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I was in a conversation with my senior engineer where he kept on insisting that we can use plural when we write down any unit. I argued that it is not the 'common' practice or even throughout my whole academic career (unfortunately) I haven't found any instance where there was any plural unit used in the text books. He argued that if I said that it was not correct then it should have a good reason for that.

When I searched for this topic I couldn't come to any conclusive decision. Such as this thread and the other links those have been referred there (some leads to English.SE). These answers gave me the impression that it is grammatically acceptable provided the right circumstances.

But I felt that it would be rather ambiguous to accept plurals on scientific and engineering notations.

For example we were talking about output rate of a boiler which is measured in $\mathrm{kg/hr}$. My senior said that it is okay if anyone writes $\mathrm{kgs/hr}$.

To me it looks ambiguous. If anyone writes $\mathrm{s}$ after $\mathrm{kg}$ it may give a plural sense but as well it may refer to second also. Moreover if anyone argues that this is acceptable in some cases (like $\mathrm{kgs/hr}$) then what would be the yard stick to find out accepted cases? For instance can we add $\mathrm{s}$ in $\mathrm{m/s}$ or $\mathrm{km/hr}$ like $\mathrm{ms/s}$ or $\mathrm{kms/hr}$?

There is The NIST Guide for the Use of the International System of Units, which has this example.

the length of the laser is $5\ \mathrm{m}$ but not: the length of the laser is five meters

But I want to have more conclusive answer to which one is acceptable i.e. $\mathrm{kg/hr}$ or $\mathrm{kgs/hr}$ (or other similar instances).

David Z
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Ahmed
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4 Answers4

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According to the International System of Units (SI)

Unit symbols are mathematical entities and not abbreviations. Therefore, they are not followed by a period except at the end of a sentence, and one must neither use the plural nor mix unit symbols and unit names within one expression, since names are not mathematical entities.

as well as to the international standard ISO/IEC 80000 Quantities and units

Symbols for units are always written in roman (upright) type, irrespective of the type used in the rest of the text. The unit symbol shall remain unaltered in the plural and is not followed by a full stop except for normal punctuation, e.g. at the end of a sentence.

it is not acceptable to use the plural of unit symbols.

By the way, it is also not permissible to use abbreviations such as “hr” for unit symbols (“h”) or unit names (“hour”).

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    "$\mathrm{hr}$" has its use in mainstream scientific and academic literature. You can see here. But the standard form is "$\mathrm{h}$" what you've mentioned. – Ahmed Feb 04 '18 at 11:25
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    See also https://chemistry.meta.stackexchange.com/a/2978/7951 –  Feb 04 '18 at 13:00
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    You will also often find "sec" for "s", even in scientific texts, which is absolutely incorrect! – freecharly Feb 04 '18 at 15:36
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    I believe the use of $\rm{hr}$ and $\rm{sec}$ is a very American convention that comes with the imperial unit system. I’ve noticed, for example, that these change when I switch my phone language to Spanish. So, I would not say that it’s any more “impermissible” or “wrong” to use $\rm{hr}$ than it is to use $\rm{\Omega!\cdot! in}$ for resistivity. It’s hideous and mathematically absurd, but not absolutely impermissible. – gen-ℤ ready to perish Feb 05 '18 at 07:10
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    When outside of the SI range, there can be issues with the understanding of unit abbreviations and symbols due to them being national or local. An abbreviation such as h does not make much sense for me as a native Dane, with another mother tongue than English, since we here have another language dependant word for hour, abbreviated differently. I only do understand hr because I have seen it used so often. This is one of the good reasons for consistent use of the SI system: That you don't end up using "local" symbols noone else understand – Steeven Feb 05 '18 at 13:11
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    "Unit symbols are mathematical entities and not abbreviations." ... This is one of the dumbest things I've ever read. Of course they're abbreviations. You can be 100% sure of this because you don't say "m" when reading it aloud; you say "meters." But because they belong in the middle of equations and attached to numbers, the mechanical rules are different than other kinds of abbreviations. Way to confuse the issue, BIPM. – jpmc26 Feb 06 '18 at 17:20
  • @jpmc26 Maybe you say "kilometers", but others will say "chiliómetra"/"quilòmetres"/"ciliméadar". You don't say "1" either you say "one"/"uno"/"ein". – OrangeDog Feb 07 '18 at 12:32
  • @OrangeDog "1" is not a letter in the first place. That the abbreviation is for a particular language doesn't make it not an abbreviation. – jpmc26 Feb 07 '18 at 19:12
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This is what I would tell your colleague: one of the main points of using units is that we can use them throughout physics formulas and they serve as a check for coherence (even though I am a mathematician, I cringe when I see physics' examples in math books that remove the units completely). So, say you have some quantity $r=a/b$, where $a$ is measured in kilograms and $b$ in kilograms per hour. Now you want to calculate $r$, and in a particular measurement/problem, $a$ is 2 kilogram, and $b$ is 1 kilogram per hour. Then $$r=\frac{2\,\mathrm{kg}}{1\frac{\mathrm{kg}}{\mathrm{h}}}=2\,\mathrm{h}, $$ where one "cancels" the kilograms. With your colleague's suggestion, the above formula would be $$r=\frac{2\,\mathrm{kgs}}{1\frac{\,\mathrm{kg}}{\mathrm{h}}}=2\,\mathrm{h}, $$ and you have the mathematical awkwardness of "cancelling" kgs with kg.

Massimo Ortolano
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Martin Argerami
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    worse yet: meters divided by a time unit gives a wrong result. $1\frac{ms}{h}=1\frac{ms}{3600s}=\frac{1}{3600}m$ – lucidbrot Feb 04 '18 at 19:03
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    @pentane: could you explain? I don't follow. – Martin Argerami Feb 04 '18 at 23:01
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    @pentane h seems to be much less common than hr, even if it's non-standard. – user253751 Feb 04 '18 at 23:26
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    https://physics.nist.gov/cuu/Units/outside.html this page says "h" is ok. So I apologize for my comment. I've just never seen "h" always "hr" – pentane Feb 04 '18 at 23:34
  • The case of hours seems to be one where the standards committee decided to make official a choice other than the pre-existing majority usage. And the committee will probably get their way in the long run (because they have a strong presence in government and industry), but I'm teaching two different physics and astronomy texts each only a few years old that use $\mathrm{hr}$ throughout for hours. – dmckee --- ex-moderator kitten Feb 04 '18 at 23:42
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    @pentane Do you measure vehicle speeds in mph or km/h? – Henry Feb 05 '18 at 08:40
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    I think that precisely because you are a mathematician, you cringe when you see people remove units. :-) – IS4 Feb 05 '18 at 11:09
  • @lucidbrot How ? Did you cancel $s$ from numerator and denominator ? If yes then then will you do the same for $1\dfrac{mol}{dm^3}= 1 M$ ? – user8277998 Feb 05 '18 at 19:30
  • @user45914123 yes I did (and I am aware that this is not correct. I'm just displaying that using the plural $ms$ for meters can lead to confusion). You make a valid point - Now I would be happier if every unit had a single character. But the difference is that $dm$ and $mol$ are standard, while $ms$ is not. So $ms$ will cause more confusion than $dm$. – lucidbrot Feb 05 '18 at 19:35
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    @lucidbrot: I get $1\frac{ms}{h}=\frac{0.001s}{3600s}=\frac{1}{3600000}$. ms already means millisecond, and beyond being syntactically wrong, it also is completely ambiguous. – James K Feb 05 '18 at 21:11
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When you write that a length is $75\,\rm metre$ or $75\,\rm m$ you are really write that your length is seventy five times bigger than a length of $1\,\rm metre$ or $1\,\rm m$ ie $75 \times (1\,\rm metre)$ or $75 \times (1\,\rm m)$

I think that this illustrates that you should not use an “s” to signify a plural for the unit name and symbol.

However this is not the end of the story as the NPL in the UK recommends the following for the unit name.

For unit values more than 1 or less than -1 the plural of the unit is used and a singular unit is used for values between 1 and -1.

This is at variance of NIST in the USA which states.

Unit symbols are unaltered in the plural. proper: l = 75 cm improper: l = 75 cms.

Using a unit symbol which is never used in the plural form removes this ambiguity.

There’s a related question on English Stack Exchange with this answer:

In Standard English, this crucially depends on whether the phrase is prenominal or not. Prenominally, the phrase will not show plural marking, while elsewhere it will have the normal plural marking, as appropriate.

Compare:

  • The bureau is 3 meters long.

  • This is a 3-meter-long bureau. (prenominal)

    <hr></li>
<li><p>The period is <i>2 week<b>s</b></i>.</p></li>
<li><p>This is a <i>2-week</i> period. (prenominal)</p>

<hr></li>
<li><p>The bill was <i>0.50 dollar<b>s</b></i>.</p></li>
<li>This is a <i>0.50-dollar</i> bill. (prenominal)</li>
</ul>

Note also that a hyphen is normally inserted to connect the words in the adjectival phrase when the phrase is prenominal.

I suggest that a scientific text should not use the plural form of the names of a unit whereas non-scientific text and oral presentations may use the plural form of the name of the unit.

Farcher
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    The NPL and NIST recommendations are not in contrast: the UK statement refers to unit names, the NIST statement to unit symbols. In fact, if you look at the NPL page, it also states that "Unit symbols are unaltered in the plural". – Massimo Ortolano Feb 04 '18 at 11:27
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    @MassimoOrtolano Thank you for your comment which has resulted in my trying to clarify my answer and in particular addressing the ambiguity which exists when answering the OP in regard to unit names rather than symbols. – Farcher Feb 04 '18 at 11:52
  • @Farcher: Actually it would be far more common to refer to "a six foot man" than "*a six feet man" (which most people would consider wrong); also "six foot four" (meaning 6'4") is used rather than "*six feet four" (but, confusingly, "six feet four inches" is correct!) – psmears Feb 05 '18 at 12:06
  • @psmears Thank you for your comment. I really think that it depends where you live and the word order and thus have got rid of the reference to foot and feet in my answer. – Farcher Feb 05 '18 at 12:38
  • @Farcher: Probably a good idea, rather than getting bogged down in all the different variations :-) – psmears Feb 05 '18 at 12:40
  • @pamears six foot man follows the same rules as far as I can see; it's just that the plural of foot is feet and not foots: His height is six feet vs. He is a six-foot man is the same rule as His height is two meters vs He is a two-meter-man. – TripeHound Feb 06 '18 at 15:34
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In addition to the other answers that point out that the language of the SI unit standards prohibits pluralization of unit symbols, I'll also point out that adding the "s" to any unit is misleading, since "s" is a unit symbol itself (for seconds). So, writing the unit "kgs" is actually indicating a unit of kilogram-seconds, and not a unit of kilograms. Pluralization of unit symbols must be avoided, or this notational error will occur.

Nuclear Hoagie
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