# 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?

• How about a dash $(-)$? – DilithiumMatrix Apr 4 '13 at 3:57
• I would just use nothing at all: |||| Safety Factor |||| – user10851 Apr 4 '13 at 3:58
• @zhermes - was thinking that, but could be confused for "negative" or "omit" or something... – Ben Apr 4 '13 at 4:11
• 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. – Nathaniel Apr 4 '13 at 6:34
• Whenever anyone omitted the units on any answer my high school physics teacher would write in "fish". – Ben Jackson Apr 5 '13 at 5:22

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

• Interesting. Shame you can't attach prefixes to "one" - I'm quite fond of yoctoone. – Michael Brown Apr 4 '13 at 11:14
• ^ Yoctoone is otherwise known as one septillion, or $10^{24}$. – Joe Z. Apr 4 '13 at 17:46
• @JoeZeng If anything, one septillion th, or $10^{-24}$ (Wikipedia, Horse). – Keep these mind Apr 4 '13 at 17:55
• @JoeZeng: or better yet, hella confusing: scitech.blogs.cnn.com/2010/03/04/hella-proposal-facebook – Jerry Schirmer Apr 4 '13 at 18:22
• 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 5 '13 at 6:12

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

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. – Keep these mind Apr 5 '13 at 10:00

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.

• How is that more formally correct ? – DilithiumMatrix Apr 4 '13 at 7:12
• @zhermes, If A = 10 m, then A/m = 10. – Jan Apr 4 '13 at 8:27
• @Jan yes, I'm well aware of why it is 'correct', you'll notice I asked why it was 'more' correct. – DilithiumMatrix Apr 4 '13 at 15:58
• @Jan: In what sort of context would A = 10 m? o_O – Joe Z. Apr 4 '13 at 17:47
• Or even better, Length/(1 m) – Jerry Schirmer Apr 4 '13 at 18:24

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.

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".

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

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

## protected by Qmechanic♦Apr 4 '13 at 14:54

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