Is there a symbol for "unitless"?

Question

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?

@zhermes - was thinking that, but could be confused for "negative" or "omit" or something... — Ben, Apr 04 '13 at 04:11
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. — N. Virgo, Apr 04 '13 at 06:34
Whenever anyone omitted the units on any answer my high school physics teacher would write in "fish". — Ben Jackson, Apr 05 '13 at 05:22
When a square bracket convention is being used, such as [km], I've seen non-dimensional parameter listed as [n/d]. — Adam Wuerl, Apr 08 '13 at 06:08
But km is a unit and not a dimension. And the square bracket notation for units is wrong regarding to ISO 80000. SI does not use any brackets at all. So "Length $l$ in m" or "Length $l$/m". To write "in 1" or "/1" would be correct but does not worth the ink... — LaRiFaRi, Sep 18 '13 at 08:17
From Wikipedia: "In another instance in the early 2000s, the International Committee for Weights and Measures discussed naming the unit of 1 as the "uno", but the idea of just introducing a new SI name for 1 was dropped." — alfC, Dec 05 '23 at 03:30

Řídící · Accepted Answer · 2013-04-04T11:37:00.500

47

Straight from the horse's mouth:

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

edited Apr 04 '13 at 11:37

answered Apr 04 '13 at 11:04

Řídící

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Interesting. Shame you can't attach prefixes to "one" - I'm quite fond of yoctoone. – Michael Apr 04 '13 at 11:14
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^ Yoctoone is otherwise known as one septillion, or $10^{24}$. – Joe Z. Apr 04 '13 at 17:46
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@JoeZeng If anything, one septillion th, or $10^{-24}$ (Wikipedia, Horse). – Řídící Apr 04 '13 at 17:55
@Gugg Whoops. Yotta and Yocto are too easy to mix up. – Joe Z. Apr 04 '13 at 17:55
In fact, you could say it's zetta confusing. – Joe Z. Apr 04 '13 at 17:58
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@JoeZeng: or better yet, hella confusing: http://scitech.blogs.cnn.com/2010/03/04/hella-proposal-facebook/ – Zo the Relativist Apr 04 '13 at 18:22
I suppose it all depends on the unit measure of confusings... - OP – Ben Apr 05 '13 at 03:43
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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. – vsz Apr 05 '13 at 06:12
@vsz Indeed. That's called homoglyphic confusion. – Řídící Apr 05 '13 at 07:00

score 15 · Answer 2 · answered Apr 04 '13 at 04:00

15

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

answered Apr 04 '13 at 04:00

wnoise

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I thought radians have the unit (rad) – Aryan May 15 '20 at 11:56
@AryanBeezadhur: https://en.wikipedia.org/wiki/Rad_%28unit%29 – wnoise May 16 '20 at 06:11
I’ve seen this in maths: $360 \deg = 2 \pi rad$ – Aryan May 16 '20 at 12:48
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@AryanBeezadhur $rad \equiv 1$, i.e. radian is just a synonym for unit-less 1 dimension – Agnius Vasiliauskas Sep 30 '20 at 11:32
@Agnius Vasiliauskas: They are dimensionally compatible in most contexts, but they are not the same unit anymore than meters and centimeters are. – wnoise Oct 02 '20 at 19:04

Colin McFaul · Answer 3 · 2013-04-05T12:46:45.810

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:

BIPM

+1 I edited the "official approval" of this (very useful) approach into your answer. If you don't appreciate that, just reject the edit. — Řídící, Apr 05 '13 at 10:00

score 7 · Answer 4 · answered Apr 04 '13 at 05:20

7

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.

answered Apr 04 '13 at 05:20

Emilio Pisanty

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How is that more formally correct ? – DilithiumMatrix Apr 04 '13 at 07:12
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@zhermes, If A = 10 m, then A/m = 10. – Jan Apr 04 '13 at 08:27
@Jan yes, I'm well aware of why it is 'correct', you'll notice I asked why it was 'more' correct. – DilithiumMatrix Apr 04 '13 at 15:58
@Jan: In what sort of context would A = 10 m? o_O – Joe Z. Apr 04 '13 at 17:47
Or even better, Length/(1 m) – Zo the Relativist Apr 04 '13 at 18:24
I guess it's (a bit) more correct in the sense that the quantity you're tabulating is really length/m. Not that the alternative is wrong, of course. – Emilio Pisanty Apr 05 '13 at 18:55

score 5 · Answer 5 · answered Apr 04 '13 at 10:32

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.

score 4 · Answer 6 · answered Apr 05 '13 at 13:41

4

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".

answered Apr 05 '13 at 13:41

user44430

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ABC · Answer 7 · 2013-04-05T13:00:09.810

3

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 : $[M^0L^0t^0]$

edited Apr 05 '13 at 13:00

answered Apr 04 '13 at 11:17

ABC

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score 1 · Answer 8 · answered Apr 04 '13 at 11:55

1

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

answered Apr 04 '13 at 11:55

AED

27

Is there a symbol for "unitless"?

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