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PhysicsIs there a symbol for "unitless"?
[+39] [8] Ben
[2013-04-04 03:49:48]
[ units notation si-units ]
[ https://physics.stackexchange.com/questions/59978/is-there-a-symbol-for-unitless ]

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?

(3) How about a dash $(-)$? - DilithiumMatrix
(16) I would just use nothing at all: |||| Safety Factor |||| - user10851
@zhermes - was thinking that, but could be confused for "negative" or "omit" or something... - Ben
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
(4) Whenever anyone omitted the units on any answer my high school physics teacher would write in "fish". - Ben Jackson
When a square bracket convention is being used, such as [km], I've seen non-dimensional parameter listed as [n/d]. - Adam Wuerl
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
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
[+47] [2013-04-04 11:04:58] Řídící [ACCEPTED]

Straight from the horse [1]'s mouth:

enter image description here enter image description here

Source: Bureau International des Poids et Mesures [2] (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 [3]

[1] http://www.phrases.org.uk/meanings/336400.html
[2] http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf
[3] http://en.wikipedia.org/wiki/BIPM

(11) Interesting. Shame you can't attach prefixes to "one" - I'm quite fond of yoctoone. - Michael
(2) ^ Yoctoone is otherwise known as one septillion, or $10^{24}$. - Joe Z.
(6) @JoeZeng If anything, one septillion th, or $10^{-24}$ (Wikipedia, Horse). - Řídící
@Gugg Whoops. Yotta and Yocto are too easy to mix up. - Joe Z.
In fact, you could say it's zetta confusing. - Joe Z.
(1) @JoeZeng: or better yet, hella confusing: scitech.blogs.cnn.com/2010/03/04/hella-proposal-facebook - Zo the Relativist
I suppose it all depends on the unit measure of confusings... - OP - Ben
(3) 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
@vsz Indeed. That's called homoglyphic confusion. - Řídící
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[+15] [2013-04-04 04:00:08] wnoise

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


(1) I thought radians have the unit (rad) - bzr
@AryanBeezadhur: en.wikipedia.org/wiki/Rad_%28unit%29 - wnoise
I’ve seen this in maths: $360 \deg = 2 \pi rad$ - bzr
(2) @AryanBeezadhur $rad \equiv 1$, i.e. radian is just a synonym for unit-less 1 dimension - Agnius Vasiliauskas
@Agnius Vasiliauskas: They are dimensionally compatible in most contexts, but they are not the same unit anymore than meters and centimeters are. - wnoise
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[+8] [2013-04-04 04:04:51] Colin McFaul

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 [1]

[1] http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf

(1) +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
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[+7] [2013-04-04 05:20:21] Emilio Pisanty

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.


(1) How is that more formally correct ? - DilithiumMatrix
(7) @zhermes, If A = 10 m, then A/m = 10. - Jan
@Jan yes, I'm well aware of why it is 'correct', you'll notice I asked why it was 'more' correct. - DilithiumMatrix
@Jan: In what sort of context would A = 10 m? o_O - Joe Z.
Or even better, Length/(1 m) - Zo the Relativist
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
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[+6] [2013-04-04 10:32:46] user20250

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.


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[+5] [2013-04-05 13:41:26] user44430

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".


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[+3] [2013-04-04 11:17:29] ABC

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


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[+2] [2013-04-04 11:55:51] AED

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


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