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I noticed from https://en.wikipedia.org/wiki/SI_derived_unit that derived units have to be written in a specific order. For example Newton Metre is written:

$$\text{m}^2⋅\text{kg}⋅\text{s}^{−2}$$

But not:

$$\text{s}^{−2}⋅\text{kg}\cdot\text{m}^2$$

I may assume that the 22 + 6 SI units have a weight order such as

$$ \text{m} > \text{kg} > \text{s} $$

Is this really the case, or are there any exceptions?

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    $\begingroup$ en.wikipedia.org/wiki/… $\endgroup$
    – Jasper
    Commented Jun 9, 2018 at 14:30
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    $\begingroup$ I've never noted any required ordering in my career, though it is usual to put denominators last. $\endgroup$
    – Kyle Kanos
    Commented Jun 9, 2018 at 14:31
  • $\begingroup$ @Jasper, Well, I am blind then :( $\endgroup$
    – nowox
    Commented Jun 9, 2018 at 14:33
  • $\begingroup$ People normally write the units of work as $\text{N}\cdot\text{m}$ rather than $\text{m}\cdot\text{N}$. I've always assumed this was to keep it from looking like millinewtons. Cf. foot-pounds. $\endgroup$
    – user4552
    Commented Jun 9, 2018 at 14:43
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    $\begingroup$ For your interest, the SI units are usually referred as MKS systems (i.e. metre-kilogram-second); whereas Gaussian units as CGS systems (i.e. centimetre-gram-second). $\endgroup$
    – Ng Chung Tak
    Commented Jun 10, 2018 at 7:37

1 Answer 1

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There seems to be an official definition that says the order is always m, kg, s, A, K, mol, cd with the appropriate exponents when only base units are used.

https://en.wikipedia.org/wiki/International_System_of_Quantities#Dimensions_of_derived_quantities

I think that derived units can be used more freely.

Also this does not seem to be too stricty used because 1C is usually 1As and not 1sA.

Other possible orderings include alphabetical or by decreasing exponent.

One can also try to use the less confusing notation: if m can be understood as both milli and meter, it might be better to put the other unit first so m is not the prefix.

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    $\begingroup$ Whooh, that's interesting. I have always written $\text{A}\cdot\text{s}$ instead of $\text{s}\cdot\text{A}$ :) $\endgroup$
    – nowox
    Commented Jun 9, 2018 at 14:37
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    $\begingroup$ What is your source for stating that there seems to be an official defintion... ? The wiki article does not refer to any convention about order or writing combinations of units. $\endgroup$
    – sammy gerbil
    Commented Jun 9, 2018 at 15:07
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    $\begingroup$ You use either a thin space or a centered dot to separate units where there is the possibility of confusing the leading abbreviation with a SI prefix. But I'll note that in many cases the common usage is historical (like $1\,\mathrm{N} = 1\,\mathrm{kg\cdot m/s^2}$ rather than $1 \,\mathrm{m \, kg \, s^{-2}}$. $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Jun 9, 2018 at 15:08
  • $\begingroup$ iso.org/obp/ui/#iso:std:iso:80000:-1:ed-1:v1:en is wiki's source for the Order of dimensions, section 3.7 $\endgroup$
    – Jasper
    Commented Jun 9, 2018 at 15:31
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    $\begingroup$ I cannot find any reference to order in s 3.7 of the ISO document. A consistent order is used for listing the 7 base units, but nothing is said about using this order for derived units. In fact, some examples have base units in a different order, eg $ML^{-3}$ and $TL^{-\frac12}$. $\endgroup$
    – sammy gerbil
    Commented Jun 9, 2018 at 17:07

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