogy! Like ‘correct usage’, like ‘syntax’, but also like ‘axioms’ and ‘theorems’, or perhaps ‘theory’.

Laws of Addition? Of Multiplication? Of Division, etc.? That seems on the right track.

I would go with one of these: Rules, Method, Laws, Theory. Actually, perhaps even Operation (reverse of what you have; although I still think operation is too close to calculation, IMHO.)

ETA: @seanblue Ah! Perhaps something like Addition (Algebra) for 加法? That seems pretty close to the mark, if I’m not mistaken. Algebra is perhaps a kind of jargon-ish word, though. But I think it does mean what I think 加法 means. (If I’m not wrong, again. :sweat_smile:)

I was thinking of it the other way around, actually:

  • 足し算・加算: addition (calculation), adding
  • 加法: addition (operation)

However, I’m saying this as someone with a mathematical background that includes a basic understanding of group theory, so to me, an (internal) operation is a map that takes a certain number of elements from a set and combines them in a certain way to generate another element of the same set. It has a number of inputs and a particular output for each combination. If you find ‘operation’ and ‘calculation’ too similar though, you don’t really think of ‘operation’ as a technical term, or ‘calculation’ doesn’t evoke the relatively mindless (I guess ‘mechanical’ is an appropriate word) process of reaching the result itself, then yeah, you might want to try some other words.

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The most appropriate association, I think, would be with ‘computation’, but most non-mathy people would probably associate ‘computation’ with something only modern computers would do, so they might think it has a more ‘need to be a computer geek/programmer to be concerned with that’ connotation than it used to have.

That’s part of the trickiness with these word-association mnemonics. It really depends on the audience. Any one of us would just pick the one that suits us best, but if you’re trying to make a deck for other people, you have to try to put yourself in their shoes, and it really depends on the audience you’re aiming for. :man_shrugging: Thankfully it’s seanblue’s problem, not ours! :smiling_imp:

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I guess. I mean, it feels that way even for me, but that’s because I learnt my university-level maths in French, and my teachers’ favourite way of referring to the mechanical bits of anything where we just follow set rules is ‘c’est juste du calcul’ (‘it’s just calculation’). That’s probably why I prefer ‘calculation’, especially since it’s relatively common even in English. (I guess my memories of my pre-university mathematical education in English aren’t super clear anymore, but I think ‘calculations’ or ‘working’ was the preferred word for the things we’d write when figuring something out on paper.)

It would actually be nice to make use of the word ‘process’, but that doesn’t preclude following a method, so it’s kinda vague and could probably fit either word.

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See, this is why these words are no good! Too ambiguous! And I’m saying this as someone who has a decent background in math (calculus, linear algebra, discrete math). I just looked up the definition of “mathematical operation” on Wikipedia, and while it’s basically what I thought it was, that doesn’t help me connect it to 加法.

I don’t know the technical definition of “algebra”, but when I hear the word I immediately associate it with variables, which arithmetic doesn’t have.

I think pretty much any English word we pick will be vague and could be applied to either of the Japanese words depending on the person and how deep their knowledge of formal math is.

Honestly, I’m considering more and more just leaving out the 法 words. They seem least useful to the average person trying to learn basic to intermediate level math terms in Japanese.