38
$\begingroup$

I'm making a table where columns are labelled with the property and the units it's measured in:

Length (m) |||| Force (N) |||| Safety Factor (unitless) ||| etc...

I'd like not to write "unitless" on several columns...and I'm quite surprised I can't seem to find a symbol for it. Any suggestions?

Improve this question
$\endgroup$
7
  • 3
    $\begingroup$ How about a dash $(-)$? $\endgroup$
    – DilithiumMatrix
    Apr 4, 2013 at 3:57
  • 16
    $\begingroup$ I would just use nothing at all: |||| Safety Factor |||| $\endgroup$
    – user10851
    Apr 4, 2013 at 3:58
  • $\begingroup$ @zhermes - was thinking that, but could be confused for "negative" or "omit" or something... $\endgroup$
    – Ben
    Apr 4, 2013 at 4:11
  • $\begingroup$ For this particular example there's no danger of confusion if you just leave out any mention of the units, since the word "factor" pretty much implies it's unitless anyway. $\endgroup$
    – N. Virgo
    Apr 4, 2013 at 6:34
  • 4
    $\begingroup$ Whenever anyone omitted the units on any answer my high school physics teacher would write in "fish". $\endgroup$
    – Ben Jackson
    Apr 5, 2013 at 5:22

8 Answers 8

Reset to default
46
$\begingroup$

Straight from the horse's mouth:

enter image description here enter image description here

Source: Bureau International des Poids et Mesures (Search for "dimensionless" for all guidelines.)

The International Bureau of Weights and Measures (French: Bureau international des poids et mesures), is an international standards organisation, one of three such organisations established to maintain the International System of Units (SI) under the terms of the Metre Convention (Convention du Mètre). The organisation is usually referred to by its French initialism, BIPM.

Wikipedia

Improve this answer
$\endgroup$
9
  • 11
    $\begingroup$ Interesting. Shame you can't attach prefixes to "one" - I'm quite fond of yoctoone. $\endgroup$
    – Michael
    Apr 4, 2013 at 11:14
  • 1
    $\begingroup$ ^ Yoctoone is otherwise known as one septillion, or $10^{24}$. $\endgroup$
    – Joe Z.
    Apr 4, 2013 at 17:46
  • 6
    $\begingroup$ @JoeZeng If anything, one septillion th, or $10^{-24}$ (Wikipedia, Horse). $\endgroup$
    – Řídící
    Apr 4, 2013 at 17:55
  • 1
    $\begingroup$ @JoeZeng: or better yet, hella confusing: scitech.blogs.cnn.com/2010/03/04/hella-proposal-facebook $\endgroup$
    – Zo the Relativist
    Apr 4, 2013 at 18:22
  • 3
    $\begingroup$ I find it very confusing as "1" looks very similar to "l", the symbol for litre. I know, it's not SI, but can be still confusing, especially if the font makes them even more similar. $\endgroup$
    – vsz
    Apr 5, 2013 at 6:12
15
$\begingroup$

I've seen "(1)" used. Radians (and steradians) are also "unitless" but they're clearly not appropriate here.

Improve this answer
$\endgroup$
5
  • $\begingroup$ I thought radians have the unit (rad) $\endgroup$
    – Aryan Beezadhur
    May 15, 2020 at 11:56
  • $\begingroup$ @AryanBeezadhur: en.wikipedia.org/wiki/Rad_%28unit%29 $\endgroup$
    – wnoise
    May 16, 2020 at 6:11
  • $\begingroup$ I’ve seen this in maths: $360 \deg = 2 \pi rad$ $\endgroup$
    – Aryan Beezadhur
    May 16, 2020 at 12:48
  • 1
    $\begingroup$ @AryanBeezadhur $rad \equiv 1$, i.e. radian is just a synonym for unit-less 1 dimension $\endgroup$
    – Agnius Vasiliauskas
    Sep 30, 2020 at 11:32
  • $\begingroup$ @Agnius Vasiliauskas: They are dimensionally compatible in most contexts, but they are not the same unit anymore than meters and centimeters are. $\endgroup$
    – wnoise
    Oct 2, 2020 at 19:04
8
$\begingroup$

The convention I have seen in journal articles, and that I prefer, is to simply omit any mention of units for dimensionless quantities.

EDIT: I also see the style Emilio Pisanty recommends, particularly in tables and graphs. For a graph, the idea is that the datapoints you are plotting are actually numbers, so you want to divide them by the relevant base units. That then scales everything so that your plot fits on the page. As an example, you might plot force vs displacement to measure a spring constant. The x-axis would then be $x/\text{m}$, and the y-axis would be $F/\text{N}$, and both would be dimensionless. You could also use SI prefixes if that were useful.

The same idea would apply to a table. For your example, you would have it as Length / m || Force / N || Safety Factor || etc. Again, you can add SI prefixes to keep the actual numbers in the table easy to read.

Additional EDIT (by Gugg) with "official approval" and an illustration of this style:

enter image description here

BIPM

Improve this answer
$\endgroup$
1
  • 1
    $\begingroup$ +1 I edited the "official approval" of this (very useful) approach into your answer. If you don't appreciate that, just reject the edit. $\endgroup$
    – Řídící
    Apr 5, 2013 at 10:00
7
$\begingroup$

An alternative is to use the (slightly) more formally correct convention Length/m and Force/N for the first two, in which case simply using Safety Factor will work.

Improve this answer
$\endgroup$
6
  • 1
    $\begingroup$ How is that more formally correct ? $\endgroup$
    – DilithiumMatrix
    Apr 4, 2013 at 7:12
  • 6
    $\begingroup$ @zhermes, If A = 10 m, then A/m = 10. $\endgroup$
    – Jan
    Apr 4, 2013 at 8:27
  • $\begingroup$ @Jan yes, I'm well aware of why it is 'correct', you'll notice I asked why it was 'more' correct. $\endgroup$
    – DilithiumMatrix
    Apr 4, 2013 at 15:58
  • $\begingroup$ @Jan: In what sort of context would A = 10 m? o_O $\endgroup$
    – Joe Z.
    Apr 4, 2013 at 17:47
  • $\begingroup$ Or even better, Length/(1 m) $\endgroup$
    – Zo the Relativist
    Apr 4, 2013 at 18:24
5
$\begingroup$

Dimensionless quantities are actually of dimension one, i.e. unity. So I think it would be most accurate to write it as $[1]$, if you're doing dimensional analysis or if you're trying to be precise about dimensions, which looks to me like the type of situation from your question.

Improve this answer
$\endgroup$
4
$\begingroup$

You could always pull something engineers seem to be fond of when they write the (unitless ratio) gain of an op-amp as "Volts per Volts".

Improve this answer
$\endgroup$
3
$\begingroup$

Just write any unit you like the most and raise it's power to null:0.

I find Bq: becquerel a hard thing to remember . (units of activity of a radioactive substance) and I would write $Bq^0$ to denote a dimensionless quantity.

Or just as in books : $[M^0L^0t^0]$

Improve this answer
$\endgroup$
1
$\begingroup$

Units I usually keep in brackets []. Like 70 [kg], 60 [GPa], 5.2 [ms^-1] and for no unit I would say 1.5 [-].

Improve this answer
$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.