# What's the policy on systems of measure?

Whilst the SI is very popular in chemistry (and in the world in general) there are a wide range of commonly used units in chemistry that are not SI or SI-derived (kcal, Bohr, Hartree, mmHg, enzyme units, PSI, the list goes on). Moreover it is inevitable that temperatures will at some point be specified in degrees Fahrenheit, masses in ounces, distances in nanocubits etc.

Do we just roll with whatever people would like to use, do we encourage or discourage the use of certain units, or do we have hard rules about units?

Bonus question: does mathjax support the excellent siunitx?

• In short, I agree with Manishearth and think we should not regulate too strictly units… chemists are, after all, quite conservative in their choice of units and still use some units that could really have been phased out decades ago… yeah, I’m looking at you, kcal/mol! – F'x Apr 26 '12 at 12:29
• Howdy i think the idea of making mathjax work with siunitx would be perfect. siunitx i widely known in the TeX community and is the best implementation of SI i know. – bloodworks Jul 28 '12 at 13:08

Physics.SE just rolls with whatever is thrown at 'em. I haven't seen any confusions caused due to units except in cases where the OP has neglectrd to specify them.

So let's not add policy creep.

Regarding units, I've always been happy with 123\:\mathrm{J} &c. I have a bookmarklet I've written that makes mathifying and unitifying easy-though it needs some improvement (ill get you the finished one next week or so-not in town for a few days)

Can't find a mathjax extension :(

• Bookmarklet sounds good! – Richard Terrett Apr 26 '12 at 12:05
• @Richard remind me after May 2, will you? Im out of town for a while, and when I come back I have the Physics.SE gobble of TP and Astro.SE to help handle, so I'm likely to f orget. ;-) – ManishEarth Apr 27 '12 at 10:28
• @Richard here ya go – ManishEarth May 3 '12 at 15:54

## You may use whatever unit you like – but please do it right

According to the relevant regulatory guides, standards, and recommendations, there is extensive international consensus on the units that shall be used in science and technology. First of all, the recommended units are the SI base units and the SI coherent derived units, including those with special names. Furthermore, various non-SI units are accepted for use.

On the other hand, many other units exist, the use of which is deprecated. Nevertheless, some obsolete or otherwise deprecated units are of historical importance in the established literature. On Chemistry Stack Exchange, deprecated units mainly appear in some questions (which is usually not the asker’s fault, but allows us to draw conclusions about the quality of the asker’s book, course, or lecture). Experience shows that the most common nonconforming units in questions on this site are

• standard atmosphere (atm)
• atomic mass unit (amu)
• calorie (cal)
• torr (Torr)
• degree Fahrenheit (°F)
• pound-force per square inch (psi)
• conventional millimetre of mercury (mmHg)

Of course, we can work with such units. In many cases, this merely requires the use of conversion factors (which is never required when only coherent SI units are used). That is why we should accept questions regardless of the used units; i.e. the use of deprecated units is not a reason to close a question and not necessarily a reason to downvote a question. However, we may comment (in our answers or in actual comments) on any nonconformity of units.

When answering such questions, we should weigh the advantages and disadvantages of using the units given in the question (e.g. to avoid rounding errors or to keep the answer short and simple) or converting the numerical values to conforming units.

Generally, the use of quantity equations (which have the advantage of being independent of the choice of units) is preferred and is strongly recommended.

instead of “speed in kilometre per hour is 3.6 times the quotient of distance in metres by time in seconds”, which corresponds to the numerical value equation

$\displaystyle v/(\mathrm{km/h})=3.6\frac {l/\mathrm m}{t/\mathrm s}$ or $\displaystyle \left\{v\right\}_{\mathrm{km/h}}=3.6\frac{\left\{l\right\}_{\mathrm m}}{\left\{t\right\}_{\mathrm s}}$

use “speed $v$ is the quotient of distance $l$ by time $t$”, preferably in form of the quantity equation

$\displaystyle v=\frac lt$

Anyway, all units (either SI units, other accepted units, or obsolete units), their names, and their symbols can and shall be written and used correctly. (Simply using coherent SI units does not solve all problems.) Compliance with the rules and style conventions, only the most important of which are presented in the following, supports the readability of questions and answers.

## Tilting at windmills

• The value of a quantity is generally expressed as the product of a number and a unit. It is not permissible to omit the unit.

the Avogadro constant is $L=6.022140857(74)\times10^{23}\ \mathrm{mol}^{-1}$, not $L=6.022140857(74)\times10^{23}$

the molar gas constant is $R=8.3144598(48)\ \mathrm{J\ mol^{-1}\ K^{-1}}$ , not $R=8.3144598(48)$

the molar mass of helium is $M=4\ \mathrm{g\ mol^{-1}}$, not $M=4$

When a problem requires calculations using values, always write the values with the correct units and carry the units through the calculation. Do not omit the units while performing intermediate steps and do not just reintroduce units at the end of the calculation.

• The unit shall be in accordance with the dimension of the quantity.

the molar mass of $\ce{H2}$ is $M=2.016\ \mathrm{g\ mol^{-1}}$, neither $M=2.016\ \mathrm g$, $M=2.016\ \mathrm u$, $M=2.016\ \mathrm{Da}$, nor $M=2.016\ \mathrm{amu}$

the relative atomic mass of the nuclide $\ce{^12C}$ is $A_{\mathrm r}=12$, neither $A_{\mathrm r}=12\ \mathrm u$, $A_{\mathrm r}=12\ \mathrm{Da}$, $A_{\mathrm r}=12\ \mathrm{amu}$, $A_{\mathrm r}=12\ \mathrm g$, nor $A_{\mathrm r}=12\ \mathrm{g\ mol^{-1}}$

the molar volume of an ideal gas at STP ($T=273.15\ \mathrm K$ and $100\ \mathrm{kPa}$) is $V_\mathrm m=22.710947(13)\ \mathrm{l\ mol^{-1}}$, not $V_\mathrm m=22.710947(13)\ \mathrm l$

the unit of change in enthalpy $\Delta H$ is joule ($\mathrm J$);
the unit of change in molar enthalpy $\Delta H_\mathrm m$ is joule per mole ($\mathrm{J/mol}$);
the unit of change in specific enthalpy $\Delta h$ is joule per kilogram ($\mathrm{J/kg}$)

the unit of heat capacity $C$ is joule per kelvin ($\mathrm{J/K}$);
the unit of specific heat capacity $c$ is joule per kilogram kelvin ($\mathrm{J/(kg\cdot K)}$);
the unit of molar heat capacity $C_\mathrm m$ is joule per mole kelvin ($\mathrm{J/(mol\cdot K)}$)

the value of the unified atomic mass constant is $m_\mathrm u=1\ \mathrm{Da}=1\ \mathrm{u}$, not $m_\mathrm u=1\ \mathrm{Da}=1\ \mathrm{g/mol}$

• While the symbols for quantities are only recommendations, the choice, style, and form of unit symbols is mandatory.

• The use of the correct symbols for units is mandatory.

the symbol for the mole is $\mathrm{mol}$, not $\mathrm{m}$

the symbol for the torr is $\mathrm{Torr}$, not $\mathrm{torr}$

the symbol for the degree Celsius is $\mathrm{^\circ C}$, not $\mathrm C$;
the symbol for the degree Fahrenheit is $\mathrm{^\circ F}$, not $\mathrm{F}$;
the symbol for the kelvin is $\mathrm K$, not $\mathrm{^\circ K}$

Most symbols for units consist of one or more letters from the Latin or Greek alphabet. They are printed in lower-case letters unless they are derived from a proper name, in which case the first letter is a capital letter.

An exception is that either the capital L or the original symbol lower-case l may be used for the litre, in order to avoid possible confusion between the numeral 1 (one) and the lower-case letter l (el), although it is not derived from a proper name of a person.

• Symbols for units are not to be confused with symbols for similar units.

the symbol for the (obsolete) unit torr is $\text{Torr}$, not $\mathrm{mmHg}$;
the symbol for the (obsolete) unit conventional millimetre of mercury is $\mathrm{mmHg}$, not $\text{Torr}$

the symbol for the unified atomic mass unit is $\mathrm u$, not $\mathrm{amu}$;
the symbol for the (obsolete) atomic mass unit is $\mathrm{amu}$, neither $\mathrm u$ nor $\mathrm{Da}$

• It is not permissible to use abbreviations for unit symbols or unit names.

do not write “gm” (for either $\mathrm g$ or gram)

do not write “sec” (for either $\mathrm s$ or second)

do not write “hr” (for either $\mathrm h$ or hour)

do not write “sq. mm” (for either $\mathrm{mm^2}$ or square millimetre)

do not write “cc” (for either $\mathrm{cm^3}$ or cubic centimetre)

do not write “amps” (for either $\mathrm{A}$ or ampere)

• The unit symbol shall remain unaltered in the plural.

write “$1\ \mathrm h=60\ \mathrm{min}$”, not “$1\ \mathrm h=60\ \mathrm{mins}$”

• In order to avoid large or small numerical values, decimal multiples and submultiples of units may be formed with the SI prefixes.

$0.002\ \mathrm l=2\ \mathrm{ml}$

When prefixes are used with SI units, the resulting units are no longer coherent, because a prefix effectively introduces a numerical factor in the expression for the unit in terms of the base units.

SI prefixes can be used with various non-SI units, but they are never used with the units of time minute (min), hour (h), and day (d).

• Prefix symbols are attached to unit symbols without a space between the prefix symbol and the unit symbol.

With the exception of da (deca), h (hecto), and k (kilo), all multiple prefix symbols are capital (upper case) letters, and all submultiple prefix symbols are lower case letters.

the symbol for the kilojoule is $\mathrm{kJ}$, not $\mathrm{KJ}$

Compound prefix symbols, that is, prefix symbols formed by the juxtaposition of two or more prefix symbols, are not permitted.

• Prefix symbols shall not stand alone.

do not write “$2\ \mathrm k$” for 2000

(Note that the expression “$2\mathrm K$” (for 2000) violates even three individual rules.)

• Expressions for units shall contain nothing else than unit symbols and mathematical symbols. Any attachment to a unit symbol as a means of giving information about the special nature of the quantity or context of measurement under consideration is not permitted.

write “the maximum electric potential difference is $U_\text{max}=1000\ \mathrm V$”, not “$U=1000\ \mathrm V_\text{max}$”

write “the gauge pressure is $p_\mathrm e=0.5\ \text{bar}$”, not “$p=0.5\ \text{bar(g)}$”

write “the mass fraction of substance $\ce B$ is $w_{\ce B}=0.76=76\ \%$”, neither “$w_{\ce B}=0.76\ (m/m)$” nor “$w_{\ce B}=76\ \%\ (m/m)$”

write “the water content is $170\ \mathrm{g/l}$”, not “$170\ \mathrm{g\ \ce{H2O}/l}$”

write “the electric power is $P_\text{el}=1300\ \mathrm{MW}$”, not “$P=1300\ \mathrm{MW_{el}}$”

• Symbols for units, including prefix symbols, are always written in roman (upright) type, not in italic type.

write “$m=10\ \mathrm{kg}$”, not “$m=10\ kg$”

Note that the upright symbol µ (for micro) can only be correctly printed using MathJax by the syntax \unicode[Times]{x3BC}. Using \mu generates the italic symbol $\mu$.

• A space is used to separate the numerical value from the unit symbol.

write “$m=10\ \mathrm{kg}$”, not “$m=10\mathrm{kg}$”

write “$\vartheta=20\ \mathrm{^\circ C}$”, neither “$\vartheta=20\mathrm{^\circ C}$” nor “$\vartheta=20\mathrm{^\circ\ C}$”

The only exceptions to this rule are for the unit symbols for degree, minute, and second for plane angle, °, ′, and ″, respectively, for which no space is left between the numerical value and the unit symbol.

write “$\tau\approx109.47^\circ$”, not “$\tau\approx109.47\ ^\circ$”

Even when the value of a quantity is used as an adjective, a space is left between the numerical value and the unit symbol.

Only when the name of the unit is spelled out would the ordinary rules of grammar apply, so that a hyphen would be used to separate the number from the unit.

write “a 35-millimetre film” not “a 35 millimetre film”

• Unit symbols are mathematical entities and not abbreviations. In expressing the value of a quantity as the product of a numerical value and a unit, both the numerical value and the unit may be treated by the ordinary rules of algebra.

• A compound unit formed by multiplication of two or more units shall be indicated by a space or a half-high (centred) dot (·), since otherwise some prefixes could be misinterpreted as a unit symbol.

for newton metre, write “$\mathrm N\cdot\mathrm m$” or “$\mathrm N\ \mathrm m$”

The latter form may also be written without a space, i.e. “$\mathrm{Nm}$”, provided that special care is taken when the symbol for one of the units is the same as the symbol for a prefix. This is the case for $\mathrm m$ (metre and milli), and for $\mathrm T$, (tesla and tera).

“$\mathrm{mN}$” means millinewton, not metre newton

• A compound unit formed by dividing one unit by another shall be indicated by a horizontal line, by a solidus (/) or by negative exponents.

write “$\displaystyle\frac{\mathrm m}{\mathrm s}$”, “$\mathrm m/\mathrm s$”, “$\mathrm m\cdot\mathrm s^{-1}$”, or “$\mathrm m\ \mathrm s^{-1}$” for metre per second

However, where it is necessary to include fractions in the body text, they shall, where possible, be reduced to a single level by using a solidus (/) or, where applicable, the negative index.

in the body text, write “$C_{\mathrm m,p} = 33.58\ \mathrm{J/(K \cdot mol)}$” or “$C_{\mathrm m,p} = 33.58\ \mathrm{J\cdot K^{-1} \cdot mol^{-1}}$”, not “$\displaystyle C_{\mathrm m,p} = 33.58\ \mathrm{\frac{J}{K \cdot mol}}$”; the small inline style of MathJax “$C_{\mathrm m,p} = 33.58\ \mathrm{\frac{J}{K \cdot mol}}$” is only a makeshift solution that is not generally considered proper typography

• When several unit symbols are combined, care should be taken to avoid ambiguities, for example by using brackets or negative exponents. A solidus (/) shall not be followed by a multiplication sign or a division sign on the same line unless parentheses are inserted to avoid any ambiguity.

write “$c_p=4.18\ \mathrm{kJ/(kg\cdot K)}$” or “$c_p=4.18\ \mathrm{kJ\ kg^{-1}\ K^{-1}}$”, not “$c_p=4.18\ \mathrm{kJ/kg\ K}$”

In complicated cases, negative powers or a horizontal bar may be used.

• If the quantity to be expressed is a sum or a difference of quantities, then either parentheses shall be used to combine the numerical values, placing the common unit symbol after the complete numerical value, or the expression shall be written as the sum or difference of expressions for the quantities.

write “$l=12\ \mathrm m-7\ \mathrm m$” or “$l=\left(12-7\right)\ \mathrm m$”, not “$l=12-7\ \mathrm m$”

Two or more quantities cannot be added or subtracted unless they belong to the same kind (the same category of mutually comparable quantities).

Hence, quantities on each side of an equal sign in an equation must also be of the same kind.

do not write “$1\ \mathrm{kg}=9.81\ \mathrm N$”

do not write “$1\ \mathrm{mol}=12\ \mathrm g$”

do not write “$1\ \mathrm{mol}=22.7\ \mathrm l$”

do not write “$1\ \mathrm{mol/l}=100\ \mathrm{g/l}=10\ \%$”

However, quantities of the same kind do not necessarily have the same unit.

$250\ \mathrm g = 0.250\ \mathrm{kg}$

$10\ \mathrm{m/s} = 36\ \mathrm{km/h}$

• In expressing the value of a quantity as the product of a numerical value and a unit, both the numerical value and the unit may be treated by the ordinary rules of algebra.

the equation $T=293\ \mathrm K$ may equally be written $T/\mathrm K=293$

It is often convenient to write the quotient of a quantity and a unit in this way for the heading of a column in a table, so that the entries in the table are all simply numbers.

$$\begin{array}{ll} \hline T/\mathrm K & p/\mathrm{kPa} \\ \hline 300.00&3.5368\\ 310.00&6.2311\\ 320.00&10.546\\ 330.00&17.213\\ \hline \end{array}$$

The axes of a graph may also be labelled in this way, so that the tick marks are labelled only with numbers.

do not write “mass [kg]” for “mass in kilogram”

• It is essential to distinguish between quantities and units.

density $\rho=m/V$ is defined as “quotient of mass by volume” or “mass per volume”, neither “mass per unit volume”, “mass per litre”, nor “kilograms per litre”

write “divide the mass by the volume”, neither “divide the grams by the volume” nor “divide the grams by the litres”

• It is important to distinguish between unit symbols and unit names.

“kilogram” is a unit name; “$\text{kg}$” is a unit symbol

“mole” is a unit name; “$\text{mol}$” is a unit symbol

“torr” is a unit name; “$\text{Torr}$” is a unit symbol

• Unit names are not mathematical entities.

• Unit symbols and unit names shall not be mixed within one expression

write “$\mathrm{g/mol}$” or “gram per mole”, neither “$\mathrm{g}/\text{mole}$”, “g per mole”, “$\text{gram}/\mathrm{mol}$”, nor “gram per mol”

• Spell out units of measure that do not follow a number.

write “several milligrams”, not “several mg”

write “a few milliliters”, not “a few ml”

However, in column headings of tables and in axis labels of figures, use unit symbols, even without numbers.

You may use unit symbols in parentheses after the definitions of variables, even without numbers.

• Since quantities are themselves always independent of the unit in which they are expressed, a quantity name shall not reflect the name of any corresponding unit.

the quantity density shall not be called “litre weight”

the quantity mass shall not be called “number of grams”

the quantity amount of substance shall not be called “number of moles”*

the quantity electric power shall not be called “wattage”

the quantity mass fraction shall not be called “percentage”

The name “voltage”, commonly used in the English language, is an exception from the principle that a quantity name should not refer to any name of unit. It is recommended to use conforming names, such as “electric tension” or “potential difference”, wherever possible.

Notwithstanding the above, the adjective “molar” is added to the name of a quantity to indicate the quotient of that quantity by the amount of substance, although the term “molar” violates the principle that the name of the quantity shall not reflect the name of a corresponding unit (in this case, mole).

• Names of units are spelled with a lower case initial in English (even when the symbol for the unit begins with a capital letter), except in the beginning of a sentence when a capital initial is used.

the unit of thermodynamic temperature is the kelvin (symbol: $\mathrm K$), not “Kelvin”

the unit of thermodynamic temperature is the joule (symbol: $\mathrm J$), not “Joule”

an obsolete unit of pressure is the torr (symbol: $\text{Torr}$), not “Torr”

For SI units, it is only the unit name degree Celsius that contains a capital letter. In keeping with the rule, the unit degree begins with a lower-case d and the modifier Celsius begins with an upper-case C because it is a proper name).

• Prefix names are inseparable from the unit names to which they are attached.

millimetre, micropascal, and meganewton are single words

• In the English language, the name of the product of two units is the concatenation of the two names, separated by a space.

for $\mathrm{N\ m}$, write “newton metre”

• The name of the quotient of two units is formed by inserting the word “per” between the two names. A compound name shall never contain more then one “per” (without parentheses).

for $\mathrm{m/s}$, write “metre per second”

for $\mathrm{J/(kg\cdot K)}$, write “joule per kilogram kelvin”, not “joule per kilogram per kelvin”

• The name of the power $a^n$ of a unit is the name of that unit followed by “to the power $n$”.

for $\mathrm s^{-1}$, write “second to the power minus one”

However, the powers two and three may be expressed by “squared” and “cubed”, respectively. These modifiers are placed after the unit name.

for $\mathrm{m/s^2}$, write “metre per second squared”

However, in the case of area or volume, as an alternative the modifiers “square” or “cubic” may be used, and these modifiers are placed before the unit name.

for $\mathrm{cm^2}$, write “square centimetre”

for $\mathrm{mm^3}$, write “cubic millimetre”

for $\mathrm{kg/m^3}$, write “kilogram per cubic metre”

• Add an “s” to form the plural of spelled-out unit names.

milligrams, poises, kelvins, amperes, watts, newtons

However, bar, hertz, lux, stokes, siemens, and torr remain unchanged; darcy becomes darcies; henry becomes henries.

• $+1$ for consistently using the proper English way to write metre. Also, see this post my M.A.R. for upright Greek in MathJax. – Jan Oct 16 '15 at 15:10
• +1 That's a very comprehensive writeup. I myself am guilty of not putting a space between $20$ and $^\circ \mathrm{C}$... – orthocresol Oct 16 '15 at 15:23