# Typography of multi-letter variables

Chemical elements are typeset with upright font ($\ce{H2O}$ for water) while variables are typeset with an italic font ($V$ for volume).

But is there a convention what to do with multi-letter variables like IC50, EC50 (or others without subscripts)? Is there any official convention for this?

Special cases may be pH and pOH where on could read p as an operator and H and OH as chemical abbreviations, so I would always write them upright. But I am not sure about the others.

In the International System of Quantities, i.e. the system of quantities that corresponds to the International System of Units (SI), as described in ISO 80000, the symbols for quantities are generally single letters from the Latin or Greek alphabet, sometimes with subscripts or other modifying signs. However, symbols for so-called characteristic numbers are written with two letters from the Latin alphabet, the initial of which is always capital. For example:

• Reynolds number $Re$ $$Re=\frac{\rho vl}\eta=\frac{vl}\nu$$

• Nusselt number $Nu$ $$Nu=\frac{Kl}\lambda$$

• Prandtl number $Pr$ $$Pr=\frac{\eta c_p}\lambda=\frac\nu a$$

(Note that such two-letter symbols should be separated from other symbols if they occur as factors in a product.)

Quantity symbols are always written in italic type.

Various other widespread multi-letter symbols are not quantity symbols in accordance with the above-mentioned systems; they are actually just abbreviations. For example in toxicology, LD50 is used as abbreviation for “median lethal dose” (or “lethal dose, 50 %“). Such abbreviations are typeset normally, i.e. generally upright.

Also note that abbreviations for quantities shall not be used in equations.

• Do you have an authoritative argument for "abbreviations shall not be used in equations"? In real life, they often are, e.g. en.wikipedia.org/wiki/IC50 – mhchem Jan 6 '18 at 20:01
• @mhchem I believe they are referring to a paragraph in section 5.1 of the SI Brochure: "It is not permissible to use abbreviations for unit symbols or unit names, such as sec (for either s or second), sq. mm (for either mm² or square millimetre), cc (for either cm³ or cubic centimetre), or mps (for either m/s or metre per second)." – LegionMammal978 Jan 7 '18 at 1:29
• In my chem engineering education, I've always seen dimensionless numbers written in upright characters: Re, Pr, Nu, etc. That might be an engineering convention, in contradiction to that of chemistry, though. – hBy2Py Jan 7 '18 at 2:48

### Two-letter physical quantities

In the IUPAP Red Book, two-letter physical quantities are written in sloping/slanted Roman.[1, pp 44] There is quite the extensive list[1, pp 45–46]. (ISO instead recommends usual italic, more on that below.[1, p 44] Note also that I am currently having trouble generating sloping Roman here, or at least fail to spot the difference. There is supposed to be a subtle variation! See, e.g., the answer by Gonzalo Medina to the question 'What is the difference between italics and slanted text?'.)

a. Dimensionless constants of matter

Prandtl number; nombre de Prandtl: $$\nu/a\ \ \ \ Pr$$

Schmidt number; nombre de Schmidt: $$\nu/D\ \ \ \ Sc$$

[---]

b. Momentum transport

Reynolds number; nombre de Reynolds: $$vl/\nu\ \ \ \ Re$$

[---]

The IUPAC Green Book often uses the IUPAP Red Book as a primary reference.[1, preface] Therefore, a similar table is available there.[2, pp 82] These quantities have in common the fact they are all dimensionless, i.e. have the dimension $$1$$. The sloping Roman style is used to distinguish the two-letter physical quantity from a product of two independent quantities carrying one-letter italic symbols.[1, pp 44]

The ISO recommendation is that two-letter dimensionless parameters be printed in sloping type in the same way as single-letter quantities. When such a symbols is a factor in a product it should be separated from other symbols by a thin space, a multiplicaton sign or brackets. This disagrees with some journals that set two-letter symbols in roman type to distiguish them from ordinary products. In this report sloping roman is used to distiguish a two-letter symbol from the product of two italic single-letter symbols.

### The symbol $$\ce{pH}$$

The official exception is, as you mentioned, $$\ce{pH}$$ and similar symbols.[2, p 70] Note, however, that the letter '$$\ce{p}$$' here cannot directly designate the operator $$-\lg()$$ since an operator cannot act on something that isn't a mathematical function, and $$\ce{H}$$ is not a function. I am aware that this is splitting hairs, but thought was deserving of mention since this has the tag. It is specifically pointed out in the IUPAC Green Book as well.[2, p 75]

Furthermore, there are a lot of misconceptions surrounding the origin of the letter $$\ce{p}$$ in $$\ce{pH}$$. It most likely stems from a variable designation for an electrochemical cell in an experimental setup, not 'power' or anything similar usually quoted. We will proabably never know for sure, however.

For further information, read Nørby, J. G. 'The Origin and the Meaning of the Little p in pH'. Trends in Biochemical Sciences, 2000, 25 (1), 36–37. DOI: 10.1016/S0968-0004(99)01517-0.

### The specific examples given in the OP

See andelisk's answer and Loong's answer for more references. I couldn't find $$\ce{IC50}$$, $$\ce{EC50}$$ specifically but $$\ce{LD50}$$ and $$\ce{ID50}$$ are given in ACS's Style Guide.[3, p 189]

$$\ce{ID50}$$ dose that is infective in 50% of test subjects (also ID50)

[---]

$$\ce{LD50}$$ dose that is lethal to 50% of test subjects (also LD50)

[1] E. Richard Cohen, Pierre Giacomo. (1987). Symbols, Units, Nomenclature and Fundamental Constants in Physics. ('IUPAP Red Book'). International Union of Pure and Applied Physics. Commission C2 – Sunamco. (2010 reprint)

[2] E. R. Cohen, T. Cvitas, J. G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H. L. Strauss, M. Takami, A. J. Thor. (2007). Quantities, Units, and Symbols in Physical Chemistry. ('IUPAC Green Book'). Third Edition. International Union of Pure and Applied Chemistry. (2008 IUPAC & RSC reprint). ISBN: 978-0-85404-433-7.

[3] Anne M. Coghill, Lorrin R. Garson. (2006). The ACS Style Guide. Effective Communication of Scientific Information. American Chemical Society. DOI: 10.1021/bk-2006-STYG, ISBN: 9780841239999 (print), 9780841228306 (online).

• Interesting that your source recommends sloping type to distinguish symbols from italic symbols. I am not sure whether all readers would recognise the difference. Usually sloping type is just considered a poor substitute if italic type is not available. And often the word “sloping” is just used to explain “italic”, although these are actually two different things. – user7951 Jan 6 '18 at 16:51
• @Loong Agreed. Not normally one to share pictures, yet in this case I feel something like this is pertinent. Do you happen to know if sloping Roman vs italic side-by-side comparison is possible in Mathjax? – Linear Christmas Jan 6 '18 at 16:58
• You write "The sloping Roman style is used to distinguish a product two letter italic symbols.". I do not read this in the original. When they write "printed in sloping type in the same way as single-letter quantities", they do not make any distinction between slanted and italic, but they mean "in the same way", identical. Don't they? – mhchem Jan 6 '18 at 19:58
• @mhchem Sorry, not sure I fully follow your question; if I misunderstood your comment, please clarify. According to the IUPAP Red Book, ISO recommends writing two-letter quantities in italic in exactly the same way as single-letter quantities. This is in contrast to some journals which use upright style for two-letter quantities. Both of these are in contrast to IUPAP's style used in the Red Book which is sloping ~ slanted Roman (not italic Roman). See, e.g., this answer for more clarification. – Linear Christmas Jan 6 '18 at 20:14
• I re-read the IUPAP Red Book a couple more times. It is really confused in itself. pp 2 and 67: "italic" and "slanted" are synonyms; p. 47 unclear; p. 44: "d in sloping type in the same way as single-letter quantities" = synonym, BUT three sentences later, they make a distinction: " In this report sloping roman is used to distiguish a two-letter symbol from the product of two italic single-letter symbols." – mhchem Jan 6 '18 at 20:34

According to IUPAC Glossary of Terms Used in Toxicology [1, pp. 1211, 1245] these and similar notations are just ordinary upright characters with corresponding indices:

effective concentration (EC)
Concentration of a substance that causes a defined magnitude of response in a given system. Note: EC50 is the median concentration that causes 50 % of maximal response.

[...]

inhibitory concentration (IC)
Concentration of a substance that causes a defined inhibition of a given system. Note: IC50 is the median concentration that causes 50 % inhibition.

### Reference

1. Duffus, J. H.; Nordberg, M.; Templeton, D. M. Pure and Applied Chemistry 2007, 79 (7). DOI: 10.1351/pac200779071153.