I researched on how to write units, constants and quantities, and variables the proper way. There’s a lot of information out in the interwebs. And, of course, not everything is correct.

In 2010, a new ISO standard was published, the ISO 80000-2, describing mathematical signs and symbols. You can buy it here (buying a ISO paper, it’s strange, right?).

There’s a LaTeX package called `isomath`

implementing this standard for your favorite typesetting tool.

Following some notes from it on *upright-edness* and *italic-ity*.

- Units are to be written
**upright**(roman). Capital, when they are based on names (`K`

for Kelvin), small when not (`m`

for meter). See more on that at Andrés blog. - Variables are to be written in
**italics**(slanted), independently if the character is latin or greek.

,*x*= 12

.*α*= 1 - Mathematical constants are to be written
**upright**. Physical ›constants‹ in**italics**.

`π`

is upright, so is`i`

as in`i`

.^{2}= -1

In italics is the speed of light,

, the Avogadro constant,*c*

.*N*_{A} - Well-known functions are
**upright**, like`sin`

or*x*`exp`

.*x*

And this means, yes, also the the`e`

in`e`

is upright, as it’s both a function and a mathematical constant.^{2x} - Indices of variables are
**upright**when they are descriptive. See the Avogadro constant above. - Differential operators are
**upright**, but not the variables/quantities they differentiate (for).`d`

.*x*/d*t* - Particle name abbreviations are
**upright**. Independently if it’s a latin letter (the electron’s`e`

) or a greek one (the pion’s`π`

).

While we are at it: The correct way to describe axes in plots is to state the measured variable (e.g.

), state a slash as a division sign (*ρ*`/`

) and then the unit of the variable (e.g. `MPa`

) – *ρ*/MPa^{1}. The order of variable and unit can be interchanged if the value given is reciprocal, e.g. `1/`

would lead to a description of *ρ*`MPa/`

. Writing square brackets for the unit is not correct (as in *ρ*`[MPa]`

).

Ressources I used to compile this list, sorted by importance:

- ISO 80000-2 standard
- NIST’s »Typefaces for Symbols in Scientific Manuscripts« handout (careful: a little old)
- Bureau International des Poids et Mesures, The International System of Units (SI), Brochure, 2008, Section 5.3
- A handy Stackexchange post, and another blog post with pictures.

Think about it: Every quantity

on the axis is divided by the unit, hence the number essentially loses its dimension, as shown on the axis. ↩*ρ*

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