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What are best practices (if any exist) for labeling axes in plots/graphs for academic documents, such as theses, publications, or presentations?

Possible options are to use the variable, spell out the variable, or a combination of both. For example, to label a time axis, we could write: t (s) or Time (s) or Time, t (s).

Are there any objective reasons to prefer one style over another, assuming the publisher does not specify which to use? Or sources suggesting a particular format?

I have browsed many journal requirements, but haven't found any that specifically address this.

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This differs widely between fields, journals and reserachers, so your Q is to broad and partly opinion based. –  fileunderwater Mar 20 at 14:29
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My intention was to determine if there were any sources suggesting a specific format. Do you know of any books, or journals that explicitly address this? I have browsed many journal requirements, but haven't found any. –  William Mar 20 at 14:31
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Specific journals have their own detailed style guides. The example without units is certainly incorrect. Often you'll be plotting something that has no precise English description, so you have to use a symbol, even if you would otherwise have preferred to use words. –  Ben Crowell Mar 20 at 15:39
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APS gives a good hint for authors on their website: journals.aps.org/authors/axis-labels-and-scales-on-graphs-h18 BTW: I do not think this question is too broad and should be reopened. –  Jonas Stein Sep 22 at 17:25
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This seems to be a question about preparing images for publication, which is firmly on topic. It asks for objective reasoning and information from other resources, not answerers' opinions. The OP is not asking for an exhaustive list of requirements of different fields, so it's not especially broad. The existing answers are concise, focused, and supported by objective reasoning. This seems like a fine question to me and I've voted to reopen. –  ff524 Sep 23 at 5:23

4 Answers 4

Good practise is to make sure the graph is understandable even when taken out of its context (the paper). Hence spelling out the label helps to avoid misunderstandings. There is, however, nothing formally wrong with the other forms you mention although the label including both variable and variable abbreviation is not common in my field. On the other hand, it serves to couple the variable name with its abbreviation so it has its merits.

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The correct way, according to the International System of Units (SI), is to write t/s (SI brochure, §5.3). And the SI is the only system of units that should be used to report experimental results.

The rationale behind this notation is the following: a quantity is the product of a numerical value and a unit, so that the ratio of a quantity (e.g. time) and the corresponding unit (e.g second) is a numerical value (a pure number), which can be used to label axes, tables, etc.

In any case, don't use brackets around the unit, like in "t [s]". The reason is that in quantity calculus brackets represent an operator which means "unit of" (not "dimension of") and should only be used around quantities, not around units. So, for instance, you can write:

[t] = s

but not [s]. For completeness, I also mention that braces are also used to denote the numerical value of a quantity. So, in L = 5 m, we have [L] = m and {L} = 5.


Edit: For those interested in learning more about quantities, units and quantity calculus, here is a list of references with a few notes:

  1. J C Maxwell, "A treatise on electricity and magnetism", vol. I, Oxford: Clarendon Press, 1873. Online. Note: Here Maxwell introduces the concept of quantity and the bracket notation.
  2. International Vocabulary of Metrology - Basic and general concepts and associated terms VIM, 3rd edition, JCGM 200:2008. Online. Note: This is the official dictionary of metrological terms where it is possible to find definition for terms like quantity, system of quantities, system of units, etc. On p. 29 there is note which explains the bracket/braces notation.
  3. I M Mills, "The language of science", Metrologia 34, pp. 101-109, 1997.
  4. B W Petley, The fundamental physical constants and the frontier of measurement, Adam Hilger, Bristol, 1988.
  5. I M Mills, "Physical quantities and units" in Recent advances in metrology and fundamental constants, Proceedings of the International School of Physics E. Fermi, Varenna, 2000. Online.
  6. J de Boer, "On the history of quantity calculus and the International System", Metrologia 31, pp. 405-429, 1995.
  7. M J ten Hoor, "Quantity calculus for chemists", Chemistry in action n. 57, 1999. Online
  8. M L McGlashan, "Physicochemical quantities and units: The grammar and spelling of physical chemistry", Royal Institute of Chemistry, London, 1971.
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Thanks for the reference, I am glad to see some "standards" have been considered. That being said, I would confusingly interpret those units as divisions. Furthermore, they recommend 1000 K / T could be rewritten as kK/T, which seems unnecessarily confusing. Thanks for the information on brackets, I've never seen them in the form of describing units of value of units. –  William Sep 25 at 0:33
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The brackets notation was introduced by Maxwell, who is the father of the concept of quantity as we know it today. The braces notation is probably more recent, but I don't know when it was first introduced. For the interpretation of / as division, the framework is that of quantity calculus: albeit not well known, its foundations are sound (see e.g. this paper). I have a book which uses '/' in tables and graphs which dates back to 1968, so it's not even a recent notation. –  Massimo Ortolano Sep 25 at 5:37
    
Could you please provide a reference on the use of brackets in quantity calculus? –  Alexey Popkov Sep 25 at 13:18
    
I've edited my answer adding a list of general references, with online links where possible. Maybe in the next days I'll add a few more notes. –  Massimo Ortolano Sep 25 at 13:36

I am very particular about figures in my papers, as when I skim a paper the first thing I do after reading the abstract is look at the figures to determine whether the results are interesting or not, and on that basis whether to read the paper in more detail. Hence I always make sure the data is clearly presented through an appropriate use of symbols, colours and typeface, as well as a detailed stand alone caption describing what the data is and what it shows. As part of this I always label the axes in the form "quantity (unit)". In my opinion a variable name 't' is insufficiently descriptive to make figures stand alone, and so doesn't communicate to the casual reader what the figure shows. Units are of course essential, and in the case of dimensionless quantities I usually include the variable name as the unit, eg t/t0.

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There is nothing technically incorrect about any of those forms. In journal submissions, there will be typesetters to check that your figures adhere to their style guidelines.

In general:

The name of the quantity (e.g. time) and its units (e.g. s) are needed for clarity. It is generally better to add some concise descriptor to the quantity (e.g. Is it reaction time? geological time? etc.)

Preferences for how the units are displayed are somewhat subjective as well. An alternative format is using / as a separator (e.g. Time / s), though I personally think this format lends itself to confusion with derived quantities that contain division (e.g. Dimensionless Time, t/tc, as another user mentioned, will also have a /)

Adding the variable name (e.g. t) is often redundant in formal publications, unless equations figure extensively into the written portion and/or the naming is non-obvious or unconventional (say you used τ). Italicization will often be used to improve clarity.

Above all, consistency is critical. Choose a format, and use it for all graphs in the same manuscript. Doing otherwise just appears sloppy.

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The only thing I dislike about spelling out variable names, is the length, e.g., I could write Q* or Dimensionless Volumetric Energy. The latter can require a larger figure if the y-axis is too short to contain the word, while the former certainly doesn't have this problem. –  William Mar 21 at 21:09
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@William As long as you define Q* in the caption then I think this is fine. I always make sure my figures are standalone because people don't always read the whole paper. –  emmalgale Sep 23 at 10:18
    
As @MassimoOrtolano's answer points out, Time/s is indeed a division. –  Federico Poloni Sep 24 at 7:01

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