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How do you correctly abbreviate that something is in "three dimensions" in formal writing? As per the title, would you write either "3D", "3d", or "3-d"?

I want to write something like:

The figure contains a 2D widget (left) and a 3D gadget (right).

Additionally, if I use the full phrase in a sentence, I gather that I write

The three-dimensional gadget is composed of independent two-dimensional widgets.

i.e. using a hyphen and the word "three". Would it also be allowed to write "3-dimensional"? Especially in a context where I want to contrast it with something else "2-dimensional" in the same (or adjacent) sentence, as the numerals stick out more?

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    It depends on the writing style of the particular journal or conference.
    – Stan
    Commented Sep 22, 2015 at 9:24
  • There's no "correct way" to abbreviate something. The entire point of abbreviations is that they don't have to be formal, and they save space and time spent vocalizing. So with this in mind, I guess either 3D or 3d are "most correct", whatever that means.
    – user180089
    Commented Jun 29, 2016 at 16:32

6 Answers 6

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I am searching for an answer to the same question. I wouldn't use 3d, 3-d, or 3-dimensional because I have never seen them. Longman dictionary says three-D or 3-D (Longman), but Oxford also says 3D (Oxford). So I think 3D or 3-D are accepted.

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  • Maybe I'm hallucinating, but I've seen n-d more often than n-D in mathematics. See also: Search results for 'math nd tensor' and Ngram. Commented May 17, 2020 at 6:47
  • It wouldn't be surprising if the mathematics usage differed from that in e.g. video games.
    – Stuart F
    Commented Jul 12, 2022 at 11:26
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According to the Microsoft Style Guide:

3D, three-dimensional

Use 3D most of the time.

Spell out three-dimensional on the first mention if your audience may be unfamiliar with the acronym. Always hyphenate three-dimensional.

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According to this Ngram, both 3d and 3D are acceptable to use. Furthermore, different dictionaries show a different form of abbreviation for "three-dimensional". Some are 3-D, some 3D, some 3d, and so on.

From this I would conclude that none of these are incorrect to use. 3-dimensional is not something that is recommended though, as shown from the results.

Ngram also shows that "three-dimensional" is used just as much as 3D or 3d. Perhaps that is the best option to consider using in formal writing, since formality doesn't have fondness for abbreviations.

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    I think you're being fooled by Ngrams. When I look at actual hits for lowercase 3d, it's often in constructions like "King George 3d". Look at the Ngram for 3-D and 3-d ... nobody uses lowercase in 3-d, so why would they for 3d? Especially when the common use of 3d predates use of the words "three dimensional". Commented Apr 21, 2016 at 19:34
  • @PeterShor I think you're right, I'm ancient enough that if I see '3d' I think "thruppence" even though it's been 50 years since they were legal tender. Three-dimentional is 3D to me.
    – BoldBen
    Commented Jul 12, 2022 at 9:50
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I was looking at the distinction between "3D" and "3d", and decided to check it by myself in technical literature (Google Scholar). It turns out that "3d" is shown in the list, but upon checking the content of the paper, it is not "3d" but "3D". In other word, use 3D for the correct one.

Update:

The link I used to search is: Google Scholar

And the first item display (07/2018) would be:

"Learning spatiotemporal features with 3d convolutional networks"

But upon further opening the link to verify it, actually the paper would show "3D". This is true for all the other titles with "3d", when further verified from the link, it is actually "3D".

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  • Could you provide some links to instances using the lower case version? Please edit your post to include those links. :)
    – JJJ
    Commented Jul 25, 2018 at 1:56
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"3d" means "third" and "2d" means "second" and these notations are used in legal terminology (although they are not used in British English, and normally one would just use "3rd" or "2nd").

3-D means three-dimensional. The hyphen is not eliminated when abbreviating the term. The same goes for 2-D/two-dimensional, or whatever numeral you decide to plug in.

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As one person wrote, "There's no "correct way" to abbreviate something". This is not true exactly. An abbreviation can only be used in a document after the entire word is used. For example, PLA is the abbreviation for Polylactic acid. before you can use PLA in your document you must write it as Polylactic acid (PLA) then after that you can use PLA to reference Polylactic acid in the rest of your writing or until you need to note that PLA will mean something else in the paper. You can in theory abbreviate any word with any abbreviation.

So going back to your question, whenever in doubt, write the word then add the abbreviation. 3D or 3d should be written out first because you do not know who is going to read your paper and 3D or 3d could mean something different to that person. Very rarely can you assume a person knows that you are talking about or referencing no matter how simple it may be. So, third dimension (3D).

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