Are there any guidelines for labeling axes in plots/graphs?

Question

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.

Answer 1

The recommended way, according to the International System of Units (SI), is to write t/s (SI brochure, §5.3; see also this guide, §7.1). 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.

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References

For those interested in learning more about quantities, units, their typographical conventions, 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. 13 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.
9. E R Cohen et al., "Quantities, Units and Symbols in Physical Chemistry", IUPAC Green Book, 3rd Edition, 2nd Printing, IUPAC & RSC Publishing, Cambridge, 2008 Online
10. Nayuki, Handling physical quantities in math formulas. This article is a lively little gem on quantity calculus with lots of practical examples.

Answer 2

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.

Answer 3

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.

Answer 4

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.