The SIunits package^{∗}

support for the International System of Units

Marcel Heldoorn^{†}

    m.heldoorn@physiology.medfac.leidenuniv.nl

File date 1999/01/22 — Printed March 10, 1999

Abstract

This article describes the SIunits package that provides support for the Système International d’Unités (SI).

The Système International d’Unités (SI), the modern form of the metric system, is the most widely used system of units and measures around the world. But despite this there is widespread misuse of the system with incorrect names and symbols used as a matter a course - even by well educated and trained people who should know better. For example how often do we see: mHz, Mhz or mhz written when referring to computer clock rates? The correct form is actually MHz. Note that the capitalisation does matter.

Hence, a clear system for the use of units is needed, satisfying the next principles:

1. the system should consist of measuring units based on unvariable quantities in nature;

2. all units other than the base units should be derived from these base units; and

3. multiples and submultiples of the units should be decimal.

The name Système International d’Unités (International System of Units) with the international abbreviation SI was adopted by the Conférence Générale des Poids et Mesures (CGPM) in 1960. It is a coherent system based on seven base units (CGPM 1960 and 1971).

The SIunits package can be used to standardise the use of units in your writings. Most macros are easily adaptable to personal preferences. However, you are welcome (and strongly invited^{1}) to suggest any improvements.

Enjoy the SIunits package!marcel h.

∗This file has version number 0.04, last revised 1999/01/22, documentation dated 1999/01/22.

†Mail: Kennedylaan 24, NL-3844 BC Harderwijk, The Netherlands 1There is an enormous L^{A}TEX Knowledge Base out there.

Contents

1 Introduction 4 1.1 Historical notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 The three classes of SI units . . . . . . . . . . . . . . . . . . . . . . 4 1.3 The SI prefixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.5 Some useful definitions . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 SI units 6

2.1 SI base units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.2 Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 SI derived units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.1 SI derived units with special names and symbols . . . . . . 9 2.2.2 Use of SI derived units with special names and symbols . . 10

2.3 Rules and style conventions for writing and using SI unit symbols . 11

3 SI Prefixes 12 3.1 Decimal multiples and submultiples of SI units . . . . . . . . . . . 12 3.2 Rules for using SI prefixes . . . . . . . . . . . . . . . . . . . . . . . 13

3.2.1 The kilogram . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.2.2 The ‘degree Celsius’ . . . . . . . . . . . . . . . . . . . . . . 14

4 Units outside the SI 14 4.1 Units accepted for use with the SI . . . . . . . . . . . . . . . . . . 14 4.2 Units temporarily accepted for use with the SI . . . . . . . . . . . 16

5 Last notes about correct usage of the SI 17

6 How to use the package 18 6.1 Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 6.2 The options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 6.3 How to compose units in your text. . . . . . . . . . . . . . . . . . . 19

6.3.1 The SI base units . . . . . . . . . . . . . . . . . . . . . . . . 19 6.3.2 The SI derived units . . . . . . . . . . . . . . . . . . . . . . 19 6.3.3 The SI prefixes . . . . . . . . . . . . . . . . . . . . . . . . . 20 6.3.4 Decimal values of the SI prefixes . . . . . . . . . . . . . . . 20 6.3.5 Division or multiplication of SI units . . . . . . . . . . . . . 21 6.3.6 Raising SI units to a power . . . . . . . . . . . . . . . . . . 22 6.3.7 Quantities and units . . . . . . . . . . . . . . . . . . . . . . 22 6.3.8 Units outside the SI . . . . . . . . . . . . . . . . . . . . . . 23 6.3.9 Ready-to-use units . . . . . . . . . . . . . . . . . . . . . . . 23

7 How the package works 25 7.1 Compatibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 7.2 Known problems and limitations . . . . . . . . . . . . . . . . . . . 25 7.3 Sending a bug report . . . . . . . . . . . . . . . . . . . . . . . . . . 26 8 In conclusion 26

8.1 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 8.2 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 8.3 Bye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

9 The Magic Code 28

9.1 Hello world . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

9.1.1 The upright (roman) ‘mu’ . . . . . . . . . . . . . . . . . . . 28 9.2 Option handling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 9.3 Spacing options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

9.3.1 The thickspace mode . . . . . . . . . . . . . . . . . . . . . . 28 9.3.2 The mediumspace mode . . . . . . . . . . . . . . . . . . . . 28 9.3.3 The thinspace mode . . . . . . . . . . . . . . . . . . . . . . 29 9.3.4 The cdot mode . . . . . . . . . . . . . . . . . . . . . . . . . 29

9.4 Spacing between quantities and units options . . . . . . . . . . . . 29 9.4.1 The thickqspace mode . . . . . . . . . . . . . . . . . . . . . 29 9.4.2 The mediumqspace mode . . . . . . . . . . . . . . . . . . . . 29 9.4.3 The thinqspace mode . . . . . . . . . . . . . . . . . . . . . . 29

9.5 International problems . . . . . . . . . . . . . . . . . . . . . . . . . 29 9.6 Personal problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 9.7 Spacing units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 9.8 Spacing between numerical quantities and unit . . . . . . . . . . . 30 9.9 Power(full) macros . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 9.10 SI decimal prefixes . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

9.10.1 Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 9.10.2 Decimal form . . . . . . . . . . . . . . . . . . . . . . . . . . 31

9.11 SI base units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 9.12 SI derived units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

9.12.1 The derivedinbase mode . . . . . . . . . . . . . . . . . . . . 34 9.12.2 The derived mode . . . . . . . . . . . . . . . . . . . . . . . . 34

9.13 Units that are used with the SI . . . . . . . . . . . . . . . . . . . . 35 9.14 SI units with compound names . . . . . . . . . . . . . . . . . . . . 36 9.15 Various ready-to-use units . . . . . . . . . . . . . . . . . . . . . . . 36 9.16 The SIunits.cfg file . . . . . . . . . . . . . . . . . . . . . . . . . 40

1 Introduction

1.1 Historical notes

In 1948 the 9th General Conference on Weights and Measures (CGPM^{2}), by its Resolution 6, instructed the International Committee for Weights and Measures (CIPM^{2}):

‘to study the establishment of a complete set of rules for units of measurement’;

‘to find out for this purpose, by official inquiry, the opinion prevailing in scientific, technical, and educational circles in all countries’; and

‘to make recommendations on the establishment of a practical system of units of measurement suitable for adoption by all signatories to the Meter Convention.’

The same General Conference also laid down, by its Resolution 7, general principles for unit symbols and also gave a list of units with special names.

The 10th CGPM (1954), by its Resolution 6, and the 14th CGPM (1971), by its Resolution 3, adopted as base units of this ‘practical system of units,’ the units of the following seven quantities: length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity.

The 11th CGPM (1960), by its Resolution 12, adopted the name Système International d’Unités (International System of Units), with the international abbreviation SI, for this practical system of units of measurement, and laid down rules for the prefixes, the derived and supplementary units, and other matters, thus establishing a comprehensive specification for units of measurement.

1.2 The three classes of SI units

SI units are divided into three classes: base units, derived units and supplementary units. The General Conference decided to base the International System on a choice of seven well-defined units which by convention are regarded as dimensionally independent: the metre, the kilogram, the second, the ampere, the kelvin, the mole, and the candela. These units are called base units.

The second class of SI units contain derived units, i. e., units that can be formed by combining base units according to the algebraic relations linking the corresponding quantities. The names and symbols of some units thus formed in terms of base units can be replaced by special names and symbols which can themselves be used to form expressions and symbols of other derived units (see section 2.2, p. 9).

The 11th CGPM (1960) admitted a third class of SI units, called supplementary units and containing the SI units of plane and solid angle.

2See section 1.4 for acronyms

The 20th CGPM (1995) decided to eliminate the class of supplementary units as a separate class in the SI. Thus the SI now consists of only two classes of units: base units and derived units, with the radian and the steradian, which are the two supplementary units, subsumed into the class of derived SI units.

1.3 The SI prefixes

The General Conference has adopted a series of prefixes to be used in forming the decimal multiples and submultiples of SI units. Following CIPM Recommendation 1 (1969), the set of prefixes is designated by the name SI prefixes.

The multiples and submultiples of SI units, which are formed by using the SI prefixes, should be designated by their complete name, multiples and submultiples of SI units, in order to make a distinction between them and the coherent set of SI units proper

1.4 Acronyms

The SI was established in 1960 by the CGPM. The CGPM is an intergovernmental treaty organisation created by a diplomatic treaty called the Meter Convention (Convention du Mètre, often called the Treaty of the Meter in the United States). The Meter Convention was signed in Paris in 1875 by representatives of seventeen nations, including the United States. There are now forty-eight Member States, including all the major industrialised countries. The Convention, modified slightly in 1921, remains the basis of all international agreement on units of measurement.

The Meter Convention also created the International Bureau of Weights and Measures (BIPM, Bureau International des Poids et Mesures) and the International Committee for Weights and Measures (CIPM, Comité International des Poids et Mesures). The BIPM, which is located in Sèvres, a suburb of Paris, France, and which has the task of ensuring worldwide unification of physical measurements, operates under the exclusive supervision of the CIPM, which itself comes under the authority of the CGPM.

CGPM General Conference on Weights and Measures (Conférence Générale des Poids et Mesures). The CGPM is the primary intergovernmental treaty organisation responsible for the SI, representing nearly 50 countries. It has the responsibility of ensuring that the SI is widely disseminated and modifying it as necessary so that it reflects the latest advances in science and technology.

CIPM International Committee for Weights and Measures (Comité International des Poids et Mesures). The CIPM comes under the authority of the CGPM. It suggests modifications to the SI to the CGPM for formal adoption. The CIPM may also on its own authority pass clarifying resolutions and recommendations regarding the SI.

BIPM International Bureau of Weights and Measures (Bureau International des Poids et Mesures). The BIPM, located outside Paris, has the task of ensuring worldwide unification of physical measurements. It is the ”international” metrology institute, and operates under the exclusive supervision of the CIPM.

1.5 Some useful definitions

quantity in the general sense A quantity in the general sense is a property ascribed to phenomena, bodies, or substances that can be quantified for, or assigned to, a particular phenomenon, body, or substance. Examples are mass and electric charge.

quantity in the particular sense A quantity in the particular sense is a quantifiable or assignable property ascribed to a particular phenomenon, body, or substance. Examples are the mass of the moon and the electric charge of the proton.

physical quantity A physical quantity is a quantity that can be used in the mathematical equations of science and technology.

unit A unit is a particular physical quantity, defined and adopted by convention, with which other particular quantities of the same kind are compared to express their value.

The value of a physical quantity is the quantitative expression of a particular physical quantity as the product of a number and a unit, the number being its numerical value. Thus, the numerical value of a particular physical quantity depends on the unit in which it is expressed.

More formally, the value of quantity A can be written as A = {A}[A], where {A} is the numerical value of A when A is expressed in the unit [A]. The numerical value can therefore be written as {A} = A/[A], which is a convenient form for use in figures and tables. Thus to eliminate the possibility of misunderstanding, an axis of a graph or the heading of a column of a table can be labelled ‘t/^{∘}C’ instead of ‘t(^{∘}C)’ or ‘Temperature (^{∘}C)’. Similarly, another example: ‘E/(V/m)’ instead of ‘E(V/m)’ or ‘Electric field strength (V/m)’.

For example: the value of the height h_{W} of the Washington Monument is h_{W} = 169 m = 555 ft. Here h_{W} is the physical quantity, its value expressed in the unit metre, unit symbol m, is 169 m, and its numerical value when expressed in metres is 169.

2 SI units

2.1 SI base units

2.1.1 Definitions

The SI is founded on seven SI base units for seven base quantities assumed to be mutually independent. The primary definitions of the SI base units are in French. Their current definitions, along with an English translation, are given below:

metre; mètre

Le mètre est la longueur du trajet parcouru dans le vide par la lumière pendant une durée de 1/299 792 458 de seconde. (17th CGPM (1983), Resolution 1).

The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.

kilogram; kilogramme

Le kilogramme est l’unité de masse; il est égal à la masse du prototype international du kilogramme. (1st CGPM (1889) and 3rd CGPM (1901)).

The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. Note: This international prototype is made of platinum-iridium and is kept at the International Bureau of Weights and Measures, Sèvres, France.

second; seconde

La seconde est la durée de 9 192 631 770 périodes de la radiation correspondant à la transition entre les deux niveaux hyperfins de l’état fondamental de l’atome de cesium 133. (13th CGPM (1967), Resolution 1).

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom.

ampere; ampère

L’ampère est l’intensité d’un courant constant qui, maintenu dans deux conducteurs parallèles, rectilignes, de longueur infinie, de section circulaire négligeable, et placés à une distance de 1 mètre l’un de l’autre dans le vide, produirait entre ces conducteurs une force égale à 2×10^{−7} newton par mètre de longueur. (9th CGPM (1948), Resolutions 2 and 7).

The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2×10^{−7} newton per metre of length.

kelvin; kelvin

Le kelvin, unité de température thermodynamique, est la fraction 1/273, 16 de la température thermodynamique du point triple de l’eau. (13th CGPM (1967), Resolution 4).

The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. The 13th CGPM (1967, Resolution 3) also decided that the unit kelvin and its symbol K should be used to express both thermodynamic temperature and an interval or a difference of temperature, instead of ‘degree Kelvin’ with symbol ^{∘}K.

In addition to the thermodynamic temperature (symbol T) there is also the Celsius (symbol t) defined by the equation t = T − T_{0} where T_{0} = 273.15 K. Celsius temperature is expressed in degree Celsius; degré Celsius (symbol ∘C). The unit ‘degree Celsius’ is equal to the unit ‘kelvin’; in this case, ‘degree Celsius’ is a special name used in place of ‘kelvin’. A temperature interval or difference of Celsius temperature can, however, be expressed in kelvins as well as in degrees Celsius.

mole; mole

1. La mole est la quantité de matière d’un système contenant autant d’entités élémentaires qu’il y a d’atomes dans 0, 012 kilogramme de carbone 12.

2. Lorsqu’on emploie la mole, les entités élémentaires doivent être spécifiées et peuvent être des atomes, des molécules, des ions, des électrons, d’autres particules ou des groupements spécifiés de telles particules. (14th CGPM (1971), Resolution 3).

1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12.

2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles or specified groups of such particle. Note: In this definition, it is understood that the carbon 12 atoms are unbound, at rest and in their ground state.

candela; candela

La candela est l’intensité lumineuse, dans une direction donnée, d’une source qui émet une radiation monochromatique de fréquence 540×10^{12} hertz et dont l’intensité énergétique dans cette direction est 1/683 watt par stéradian. (16th CGPM (1979), Resolution 3).

The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of a frequency 540×10^{12} hertz and has a radiant intensity in that direction of 1/683 watt per steradian.

2.1.2 Symbols

The base units of the International System are collected in table 1 with their names and their symbols (10th CGPM (1954), Resolution 6; 11th CGPM (1960), Resolution 12; 13th CGPM (1967), Resolution 3; 14th CGPM (1971), Resolution 3).

Quantity  Name  Symbol
length  metre  m
mass  kilogram  kg
time  second  s

electric current  ampere  A
thermodynamic temperature  kelvin  K
amount of substance  mole  mol
luminous intensity  candela  cd

Table 1 — SI base unit —

2.2 SI derived units

SI derived units are expressed algebraically in terms of base units by means of the mathematical symbols of multiplication and division (see table 2 for some examples).

Derived quantity  Name  Symbol
area  square metre  m^{2}
volume  cubic metre  m^{3}
speed, velocity  metre per second  m/s
acceleration  metre per second squared  m/s^{2}
wave number  reciprocal metre  m^{−1}
mass density  kilogram per cubic metre  kg/m^{3}
specific volume  cubic metre per kilogram  m^{3}/kg
current density  ampere per square metre  A/m^{2}

magnetic field strength ampere per metre A/m amount-of-substance

concentration  mole per cubic metre  mol/m^{3}
luminance  candela per square metre  cd/m^{2}
mass fraction  kilogram per kilogram  kg/kg = 1^{(a)}

Table 2 — Examples of SI derived units — (a)the symbol 1 for quantities of dimension 1 such as mass fraction is generally omitted.

2.2.1 SI derived units with special names and symbols

For ease of understanding and convenience, 21 SI derived units have been given special names and symbols, as shown in Table 3. They may themselves be used to express other derived units.

Name  Expression in  Symbol  Expression in

SI base units SI derived units

radian^{(a)}  m m^{−1} = 1^{(b)}  rad  m m^{−1}
steradian^{(a)}  m^{2} m^{−2} = 1^{(b)}  sr^{(c)}  m^{2} m^{−2}
hertz  s^{−1}  Hz  s^{−1}

newton  m kg s^{−2}  N  m kg s^{−2}
pascal  m^{−1} kg s^{−2}  Pa  N m^{−2}
joule  m^{2} kg s^{−2}  J  N m
watt  m^{2} kg s^{−3}  W  J s^{−1}
coulomb  s A  C  A s
volt  m^{2} kg s^{−3} A^{−1}  V  W A^{−1}
farad  m^{−2} kg^{−1} s^{4} A^{2}  F  C V^{−1}
ohm  m^{2} kg s^{−3} A^{−2}  Ω  V A^{−1}
siemens  m^{−2} kg^{−1} s^{3} A^{2}  S  A V^{−1}
weber  m^{2} kg s^{−2} A^{−1}  Wb  m^{2} kg s^{−2} A^{−1}
tesla  kg s^{−2} A^{−1}  T  Wb m^{−2}
henry  m^{2} kg s^{−2} A^{−2}  H  Wb A^{−1}
celsius  K  ^{∘}C  K
lumen  cd m^{2} m^{−2}^{(c)}  lm  cd sr
lux  cd m^{2} m^{−4}  lx  lm m^{−2}
becquerel  s^{−1}  Bq  s^{−1}
gray  m^{2} s^{−2}  Gy  J kg^{−1}
sievert^{(d)}  m^{2} s^{−2}  Sv  J kg^{−1}

Table 3 — SI derived units with special names and symbols — (a)The radian and steradian may be used advantageously in expressions for derived units to distinguish between quantities of a different nature but of the same dimension; some examples are given in Table 4. (b)In practice, the symbols rad and sr are used where appropriate, but the derived unit ‘1’ is generally omitted. (c)In photometry, the unit name steradian and the unit symbol sr are usually retained in expressions for derived units. (d)Other quantities expressed in sieverts are ambient dose equivalent, directional dose equivalent, personal dose equivalent, and organ equivalent dose.

2.2.2 Use of SI derived units with special names and symbols

Examples of SI derived units that can be expressed with the aid of SI derived units having special names and symbols (including the radian and steradian) are given in Table 4. The advantages of using the special names and symbols of SI derived units are apparent in Table 4. Consider, for example, the quantity molar entropy: the unit J/mol K is obviously more easily understood than its SI base-unit equivalent, m^{2} kg s^{−2} K^{−1}mol^{−1}. Nevertheless, it should always be recognised that the special names and symbols exist for convenience. Tables 2 and 3 also show that the values of several different quantities are expressed in the same SI unit. For example, the joule per kelvin (J/K) is the SI unit for heat capacity as well as for entropy. Thus the name of the unit is not sufficient to define the quantity measured. A derived unit can often be expressed in several different ways through the use of base units and derived units with special names. In practice, with certain quantities, preference is given to using certain units with special names, or combinations of units, to facilitate the distinction between quantities whose values have identical expressions in terms of SI base units. For example, the SI unit of frequency is specified as the hertz (Hz) rather than the reciprocal second (s^{−1}), and the SI unit of moment of force is specified as the newton metre (N m) rather than the joule (J).

Derived quantity  Name  Symbol
angular velocity  radian per second  rad/s
angular acceleration  radian per second squared  rad/s^{2}
dynamic viscosity  pascal second  Pa s
moment of force  newton metre  N m
surface tension  newton per metre  N/m

heat flux density,

irradiance  watt per square metre  W/m^{2}
radiant intensity  watt per steradian  W/sr

radiance watt per square metre steradian W/m^{2} sr heat capacity, entropy joule per kelvin J/K specific heat capacity,

specific entropy  joule per kilogram kelvin  J/kg K
specific energy  joule per kilogram  J/kg
thermal conductivity  watt per metre kelvin  W/m K
energy density  joule per cubic metre  J/m^{3}
electric field strength  volt per metre  V/m
electric charge density  coulomb per cubic metre  C/m^{3}
electric flux density  coulomb per square metre  C/m^{2}
permittivity  farad per metre  F/m
permeability  henry per metre  H/m
molar energy  joule per mole  J/mol

molar entropy, molar heat capacity joule per mole kelvin J/mol K exposure (x and γ rays) coulomb per kilogram C/kg

absorbed dose rate  gray per second  Gy/s

Table 4 — Examples of SI derived units expressed with the aid of SI derived units having special names and symbols

2.3 Rules and style conventions for writing and using SI unit symbols

The general principles concerning writing the unit symbols were adopted by the 9th CPGM (1948), by its Resolution 7:

1. Roman (upright) type, in general lower case^{3}, is used for the unit symbols. If, however, the name of the unit is derived from a proper name, the first letter of the symbol is in upper case.

2. Unit symbols are unaltered in the plural.

3The recommended symbol for the litre (‘liter’) in the United States is L.

3. Unit symbols are not followed by a period^{4}.

To ensure uniformity in the use of the SI unit symbols, ISO International Standards give certain recommendations. Following these recommendations:

a) The product of two or more units are indicated by means of either a half-high (that is, centred) dot or a space^{5}. The half-high dot is preferred, because it is less likely to lead to confusion,

for example:

N·m or N m.

b) A solidus (oblique stroke,/), a horizontal line, or negative exponents may be used to express a derived unit formed from two others by division,

for example:

m/s, \frac{m}{s}, or m s^{−1}

c) The solidus must not be repeated on the same line unless ambiguity is avoided by parentheses. In complicated cases negative exponents or parentheses should be used,

for example:

m/s^{2} or m s^{−2} but not: m/s/s

m kg/(s^{3} A) or m kg s^{−3} A^{−1} but not: m kg/s^{3}/A

3 SI Prefixes

3.1 Decimal multiples and submultiples of SI units

The 11th CGPM (1960), by its Resolution 12, adopted a first series of prefixes and symbols of prefixes to form the names and symbols of the decimal multiples and submultiples of SI units. Prefixes for 10^{−15} and 10^{−18} were added by the 12th CGPM (1964), by its Resolution 8, those for 10^{15} and 10^{18} by the CGPM (1975), by its Resolution 10, and those for 10^{21}, 10^{24}, 10^{−21}, and 10^{−24} were proposed by the CIPM for approval by the 19th CGPM (1991), and adopted.

Prefix Symbol Factor

yocto  y  10^{−24}= (10^{3})^{−8}
zepto  z  10^{−21}= (10^{3})^{−7}
atto  a  10^{−18}= (10^{3})^{−6}
femto  f  10^{−15}= (10^{3})^{−5}
pico  p  10^{−12}= (10^{3})^{−4}
nano  n  10^{−9}= (10^{3})^{−3}

4Unless at the end of a sentence.

5ISO suggests that if a space is used to indicate units formed by multiplication, the space may be omitted if it does not cause confusion. This possibility is reflected in the common practice of using the symbol kWh rather than kW·h or kW h for the kilowatt hour.

micro  μ  10^{−6}= (10^{3})^{−2}
milli  m  10^{−3}= (10^{3})^{−1}
centi  c  10^{−2}
deci  d  10^{−1}

deca^{(a)} da 10^{1}

hecto  h  10^{2}
kilo  k  10^{3}= (10^{3})^{1}
mega  M  10^{6}= (10^{3})^{2}
giga  G  10^{9}= (10^{3})^{3}
tera  T  10^{12}= (10^{3})^{4}
peta  P  10^{15}= (10^{3})^{5}
exa  E  10^{18}= (10^{3})^{6}
zetta  Z  10^{21}= (10^{3})^{7}
yotta  Y  10^{24}= (10^{3})^{8}

Table 5 — SI prefixes — (a)In the USA, the spelling ‘deka’ is extensively used.

3.2 Rules for using SI prefixes

In accord with the general principles adopted by the ISO^{6}, the CIPM recommends that the following rules for using the SI prefixes be observed:

1. Prefix symbols are printed in roman (upright) type without spacing between the prefix symbol and the unit symbol.

2. The grouping formed by the prefix symbol attached to the unit symbol constitutes a new inseparable symbol (of a multiple of the unit concerned) which can be raised to a positive or negative power and which can be combined with other unit symbols to form compound unit symbols,

for example:

1 cm^{3} = (10^{−2} m)^{3} = 10^{−6} m^{3}

1 cm^{−1} = (10^{−2} m)^{−1} = 10^{2} m^{−1} 1 V/cm = (1 V)/(10^{−2} m) = 10^{2} V/m

3. Compound prefixes, i. e., prefixes formed by juxtaposition of two or more SI prefixes are not to be used,

for example:

1 pg (one picogram), but not 1 mng (one millinanogram)

4. A prefixes should never be used alone,

for example:

10^{6}/m^{3}, but not M/m^{3} 3.2.1 The kilogram

6ISO 31, in ‘Units of measurement,’ ISO Standards Handbook 2, 2nd Edition, ISO, Geneva, 1982, pp. 17–238

It is important to note that the kilogram is the only SI unit with a prefix as part of its name and symbol. Because multiple prefixes may not be used, in the case of the kilogram the prefix names are used with the unit name ‘gram’ and the prefix symbols are used with the unit symbol g, for example: 10^{−6} kg = 1 mg (one milligram), but not 10^{−6} kg = 1 μkg (one microkilogram).

3.2.2 The ‘degree Celsius’

Except for the kilogram, any SI prefix may be used with any SI unit, including the ‘degree Celsius’ and its symbol ^{∘}C, for example: 10^{−3} ^{∘}C = 1 m^{∘}C (one millidegree Celsius), or 10^{6} ^{∘}C = 1 M^{∘}C.

Note

Because the SI prefixes strictly represent powers of 10, they should not be used to represent powers of 2. Thus, one kilobit, or 1 kbit, is 1000 bit and not 2^{10} bit = 1024 bit.

New prefixes for binary multiples have been proposed by Technical Committee of the International Electrotechnical Commission (IEC) for use in information technology to alleviate this ambiguity, and they are currently under consideration internationally.

4 Units outside the SI

Units that are outside the SI may be divided into three categories:

1. those units that are accepted for use with the SI;

2. those units that are temporarily accepted for use with the SI; and

3. those units that are not accepted for use with the SI and thus must strictly be avoided.

4.1 Units accepted for use with the SI

The CIPM (1969) recognised that users of SI will also wish to employ with it certain units not part of it, but which are important and are widely used. These units are given in table 6. The combination of units of this table with SI units to form compound units should be restricted to special cases in order not to lose the advantage of the coherence of SI units.

Name Symbol Value in SI units

minute (time)  min  1 min = 60 s
hour  h  1 h = 60 min = 3600 s
day  d  1 d = 24 h = 86 400 s
degree  ^{∘}  1 ^{∘} = (π/180) rad
minute (plane angle)  ′  1 ′ = (1/60) ^{∘} = (π/10 800) rad

second (plane angle)  ′′  1 ′′ = (1/60) ′ = (π/648 000) rad
litre  l, L^{(a)}  1 l = 1 L = 1 dm^{3} = 10^{−3} m^{3}
tonne^{(b)}  t  1 t = 10^{3} kg

Table 6 — Units accepted for use with the SI — (a)The alternative symbol for the litre, L, was adopted by the CGPM in order to avoid the risk of confusion between the letter l and the number 1. Thus, although both l and L are internationally accepted symbols for the litre, to avoid this risk the symbol to be used in the United States is L. (b)In some English-speaking countries this unit is called ‘metric ton’.

It is likewise necessary to recognise, outside the International System, some other units that are useful in specialised fields, because their values expressed in SI units must be obtained by experiment, and are therefore not known exactly (table 7).

Name Symbol Definition

electronvolt  eV  ^{(a)}
unified atomic mass unit  u  ^{(b)}

Table 7 — Units accepted for use with the SI whose values in SI units are obtained experimentally — (a)The electronvolt is the kinetic energy acquired by an electron in passing through a potential difference of 1 V in vacuum; 1 eV = 1.602 177 33 × 10^{−19} J with a combined standard uncertainty of 0.000 000 49 × 10^{−19} J (b)The unified atomic mass unit is equal to 1/12 of the mass of an atom of the nuclide ^{12}C; 1 u = 1.660 540 2 × 10^{−27} kg with a combined standard uncertainty of 0.000 001 0 × 10^{−27} kg

4.2 Units temporarily accepted for use with the SI

Because of existing practice in certain fields or countries, in 1978 the CIPM considered that it was permissible for the units given in Table 8 to continue to be used with the SI until the CIPM considers that their use is no longer necessary. However, these units must not be introduced where they are not presently used.

Name Symbol Value in SI units

nautical mile^{(a)} 1 nautical mile = 1852 m

knot 1 nautical mile per hour = (1852/3600) m/s

ångström  Å  1 Å = 0.1 nm = 10^{−10} m
are^{(b)}  a  1 a = 1 dam^{2} = 10^{2} m^{2}
hectare^{(b)}  ha  1 ha = 1 hm^{2} = 10^{4} m^{2}
barn^{(c)}  b  1 b = 1 fm^{2} = 10^{−28} m^{2}
bar^{(d)}  bar  1 bar = 0.1 MPa = 10^{5} Pa
gal^{(e)}  Gal  1 Gal = 1 cm/s^{2} = 10^{−2} m/s^{2}
curie^{(f)}  Ci  1 Ci = 3.7 × 10^{10} Bq
roentgen^{(g)}  R  1 R = 2.58 × 10^{−4} C/s
rad^{(h)}  rad  1 rad = 1 cGy = 10^{−2} Gy
rem^{(i)}  rem  1 rem = 1 cSv = 10^{−2} Sv

Table 8 — Units in use temporarily with the SI — (a)The nautical mile is a special unit employed for marine and aerial navigation to express distances. The conventional value given above was adopted by the First International Extraordinary Hydrographic Conference, Monaco, 1929, under the name “International nautical mile”. (b)This unit and its symbol were adopted by the CIPM in 1879 (BIPM Proc. Verb. Com. Int. Poids et Mesures, 1879, p. 41) and are used to express agrarian areas. (c)The barn is a special unit employed in nuclear physics to express effective cross sections.

(d)This unit and its symbol are included in Resolution 7 of the 9th CGPM (1948). (e)The gal is a special unit employed in geodesy and geophysics to express the acceleration due to gravity. (f)The curie is a special unit employed in nuclear physics to express activity of radionuclides (12th CGPM (1964), Resolution 7). (g)The roentgen is a special unit employed to express exposure of x or γ radiations. (h)The rad is a special unit employed to express absorbed dose of ionising radiations. When there is risk of confusion with the symbol for radian, rd may be used as the symbol for rad. (i)The rem is a special unit used in radioprotection to express dose equivalent.

5 Last notes about correct usage of the SI

The following points underline some of the important aspects about using SI units and their symbols, and also mention some of the common errors that are made. The SI differs from some of the older systems in that it has definite rules governing the way the units and symbols are used.

• The unit of measure is the ‘metre’, not ‘meter’. The latter is a device used for measuring things. (Unless you live in the USA - in which case you will just have to live with the ambiguity.)

• Using a comma to separate groups of three digits is not recommended - a space is preferable, since many countries use the comma as the decimal point marker. Both the USA and UK use the ‘dot on the line’ (full stop). So the following would be correct: 1 234 555.678 990.

• The term billion should be avoided since in most countries outside the USA (including the UK) it means a million-million (prefix tera), whereas in the USA it means a thousand million (prefix giga). Likewise the term trillion means million-million-million (prefix exa) in most countries outside the USA.

• The ‘litre’ (‘liter’ in the US) is one of those units which is approved by the CGPM for use with the metric system. The official unit of volume in the SI is the cubic metre. However, since this is not convenient for much day-to-day use the CGPM has approved the use of the ‘other unit’, the litre. The litre represents a cubic decimetre and you may use either the symbol ‘l’ or ‘L’^{7} (small or capital ‘ell’) to represent it. They do not approve using any prefixes other than milli or micro with it. It was originally defined as the volume occupied by 1 kg of water. Subsequently it was found that this was not precisely 1 cubic decimetre, so the term litre was withdrawn. Later it was re-introduced officially as 1 cubic decimetre exactly. So, 1 l = 1 dm^{3} = 1 L.

7Recommended symbol for the ‘liter’ in the USA

6 How to use the package

6.1 Loading

Most features are controlled by package options that can be selected when the package is loaded (e. g \usepackage[options]{SIunits}) or at ‘runtime’ as an optional argument(list) to the \SIunits command (e. g. \SIunits[options]).

    \documentclass[]{article}
    \usepackage[options]{SIunits}
    \begin{document}
    \ldots
    \SIunits[options]
    \ldots
    \end{document}

6.2 The options

The features are controlled by package options that can be selected when the

package is loaded (e. g \usepackage[cdot]{SIunits}).

The package supports the following options:

cdot This mode provides the use of \cdot as spacing in units.

thickspace This mode provides the use of \; (thick math space) as spacing in units.

mediumspace This mode provides the use of \: (medium math space) as spacing in units.

thinspace This mode provides the use of \, (thin math space) as spacing in units.

thickqspace This mode provides the use of \; (thick math space) as spacing between numerical quantities and units.

mediumqspace This mode provides the use of \: (medium math space) as spacing between numerical quantities and units.

thinqspace This mode provides the use of \, (thin math space) as spacing between numerical quantities and units.

derivedinbase This mode provides the ready-to-use expressions of SI derived units in SI base units, e. g. \pascalbase to get ‘m^{−1} kg s^{−2}’. This option is used to make the generation of the documentation easier.

derived This mode provides the ready-to-use expressions of SI derived units in SI derived units, e. g. \derpascal to get ‘N m^{−2}’. This option is used to make the generation of the documentation easier.

See the next table for examples of the spacing options.

Option Example

cdot N · m thickspace N m mediumspace N m thinspace N m thickqspace 10 N · m mediumqspace 10 N · m thinqspace 10 N · m

Table 9 — Spacing options —

Command Reference

6.3 How to compose units in your text.

The purpose of the SIunits package is: to give an author an intuitive system for writing units. Just type (in L^{A}TEX-kind commands) what you would say:

\kilogram or \degreecelsius to get ‘kg’ or ‘^{∘}C’.

6.3.1 The SI base units

Command Gives

\metre m — The command \meter can also be used.

\kilogram  kg
\second  s
\ampere  A
\kelvin  K
\mole  mol
\candela  cd

6.3.2 The SI derived units

Command Gives

\hertz  Hz
\newton  N
\pascal  Pa
\joule  J
\watt  W
\coulomb  C

\volt  V
\farad  F
\ohm  Ω
\siemens  S
\weber  Wb
\tesla  T
\henry  H

\degreecelsius ^{∘}C — The command \celsius can also be used.

\lumen  lm
\lux  lx
\becquerel  Bq
\gray  Gy
\sievert  Sv

6.3.3 The SI prefixes

To use the prefixes with SI units simply place them before the unit, e. g.

\milli\ampere, \deca\metre (or \deka\meter) or \mega\ohm to get: ‘mA’,

‘dam’ or ‘MΩ’.

Command Gives

\yocto  y
\zepto  z
\atto  a
\femto  f
\pico  p
\nano  n
\micro  μ
\milli  m
\centi  c
\deci  d

\deca da — The command \deka can also be used.

\hecto  h
\kilo  k
\mega  M
\giga  G
\tera  T
\peta  P
\exa  E
\zetta  Z
\yotta  Y

6.3.4 Decimal values of the SI prefixes

Decimal values of the prefixes can be made by adding d behind the prefix command:

Command Gives

\yoctod  10^{−24}
\zeptod  10^{−21}
\attod  10^{−18}
\femtod  10^{−15}
\picod  10^{−12}
\nanod  10^{−9}
\microd  10^{−6}
\millid  10^{−3}
\centid  10^{−2}
\decid  10^{−1}

\decad 10^{1} — The command \dekad can also be used.

\hectod  10^{2}
\kilod  10^{3}
\megad  10^{6}
\gigad  10^{9}
\terad  10^{12}
\petad  10^{15}
\exad  10^{18}
\zettad  10^{21}
\yottad  10^{24}

6.3.5 Division or multiplication of SI units

The next step is the formation of units based on division and/or multiplication of SI units.

Division How to get the unit of speed?

1. Write down the unit in words: metre per second

2. Replace the spaces with backlashes to get the command: \metre\per\second\

3. The result is: ‘m/s’.

Simple! Ready!

Multiplication Now an example of multiplication of units, the unit of torque (newton metre):

1. Write down the unit in words: newton metre

2. To get an separation character between the two units use the command \usk

 (unitskip): \newton\usk\metre

3. The result is: ‘N m’. The spacing between the units depends on the spacing options (see: page 18).

Mixed case The mixed case should be simple now; the unit of thermal conductivity (watt per metre kelvin):

1. Use your just-learned-knowledge:\watt\per\metre\usk\kelvin

2. The result is: ‘W/m K’. Now, you can do it all in one step! Intuitive & simple. 6.3.6 Raising SI units to a power The SIunits package provides a set of functions to get units raised to a particular power. Squaring and cubing How to get the units of area (square metre) and volume (cubic metre)?

1. Write down the unit in words: square metre and cubic metre

2. Replace the spaces with backlashes to get the commands: \square\metre

     and \cubic\metre

3. The result is: ‘ m^{2}’ and ‘m^{3}’. I can hear you say: “We only use the word ‘square’ before the unit metre, normally we place the word ‘squared’ behind the unit name.”. OK, lets try: \second\squared and \second\cubed gives: ‘s^{2}’ and ‘s^{3}’. Thus, no problem. The reciprocal, reciprocal squaring and - cubing How to get negative powers?

  1. Use \rpsquare or \rpsquared, and \rpcubic and \rpcubed
  2. For example: \rpsquare\metre and \second\rpcubed

3. The result is: ‘ m^{−2}’ and ‘s^{−3}’. Normally, we leave out the exponent 1, but sometimes we want to use the exponent −1. How to form the unit of frequency (reciprocal second = Hz)

1. Write down the unit in words: reciprocal second,

2. Replace the spaces with backlashes to get the commands: \reciprocal\second,

3. The result is: ‘s^{−1}’. The power function The power macro has been added to be able to form the wildest types of power raising: \power{10}{35} gives: 10^{35}. 6.3.7 Quantities and units Use the command \unit to get consistent spacing between numerical quantities and units. Usage:

\unit {120} {\kilo\meter\per\hour} gives: 120 km/h.

6.3.8 Units outside the SI

Command Gives

\angstrom  Å
\are  a
\atomicmass  u
\barn  b

\bbar bar — The command \bar was already defined.

\curie  Ci

\dday d — The command \day was already defined.

\degree           ^{∘}
\electronvolt  eV
\gal  Gal
\gram  g
\hectare  ha
\hour  h

\liter L — The US unit for ‘litre’.

\litre  l
\minute  min

\paminute ′ — The command \minute was already defined. \pasecond ′′ — The command \second was already defined.

\rad  rad
\rem  rem
\roentgen  R
\rperminute  r/min

\tonne t — The command \ton can also be used.

6.3.9 Ready-to-use units

Command Gives

\amperemetresecond  A m s
\amperepermetre  A/m
\amperepermetrenp  A m^{−1}
\amperepersquaremetre  A/m^{2}
\amperepersquaremetrenp  A m^{−2}
\candelapersquaremetre  cd/m^{2}
\candelapersquaremetrenp  cd m^{−2}
\coulombpercubicmetre  C/m^{3}
\coulombpercubicmetrenp  C m^{−3}
\coulombperkilogram  C/kg
\coulombperkilogramnp  C kg^{−1}
\coulombpermol  C/mol
\coulombpermolnp  C mol^{−1}
\coulombpersquaremetre  C/m^{2}
\coulombpersquaremetrenp  C m^{−2}
\cubicmetre  m^{3}

\faradpermetre  F/m
\faradpermetrenp  F m^{−1}
\graypersecond  Gy/s
\graypersecondnp  Gy s^{−1}
\henrypermetre  H/m
\henrypermetrenp  H m^{−1}
\jouleperkelvin  J/K
\jouleperkelvinnp  J K^{−1}
\jouleperkilogram  J/kg
\jouleperkilogramnp  J kg^{−1}
\joulepermole  J/mol
\joulepermolenp  J mol^{−1}
\joulepermolekelvin  J/mol K
\joulepermolekelvinnp  J mol^{−1} K^{−1}
\joulepersquaremetre  J/m^{2}
\joulepersquaremetrenp  J m^{−2}
\joulepertesla  J/T
\jouleperteslanp  J T^{−1}
\kilogrammetrepersecond  kg m/s
\kilogrammetrepersecondnp  kg m s^{−1}
\kilogrammetrepersquaresecond  kg m/s^{2}
\kilogrammetrepersquaresecondnp  kg m s^{−2}
\kilogrampercubicmetre  kg/m^{3}
\kilogrampercubicmetrenp  kg m^{−3}
\kilogramperkilomole  kg/kmol
\kilogramperkilomolenp  kg kmol^{−1}
\kilogrampermetre  kg/m
\kilogrampermetrenp  kg m^{−1}
\kilogrampersecond  kg/s
\kilogrampersecondnp  kg s^{−1}
\kilogrampersquaremetre  kg/m^{2}
\kilogrampersquaremetrenp  kg m^{−2}
\kilogrampersquaremetresecond  kg/m^{2} s
\kilogrampersquaremetresecondnp  kg m^{−2} s^{−1}
\kilogramsquaremetre  kg m^{2}
\kilogramsquaremetrenp  kg m^{2}
\kilogramsquaremetrepersecond  kg m^{2}/s
\kilogramsquaremetrepersecondnp  kg m^{2} s^{−1}
\kilowatthour  kWh
\metrepersquaresecond  m/s^{2}
\metrepersquaresecondnp  m s^{−2}
\molepercubicmetre  mol/m^{3}
\molepercubicmetrenp  mol m^{−3}
\newtonpercubicmetre  N/m^{3}
\newtonpercubicmetrenp  N m^{−3}
\newtonperkilogram  N/kg
\newtonperkilogramnp  N kg^{−1}
\newtonpersquaremetre  N/m^{2}
\newtonpersquaremetrenp  N m^{−2}

\ohmmetre  Ω m
\pascalsecond  Pa s
\pascalsecondnp  kg s^{−1}
\persquaremetresecond  1/m^{2} s
\persquaremetresecondnp  m^{−2} s^{−1}
\radianpersecond  rad/s
\radianpersecondnp  rad s^{−1}
\radianpersquaresecond  rad/s^{2}
\radianpersquaresecondnp  rad s^{−2}
\rpsquaremetrepersecond  m^{2} s^{−1}
\rpsquaremetrepersquaresecond  m^{2} s^{−2}
\squaremetre  m^{2}
\squaremetrepercubicmetre  m^{2}/m^{3}
\squaremetrepercubicmetrenp  m^{2} m^{−3}
\squaremetrepernewtonsecond  m^{2}/N s
\squaremetrepernewtonsecondnp  m^{2} N^{−1} s^{−1}
\squaremetrepersecond  m^{2}/s
\squaremetrepersquaresecond  m^{2}/s^{2}
\voltpermetre  V/m
\voltpermetrenp  V m^{−1}
\wattpercubicmetre  W/m^{3}
\wattpercubicmetrenp  W m^{−3}
\wattperkilogram  W/kg
\wattperkilogramnp  W kg^{−1}
\wattpersquaremetre  W/m^{2}
\wattpersquaremetrenp  W m^{−2}
\wattpersquaremetresteradian  W/m^{2} sr
\wattpersquaremetresteradiannp  W m^{−2} sr^{−1}

7 How the package works

7.1 Compatibility

The package has been tested using:

1. MiKTEX 1.10b, including L^{A}TEX 2ε standard classes (L^{A}TEX 2ε [1997/12/01] patch level 1) and TEX 3.14159, both under Microsoft Windows 95 and Windows NT 4.0.

2. MiKTEX 1.11 , including L^{A}TEX 2ε standard classes (L^{A}TEX 2ε [1998/06/01]) and TEX 3.14159, both under Microsoft Windows 95 and Windows NT 4.0.

The SIunits package mainly uses (and relies on) the L^{A}TEX command \newcommand which is expected to keep its current meaning in future L^{A}TEX releases.

7.2 Known problems and limitations

1. When you don’t have the AMS font eurm10 add the next command to the preamble of your document:

 \NoAMS.

No further known problems or limitations. That doesn’t mean this package is bug free, but it indicates the lack of testing that’s been done on the package.

7.3 Sending a bug report

Reports of new bugs in the package are most welcome. However, I do not consider this to be a ‘supported’ package. This means that there is no guarantee I (or anyone else) will put any effort into fixing the bug (of course I will try to find some time). But, on the other hand, someone may try debugging, so filing a bug report is always a good thing to do! (If nothing else, your discoveries may end up in future releases of this document.) Before filing a bug report, please take the following actions:

1. Ensure your problem is not due to your input file;

2. Ensure your problem is not due to your own package(s) or class(es);

3. Ensure your problem is not covered in the section “Known problems and limitations” above;

4. Try to locate the problem by writing a minimal L^{A}TEX 2ε input file which reproduces the problem. Include the command

     \setcounter{errorcontextlines}{999}

in your input;

5. Run your file through L^{A}TEX 2ε;

6. Send a description of your problem, the input file and the log file via e-mail

     to: m.heldoorn@physiology.medfac.leidenuniv.nl.

8 In conclusion

8.1 Acknowledgements

I want to thank Werenfried Spit (w.spit@WITBO.NL) answering my question to TEX-NL@NIC.SURFNET.NL about the “power functie”, as well as Hans Hagen (pragma@WXS.NL) for the kind reaction to that question.

v0.01: Typos Juergen von Haegen (vonHagen@engr.psu.edu)

v0.02 Beta 1: addunit macro added Hint: Hans Bessem

       (j.m.bessem@wbmt.tudelft.nl)

v0.02 Beta 4: Typos Rafael Rodriguez Pappalardo (rafapa@cica.es)

v0.02 Beta 5: Tips/non-SI units Timothy C. Burt

       (tcburt@comp.uark.edu)

v0.02 Beta 7: angstrom definition changed Hint: Lutz Schwalowsky

       (schalow@mineralogie.uni-hamburg.de); Solution: Piet van Oostrum
       (piet@cs.uu.nl)

v0.04: ohm definition corrected Juergen von Haegen (vonHagen@engr.psu.edu)

8.2 References

1. National Institute of Standards and Technology Special Publication 330, The International System of Units (SI), 1991 Edition, by Barry N. Taylor, 62 p.:

http://physics.nist.gov/Document/sp330.pdf

2. National Institute of Standards and Technology Special Publication 811, Guide for the Use of the International System of Units (SI), 1995 Edition, by

Barry N. Taylor, 84 p.: http://physics.nist.gov/Document/sp811.pdf

3. National Institute of Standards and Technology, Diagram of SI unit relation-

ships: http://physics.nist.gov/cuu/Units/SIdiagram2.html

4. National Physical Laboratory, The International System of Units:

http://www.npl.co.uk/npl/reference/si_units.html

5. National Institute of Standards and Technology, The NIST reference on Constants, Units and Uncertainty:

http://physics.nist.gov/cuu/Units/introduction.html

6. David Barlett, The Metric System: a concise reference guide:

http://subnet.virtual-pc.com/ba424872/

8.3 Bye

I hope that some users will find the package useful and not too bugful. :–) Comments and suggestions for improvements are always most welcome!

L^{A}TEX, enjoy it! marcel h.

9 The Magic Code

9.1 Hello world

First, we announce the package.

 1 \NeedsTeXFormat{LaTeX2e}[1997/12/01]
 2 \ProvidesPackage{SIunits}[\filedate\space v\fileversion\space \packagename (MH)]
 3 \typeout{Package: `\packagename' v\fileversion\space <\filedate> (MH)}

9.1.1 The upright (roman) ‘mu’

The next four lines of code are necessary to get an upright (roman) mu (Greek ‘em’).

 4 \DeclareFontFamily{OML}{eur}{\skewchar\font127}
 5 \DeclareFontShape{OML}{eur}{m}{n}{<5> <6> <7> <8> <9> gen * eurm <10><10.95><12><14.4><17.28><20.74><24.88>eurm10}{}
 6 \DeclareSymbolFont{greek}{OML}{eur}{m}{n}
\upmu
 7 \DeclareMathSymbol{\upmu}{\mathord}{greek}{"16}

9.2 Option handling

Every package option is passed to the macro \SIunits@execopt.

 8 \DeclareOption*{\SIunits@execopt\CurrentOption}

\SIunits The \SIunits macro allows runtime option requests. Every argument of the optional argument list is passed to the macro \SIunits@execopt. The options thickspace & thickqspace is selected by default.

 9 \newcommand*\SIunits[1][thickspace,thickqspace]{\@for\SIunits@@:=#1%
10 \do{\SIunits@execopt\SIunits@@}}

\SIunits@execopt Every execution of this macro with an argument n leads to the execution of a macro \SIunits@opt@n or a warning if no such exists.

11 \newcommand*\SIunits@execopt[1]{\@ifundefined{SIunits@opt@#1}%
12 {\PackageWarning{SIunits}{Requested option `#1' not provided}}%
13 {\@nameuse{SIunits@opt@#1}}}

9.3 Spacing options

9.3.1 The thickspace mode

\SIunits@opt@thickspace This macro provides a thick math space (\;) between units.

14 \newcommand*\SIunits@opt@thickspace{%
15 \renewcommand{\usk}{\ensuremath{\;}}
16  \typeout{Option `thickspace' provided! ^^J}}

9.3.2 The mediumspace mode

\SIunits@opt@mediumspace This macro provides a medium math space (\:) between units.

17 \newcommand*\SIunits@opt@mediumspace{%
18 \renewcommand{\usk}{\ensuremath{\:}}
19  \typeout{Option `mediumspace' provided! ^^J}}

9.3.3 The thinspace mode

\SIunits@opt@thinspace This macro provides a thin math space (\,) between units.

20 \newcommand*\SIunits@opt@thinspace{%
21 \renewcommand{\usk}{\ensuremath{\,}}
22  \typeout{Option `thinspace' provided! ^^J}}

9.3.4 The cdot mode

\SIunits@opt@cdot This macro provides a \cdot (·) between units.

23 \newcommand*\SIunits@opt@cdot{%
24 \renewcommand{\usk}{\ensuremath        {\cdot}}
25  \typeout{Option `cdot' provided! ^^J}}

9.4 Spacing between quantities and units options

9.4.1 The thickqspace mode

\SIunits@opt@thickqspace This macro provides a thick math space (\;) between quantities and units.

26 \newcommand*\SIunits@opt@thickqspace{%
27 \renewcommand{\qsk}{\ensuremath{\;}}
28  \typeout{Option `thickqspace' provided! ^^J}}

9.4.2 The mediumqspace mode

\SIunits@opt@mediumqspace This macro provides a medium math space (\:) between quantities and units.

29 \newcommand*\SIunits@opt@mediumqspace{%
30 \renewcommand{\qsk}{\ensuremath{\:}}
31  \typeout{Option \mediumqspace' provided! ^^J}}

9.4.3 The thinqspace mode

\SIunits@opt@thinqspace This macro provides a thin math space (\;) between quantities and units.

32 \newcommand*\SIunits@opt@thinqspace{%
33 \renewcommand{\qsk}{\ensuremath{\,}}
34  \typeout{Option `thinqspace' provided! ^^J}}

9.5 International problems

\meter To prevent international problems, one can use both \meter and \metre for the SI

\deka
\dekad

length unit, and \deka and \dekad for the SI prefix commands \deca and \decad.

35 \newcommand{\meter}{\metre}
36 \newcommand{\deka}{\deca}
37 \newcommand{\dekad}{\decad}

9.6 Personal problems

\NoAMS The \NoAMS macro has to be added in the preamble, when you don’t have the AMS font eurm10

38 \newcommand{\NoAMS}{\renewcommand {\micro}{\ensuremath{\mathrm{\mu}}}}

\addunit The \addunit macro gives one the possibility to add units. This possibility was added after a lot of questions for support of non SI units, that can not be added to this package (it’s called SI units!). Usage: \addunit{\foot}{ft}; then the unit can be used: 1 \foot gives 1 ft.

39 \newcommand*{\addunit}[2]{\newcommand{#1}{\ensuremath{\mathrm{#2}}}}

\unitskip The \unitskip macro gives one the possibility to choose spacing characters that are not already defined, by the spacing options (page 18). It also gives the possibility to use various spacing character in your documents.

40 \newcommand*{\unitskip}[1]{\renewcommand{\usk}{\ensuremath{#1}}}

\quantityskip The \quantityskip macro gives one the possibility to choose spacing characters that are not already defined, by the spacing options (page 18). It also gives the possibility to use various spacing character in your documents.

41 \newcommand*{\quantityskip}[1]{\renewcommand{\qsk}{\ensuremath{#1}}}

9.7 Spacing units

\per In version 0.04 of the SIunits package, one has to do the spacing of units by

\usk
\qsk

hand. I have plans to get some things automated in a future version. The \per macro gives / to be used in a quotient of two units; \usk (unitskip) makes a thick math space by default, but can be changed by the spacing options (page 18) or the \unitskip command. Usage: \metre\per\second (unit of speed) gives: m/s \newton\usk\metre (unit of torque) gives: N m. \qsk (space between quantity and unit) makes a thick math space by default, but can be changed by the options for spacing between quantity and unit (page 18) or the \quantityskip command. \qsk is used in the \unit macro.

42 \newcommand{\per}{\ensuremath{\mathrm{/}}}
43 \newcommand{\usk}{\ensuremath{\;}}
44 \newcommand{\qsk}{\ensuremath{\;}}

9.8 Spacing between numerical quantities and unit

\unit The \unitmacro is used to typeset conjunction of a numerical quantity and a unit.

Usage: \unit {120} {\kilo\meter\per\hour} 33.3 m/s= to get: 120 km/h =

33.3 m/s

45 \newcommand*{\unit}[2]{\ensuremath{\mathrm{#1\qsk#2}}}

9.9 Power(full) macros

\power The \power^{1}macro is used to typeset a superscript. Usage: \power{\metre}{2} to get: m^{2}

46 \newcommand*{\power}[2]{\ensuremath{\mathrm{#1}^{#2}}}

\square The above example can be realised in a more intuitive way: \square\metre: m^{2}.

\squared
\cubic
\cubed
\fourth

The same goes for \cubic & \fourth: m^{3} & m^{4}.

47 \newcommand*{\square}[1]{\power{#1}{2}}
48 \newcommand*{\squared}{\ensuremath{^{\mathrm{2}}}}
49 \newcommand*{\cubic}[1]{\power{#1}{3}}

7Thanks to Werenfried Spit — (w.spit@WITBO.NL)

50 \newcommand*{\cubed}{\ensuremath{^{\mathrm{3}}}}
51 \newcommand*{\fourth}[1]{\power{#1}{4}}
\reciprocal The macros \reciprocal, \rpsquare, \rpsquared, \rpcubic, \rpcubed and
\rp
\rpsquare
\rpsquared
\rpcubic
\rpcubed
\rpfourth

\rpfourth provide the reciprocal (negative power): e. g. m^{−1}, m^{−2}, m^{−3} and m^{−4}. \rp is a short form for \reciprocal.

52 \newcommand*{\reciprocal}[1]{\power{#1}{-1}}
53 \newcommand{\rp}{\reciprocal}
54 \newcommand*{\rpsquare}[1]{\power{#1}{-2}}
55 \newcommand*{\rpsquared}{\ensuremath{^{\mathrm{-2}}}}
56 \newcommand*{\rpcubic}[1]{\power{#1}{-3}}
57 \newcommand*{\rpcubed}{\ensuremath{^{\mathrm{-3}}}}
58 \newcommand*{\rpfourth}[1]{\power{#1}{-4}}

9.10 SI decimal prefixes

Prefixes These prefixes may be used to construct decimal fractions or multiples of units. Two different forms are provided, e. g. \milli and \millid.

9.10.1 Symbols

symbols The first form gives the symbol of the prefix: \milli\second: ms;

59 \newcommand{\yocto}{\ensuremath{\mathrm{y}}}
60 \newcommand{\zepto}{\ensuremath{\mathrm{z}}}
61 \newcommand{\atto}{\ensuremath{\mathrm{a}}}
62 \newcommand{\femto}{\ensuremath{\mathrm{f}}}
63 \newcommand{\pico}{\ensuremath{\mathrm{p}}}
64 \newcommand{\nano}{\ensuremath{\mathrm{n}}}
65 \newcommand{\micro}{\ensuremath{\mathrm{\upmu}}}
66 \newcommand{\milli}{\ensuremath{\mathrm{m}}}
67 \newcommand{\centi}{\ensuremath{\mathrm{c}}}
68 \newcommand{\deci}{\ensuremath{\mathrm{d}}}
69 \newcommand{\deca}{\ensuremath{\mathrm{da}}}
70 \newcommand{\hecto}{\ensuremath{\mathrm{h}}}
71 \newcommand{\kilo}{\ensuremath{\mathrm{k}}}
72 \newcommand{\mega}{\ensuremath{\mathrm{M}}}
73 \newcommand{\giga}{\ensuremath{\mathrm{G}}}
74 \newcommand{\tera}{\ensuremath{\mathrm{T}}}
75 \newcommand{\peta}{\ensuremath{\mathrm{P}}}
76 \newcommand{\exa}{\ensuremath{\mathrm{E}}}
77 \newcommand{\zetta}{\ensuremath{\mathrm{Z}}}
78 \newcommand{\yotta}{\ensuremath{\mathrm{Y}}}

9.10.2 Decimal form

decimals The other form gives the decimal factor: \kilod\usk\hertz: 10^{3} Hz

79 \newcommand{\yoctod}{\power{10}{-24}}
80 \newcommand{\zeptod}{\power{10}{-21}}
81 \newcommand{\attod}{\power{10}{-18}}
82 \newcommand{\femtod}{\power{10}{-15}}
83 \newcommand{\picod}{\power{10}{-12}}
84 \newcommand{\nanod}{\power{10}{-9}}
85 \newcommand{\microd}{\power{10}{-6}}

86 \newcommand{\millid}{\power{10}{-3}}
87 \newcommand{\centid}{\power{10}{-2}}
88 \newcommand{\decid}{\power{10}{-1}}
89 \newcommand{\decad}{\power{10}{1}}
90 \newcommand{\hectod}{\power{10}{2}}
91 \newcommand{\kilod}{\power{10}{3}}
92 \newcommand{\megad}{\power{10}{6}}
93 \newcommand{\gigad}{\power{10}{9}}
94 \newcommand{\terad}{\power{10}{12}}
95 \newcommand{\petad}{\power{10}{15}}
96 \newcommand{\exad}{\power{10}{18}}
97 \newcommand{\zettad}{\power{10}{21}}
98 \newcommand{\yottad}{\power{10}{24}}

The SI exception

\gram In the SI, Base units, Supplementary units and Derived units do not have prefixes, except for the base unit of mass: kilogram, not: gram. However, the macro \gram provides the symbol of gram: g.

99 \newcommand{\gram}{\ensuremath{\mathrm{g}}}

9.11 SI base units

\metre length: metre — m

\meter Both \metre and \meter can be used.
100 \newcommand{\metre}{\ensuremath{\mathrm{m}}}

\kilogram mass: kilogram — kg

101 \newcommand{\kilogram}{\kilo\gram}

\second time: second — s

102 \newcommand{\second}{\ensuremath{\mathrm{s}}}

\ampere electric current: ampere — A

103 \newcommand{\ampere}{\ensuremath{\mathrm{A}}}

\kelvin thermodynamic temperature: kelvin — K

104 \newcommand{\kelvin}{\ensuremath{\mathrm{K}}}

\mole amount of substance: mole — mol

105 \newcommand{\mole}{\ensuremath{\mathrm{mol}}}

\candela luminous intensity: candela — cd

106 \newcommand{\candela}{\ensuremath{\mathrm{cd}}}

9.12 SI derived units

\radian plane angle

107 \newcommand{\radian}{\ensuremath{\mathrm{rad}}}
\steradian solid angle
108 \newcommand{\steradian}{\ensuremath{\mathrm{sr}}}

\hertz frequency

109 \newcommand{\hertz}{\ensuremath{\mathrm{Hz}}}
\newton force
110 \newcommand{\newton}{\ensuremath{\mathrm{N}}}

\pascal pressure

111 \newcommand{\pascal}{\ensuremath{\mathrm{Pa}}}

\joule energy, work, quantity of heat

112 \newcommand{\joule}{\ensuremath{\mathrm{J}}}

\watt power, radiant flux

113 \newcommand{\watt}{\ensuremath{\mathrm{W}}}

\coulomb electric charge, quantity of electricity

114 \newcommand{\coulomb}{\ensuremath{\mathrm{C}}}

\volt electrical potential, potential difference, electromotive force

115 \newcommand{\volt}{\ensuremath{\mathrm{V}}}

\farad capacitance

116 \newcommand{\farad}{\ensuremath{\mathrm{F}}}

\ohm electrical resistance

117 \newcommand{\ohm}{\ensuremath{\mathrm{\Omega}}}

\siemens electrical conductance

118 \newcommand{\siemens}{\ensuremath{\mathrm{S}}}

\weber magnetic flux, magnetic field strength

119 \newcommand{\weber}{\ensuremath{\mathrm{Wb}}}

\tesla magnetic flux density

120 \newcommand{\tesla}{\ensuremath{\mathrm{T}}}

\henry inductance

121 \newcommand{\henry}{\ensuremath{\mathrm{H}}}

\degreecelsius Celsius temperature unit name : “degree Celsius”

\celsius both \degreecelsius and \celsius can be used.
122 \newcommand{\degreecelsius}{\degree\Celsius}
123 \newcommand{\celsius}{\degreecelsius}

\lumen luminous flux

124 \newcommand{\lumen}{\ensuremath{\mathrm{lm}}}

\lux illuminance

125 \newcommand{\lux}{\ensuremath{\mathrm{lx}}}

\becquerel activity of a radionuclide

126 \newcommand{\becquerel}{\ensuremath{\mathrm{Bq}}}

\gray absorbed dose, specific energy imparted, kerma

127 \newcommand{\gray}{\ensuremath{\mathrm{Gy}}}

\sievert dose equivalent

128 \newcommand{\sievert}{\ensuremath{\mathrm{Sv}}}

9.12.1 The derivedinbase mode

Expression of derived SI units in SI base units

\SIunits@opt@derivedinbase This macro provides the expression of derived SI units in SI base units. These macros can be accessed by putting ‘base’ behind the SI derived unit command, e. g. (\pascalbase) to get ’m^{−1} kg s^{−2}‘.

129 \newcommand*\SIunits@opt@derivedinbase{%
130 \newcommand{\radianbase}{\metre\usk\reciprocal\metre}
131 \newcommand{\steradianbase}{\square\metre\usk\rpsquare\metre}
132 \newcommand{\hertzbase}{\reciprocal\second}
133 \newcommand{\newtonbase}{\metre\usk\kilogram\usk\second\rpsquared}
134 \newcommand{\pascalbase}{\reciprocal\metre\usk\kilogram\usk\second\rpsquared}
135 \newcommand{\joulebase}{\square\metre\usk\kilogram\usk\second\rpsquared}
136 \newcommand{\wattbase}{\square\metre\usk\kilogram\usk\rpcubic\second}
137 \newcommand{\coulombbase}{\second\usk\ampere}
138 \newcommand{\voltbase}{\square\metre\usk\kilogram\usk\rpcubic\second\usk\reciprocal\ampere}
139 \newcommand{\faradbase}{\rpsquare\metre\usk\reciprocal\kilogram\usk\fourth\second\usk\ampere\squared}
140 \newcommand{\ohmbase}{\square\metre\usk\kilogram\usk\rpcubic\second\usk\rpsquare\ampere}
141 \newcommand{\siemensbase}{\rpsquare\metre\usk\reciprocal\kilogram\usk\cubic\second\usk\ampere\squared}
142 \newcommand{\weberbase}{\square\metre\usk\kilogram\usk\second\rpsquared\usk\reciprocal\ampere}
143 \newcommand{\teslabase}{\kilogram\usk\second\rpsquared\usk\reciprocal\ampere}
144 \newcommand{\henrybase}{\square\metre\usk\kilogram\usk\second\rpsquared\usk\rpsquare\ampere}
145 \newcommand{\celsiusbase}{\kelvin}
146 \newcommand{\lumenbase}{\candela\usk\square\metre\usk\rpsquare\metre}
147 \newcommand{\luxbase}{\candela\usk\square\metre\usk\rpfourth\metre}
148 \newcommand{\becquerelbase}{\hertzbase}
149 \newcommand{\graybase}{\square\metre\usk\second\rpsquared}
150 \newcommand{\sievertbase}{\graybase}
151  \typeout{Option 'derivedinbase' provided!^^J}}

9.12.2 The derived mode

Expression of derived SI units in other derived SI units

\SIunits@opt@derived This macro provides the expression of derived SI units in other SI derived units (if possible). These macros can be accessed by putting ‘der’ in front of the SI derived unit command, e. g. (\derpascal) to get ’N m^{−2}‘.

152 \newcommand*\SIunits@opt@derived{%
153 \newcommand{\derradian}{\metre\usk\reciprocal\metre}
154 \newcommand{\dersteradian}{\square\metre\usk\rpsquare\metre}
155 \newcommand{\derhertz}{\reciprocal\second}
156 \newcommand{\dernewton}{\metre\usk\kilogram\usk\second\rpsquared}
157 \newcommand{\derpascal}{\newton\usk\rpsquare\metre}
158 \newcommand{\derjoule}{\newton\usk\metre}
159 \newcommand{\derwatt}{\joule\usk\reciprocal\second}
160 \newcommand{\dercoulomb}{\ampere\usk\second}
161 \newcommand{\dervolt}{\watt\usk\reciprocal\ampere}
162 \newcommand{\derfarad}{\coulomb\usk\reciprocal\volt}
163 \newcommand{\derohm}{\volt\usk\reciprocal\ampere}
164 \newcommand{\dersiemens}{\ampere\usk\reciprocal\volt}
165 \newcommand{\derweber}{\square\metre\usk\kilogram\usk\second\rpsquared\usk\reciprocal\ampere}
166 \newcommand{\dertesla}{\weber\usk\rpsquare\metre}

167 \newcommand{\derhenry}{\weber\usk\reciprocal\ampere}
168 \newcommand{\dercelsius}{\kelvin}
169 \newcommand{\derlumen}{\candela\usk\steradian}
170 \newcommand{\derlux}{\lumen\usk\rpsquare\metre}
171 \newcommand{\derbecquerel}{\derhertz}
172 \newcommand{\dergray}{\joule\usk\reciprocal\kilogram}
173 \newcommand{\dersievert}{\dergray}
174  \typeout{Option `derived' provided! ^^J}}

9.13 Units that are used with the SI

\minute Time: \day was already used

\hour
\dday

175 \newcommand{\minute}{\ensuremath{\mathrm{min}}}
176 \newcommand{\hour}{\ensuremath{\mathrm{h}}}
177 \newcommand{\dday}{\ensuremath{\mathrm{d}}}

\degree Plane angle: \minute and \second were already used

\paminute
\pasecond

178 \newcommand{\degree}{\ensuremath{^{\circ}}}
179 \newcommand{\paminute}{\ensuremath{'}}
180 \newcommand{\pasecond}{\ensuremath{''}}

\ton Mass: metric ton or tonne

\tonne
181 \newcommand{\ton}{\ensuremath{\mathrm{t}}}
182 \newcommand{\tonne}{\ensuremath{\mathrm{t}}}

\liter Volume: litre or liter

\litre
183 \newcommand{\liter}{\ensuremath{\mathrm{L}}}
184 \newcommand{\litre}{\ensuremath{\mathrm{l}}}

\curie Radioactivity

185 \newcommand{\curie}{\ensuremath{\mathrm{Ci}}}

\rad Absorbed dose: rad. When there is risk of confusion with the symbol for radian \arad (rad), rd may be used as the symbol for rad.

186 \newcommand{\rad}{\ensuremath{\mathrm{rad}}}
187 \newcommand{\arad}{\ensuremath{\mathrm{rd}}}

\rem Dose equivalent

188 \newcommand{\rem}{\ensuremath{\mathrm{rem}}}
\roentgen Exposure
189 \newcommand{\roentgen}{\ensuremath{\mathrm{R}}}
\electronvolt Energy
190 \newcommand{\electronvolt}{\ensuremath{\mathrm{e}\volt}}

\atomicmass Unified atomic mass unit

191 \newcommand{\atomicmass}{\ensuremath{\mathrm{u}}}
\are Area
\hectare
\barn

192 \newcommand{\are}{\ensuremath{\mathrm{a}}}
193 \newcommand{\hectare}{\ensuremath{\mathrm{ha}}}
194 \newcommand{\barn}{\ensuremath{\mathrm{b}}}

\bbar Pressure

195 \newcommand{\bbar}{\ensuremath{\mathrm{bar}}}

\gal Acceleration

196 \newcommand{\gal}{\ensuremath{\mathrm{Gal}}}
\angstrom Length
197 \newcommand{\angstrom}{\mbox{\textrm{\AA}}}

\rperminute Rotational frequency: revolutions per minute

198 \newcommand{\rperminute}{\ensuremath{\mathrm{r}\per\minute}}

9.14 SI units with compound names

\squaremetre Area
199 \newcommand{\squaremetre}{\square\metre}
\cubicmetre Volume
200 \newcommand{\cubicmetre}{\cubic\metre}

9.15 Various ready-to-use units

These units are provided for the ease of the users of the SIunits package. Normally, two forms of the units are provided, e. g. \graypersecond and \graypersecondnp. The commandnp form uses negative powers instead of /: ‘Gy/s’ and ‘ Gy s^{−1}’. absorbed dose rate

201 \newcommand{\graypersecond}{\gray\per\second}
202 \newcommand{\graypersecondnp}{\gray\usk\reciprocal\second}

acceleration

203 \newcommand{\metrepersquaresecond}{\metre\per\second\squared}
204 \newcommand{\metrepersquaresecondnp}{\metre\usk\second\rpsquared}

activation energy, molar energy

205 \newcommand{\joulepermole}{\joule\per\mole}
206 \newcommand{\joulepermolenp}{\joule\usk\reciprocal\mole}

amount-of-substance concentration

207 \newcommand{\molepercubicmetre}{\mole\per\cubic\metre}
208 \newcommand{\molepercubicmetrenp}{\mole\usk\rpcubic\metre}

angular acceleration

209 \newcommand{\radianpersquaresecond}{\radian\per\second\squared}
210 \newcommand{\radianpersquaresecondnp}{\radian\usk\second\rpsquared}

angular momentum

211 \newcommand{\kilogramsquaremetrepersecond}{\kilogram\usk\square\metre\per\second}
212 \newcommand{\kilogramsquaremetrepersecondnp}{\kilogram\usk\square\metre\usk\reciprocal\second}

angular velocity

213 \newcommand{\radianpersecond}{\radian\per\second}
214 \newcommand{\radianpersecondnp}{\radian\usk\reciprocal\second}

area per unit volume

215 \newcommand{\squaremetrepercubicmetre}{\square\metre\per\cubic\metre}
216 \newcommand{\squaremetrepercubicmetrenp}{\square\metre\usk\rpcubic\metre}

charge per mole

217 \newcommand{\coulombpermol}{\coulomb\per\mole}
218 \newcommand{\coulombpermolnp}{\coulomb\usk\reciprocal\mole}

current density

219 \newcommand{\amperepersquaremetre}{\ampere\per\square\metre}
220 \newcommand{\amperepersquaremetrenp}{\ampere\usk\rpsquare\metre}

density

221 \newcommand{\kilogrampercubicmetre}{\kilogram\per\cubic\metre}
222 \newcommand{\kilogrampercubicmetrenp}{\kilogram\usk\rpcubic\metre}

dynamic fluidity (1/viscosity)

223 \newcommand{\squaremetrepernewtonsecond}{\square\metre\per\newton\usk\second}
224 \newcommand{\squaremetrepernewtonsecondnp}{\square\metre\usk\reciprocal\newton\usk\reciprocal\second}

dynamic viscosity

225 \newcommand{\pascalsecond}{\pascal\usk\second}
226 \newcommand{\pascalsecondnp}{\kilogram\usk\reciprocal\second}

electric charge density

227 \newcommand{\coulombpercubicmetre}{\coulomb\per\cubic\metre}
228 \newcommand{\coulombpercubicmetrenp}{\coulomb\usk\rpcubic\metre}

electric dipole moment

229 \newcommand{\amperemetresecond}{\ampere\usk\metre\usk\second}

electric field strength

230 \newcommand{\voltpermetre}{\volt\per\metre}
231 \newcommand{\voltpermetrenp}{\volt\usk\reciprocal\metre}

electric flux density

232 \newcommand{\coulombpersquaremetre}{\coulomb\per\square\metre}
233 \newcommand{\coulombpersquaremetrenp}{\coulomb\usk\rpsquare\metre}

electrical permittivity

234 \newcommand{\faradpermetre}{\farad\per\metre}
235 \newcommand{\faradpermetrenp}{\farad\usk\reciprocal\metre}

electrical resistivity

236 \newcommand{\ohmmetre}{\ohm\usk\metre}

energy

237 \newcommand{\kilowatthour}{\kilo\watt\hour}

energy flux

238 \newcommand{\wattpersquaremetre}{\watt\per\square\metre}
239 \newcommand{\wattpersquaremetrenp}{\watt\usk\rpsquare\metre}

energy per unit area

240 \newcommand{\joulepersquaremetre}{\joule\per\square\metre}
241 \newcommand{\joulepersquaremetrenp}{\joule\usk\rpsquare\metre}

force (body)

242 \newcommand{\newtonpercubicmetre}{\newton\per\cubic\metre}
243 \newcommand{\newtonpercubicmetrenp}{\newton\usk\rpcubic\metre}

force per unit mass

244 \newcommand{\newtonperkilogram}{\newton\per\kilogram}
245 \newcommand{\newtonperkilogramnp}{\newton\usk\reciprocal\kilogram}

heat capacity, entropy

246 \newcommand{\jouleperkelvin}{\joule\per\kelvin}
247 \newcommand{\jouleperkelvinnp}{\joule\usk\reciprocal\kelvin}

heat of combustion, fusion or vaporisation

248 \newcommand{\jouleperkilogram}{\joule\per\kilogram}
249 \newcommand{\jouleperkilogramnp}{\joule\usk\reciprocal\kilogram}

intensity of ionising radiation

250 \newcommand{\coulombperkilogram}{\coulomb\per\kilogram}
251 \newcommand{\coulombperkilogramnp}{\coulomb\usk\reciprocal\kilogram}

kinematic viscosity

252 \newcommand{\squaremetrepersecond}{\squaremetre\per\second}
253 \newcommand{\rpsquaremetrepersecond}{\squaremetre\usk\reciprocal\second}

kinematic energy of turbulence

254 \newcommand{\squaremetrepersquaresecond}{\square\metre\per\second\squared}
255 \newcommand{\rpsquaremetrepersquaresecond}{\square\metre\usk\second\rpsquared}

linear momentum

256 \newcommand{\kilogrammetrepersecond}{\kilogram\usk\metre\per\second}
257 \newcommand{\kilogrammetrepersecondnp}{\kilogram\usk\metre\usk\reciprocal\second}

luminance

258 \newcommand{\candelapersquaremetre}{\candela\per\square\metre}
259 \newcommand{\candelapersquaremetrenp}{\candela\usk\rpsquare\metre}

magnetic field strength

260 \newcommand{\amperepermetre}{\ampere\per\metre}
261 \newcommand{\amperepermetrenp}{\ampere\usk\reciprocal\metre}

magnetic moment

262 \newcommand{\joulepertesla}{\joule\per\tesla}
263 \newcommand{\jouleperteslanp}{\joule\usk\reciprocal\tesla}

magnetic permeability

264 \newcommand{\henrypermetre}{\henry\per\metre}
265 \newcommand{\henrypermetrenp}{\henry\usk\reciprocal\metre}

mass flow rate

266 \newcommand{\kilogrampersecond}{\kilogram\per\second}
267 \newcommand{\kilogrampersecondnp}{\kilogram\usk\reciprocal\second}

mass flux

268 \newcommand{\kilogrampersquaremetresecond}{\kilogram\per\square\metre\usk\second}
269 \newcommand{\kilogrampersquaremetresecondnp}{\kilogram\usk\rpsquare\metre\usk\reciprocal\second}

mass per unit area

270 \newcommand{\kilogrampersquaremetre}{\kilogram\per\square\metre}
271 \newcommand{\kilogrampersquaremetrenp}{\kilogram\usk\rpsquare\metre}

mass per unit length

272 \newcommand{\kilogrampermetre}{\kilogram\per\metre}
273 \newcommand{\kilogrampermetrenp}{\kilogram\usk\reciprocal\metre}

molar heat capacity, molar entropy

274 \newcommand{\joulepermolekelvin}{\joule\per\mole\usk\kelvin}
275 \newcommand{\joulepermolekelvinnp}{\joule\usk\reciprocal\mole\usk\reciprocal\kelvin}

molecular weight

276 \newcommand{\kilogramperkilomole}{\kilogram\per\kilo\mole}
277 \newcommand{\kilogramperkilomolenp}{\kilogram\usk\kilo\reciprocal\mole}

moment of inertia

278 \newcommand{\kilogramsquaremetre}{\kilogram\usk\square\metre}
279 \newcommand{\kilogramsquaremetrenp}{\kilogramsquaremetre}

momentum flow rate

280 \newcommand{\kilogrammetrepersquaresecond}{\kilogram\usk\metre\per\second\squared}
281 \newcommand{\kilogrammetrepersquaresecondnp}{\kilogram\usk\metre\usk\second\rpsquared}

momentum flux

282 \newcommand{\newtonpersquaremetre}{\newton\per\square\metre}
283 \newcommand{\newtonpersquaremetrenp}{\newton\usk\rpsquare\metre}

photon emission rate

284 \newcommand{\persquaremetresecond}{1\per\square\metre\usk\second}
285 \newcommand{\persquaremetresecondnp}{\rpsquare\metre\usk\reciprocal\second}

power per unit mass

286 \newcommand{\wattperkilogram}{\watt\per\kilogram}
287 \newcommand{\wattperkilogramnp}{\watt\usk\reciprocal\kilogram}

power per unit volume

288 \newcommand{\wattpercubicmetre}{\watt\per\cubic\metre}
289 \newcommand{\wattpercubicmetrenp}{\watt\usk\rpcubic\metre}

radiance

290 \newcommand{\wattpersquaremetresteradian}{\watt\per\squaremetre\usk\steradian}
291 \newcommand{\wattpersquaremetresteradiannp}{\watt\usk\rpsquare\metre\usk\rp\steradian}

specific heat capacity

292 \newcommand{\jouleperkilogramkelvin}{\joule\per\kilogram\usk\kelvin}
293 \newcommand{\jouleperkilogramkelvinnp}{\joule\usk\reciprocal\kilogram\usk\reciprocal\kelvin}

specific surface

294 \newcommand{\squaremetreperkilogram}{\square\metre\per\kilogram}
295 \newcommand{\rpsquaremetreperkilogram}{\square\metre\usk\reciprocal\kilogram}

specific volume

296 \newcommand{\cubicmetreperkilogram}{\cubic\metre\per\kilogram}
297 \newcommand{\rpcubicmetreperkilogram}{\cubic\metre\usk\reciprocal\kilogram}

surface tension

298 \newcommand{\newtonpermetre}{\newton\per\metre}
299 \newcommand{\newtonpermetrenp}{\newton\usk\reciprocal\metre}

derived SI unit: ^{∘}C

300 \newcommand{\Celsius}{\ensuremath{\mathrm{C}}}

thermal conductivity

301 \newcommand{\wattpermetrekelvin}{\watt\per\metre\usk\kelvin}
302 \newcommand{\wattpermetrekelvinnp}{\watt\usk\reciprocal\metre\usk\reciprocal\kelvin}

torque

303 \newcommand{\newtonmetre}{\newton\usk\metre}
304 \newcommand{\newtonmetrenp}{\newtonmetre}

turbulence energy dissipation rate

305 \newcommand{\squaremetrepercubicsecond}{\square\metre\per\cubic\second}
306 \newcommand{\squaremetrepercubicsecondnp}{\square\metre\usk\rpcubic\second}

velocity

307 \newcommand{\metrepersecond}{\metre\per\second}
308 \newcommand{\metrepersecondnp}{\metre\usk\reciprocal\second}

volumetric calorific value

309 \newcommand{\joulepercubicmetre}{\joule\per\cubicmetre}
310 \newcommand{\joulepercubicmetrenp}{\joule\usk\rpcubic\metre}

volumetric coefficient of expansion

311 \newcommand{\kilogrampercubicmetrecoulomb}{\kilogram\per\cubic\metre\usk\coulomb}
312 \newcommand{\kilogrampercubicmetrecoulombnp}{\kilogram\usk\rpcubic\metre\usk\reciprocal\coulomb}

volumetric flow rate

313 \newcommand{\cubicmetrepersecond}{\cubicmetre\per\second}
314 \newcommand{\rpcubicmetrepersecond}{\cubicmetre\usk\reciprocal\second}

volumetric mass flow rate

315 \newcommand{\kilogrampersecondcubicmetre}{\kilogram\per\second\usk\cubicmetre}
316 \newcommand{\kilogrampersecondcubicmetrenp}{\kilogram\usk\reciprocal\second\usk\rpcubic\metre}

 9.16 The SIunits.cfg file
 Load the SIunits.cfg file, after redefining \ExecuteOptions to \SIunits@execopt

(we cannot simply use \ExecuteOptions to preselect options, because we want to

 pass them to \SIunits@execopt).
317 \let\SIunits@origExecuteOptions\ExecuteOptions
318 \let\ExecuteOptions\SIunits@execopt
319 \InputIfFileExists{SIunits.cfg}{}{%
320 \PackageWarningNoLine{SIunits}{%
321 You have no `SIunits.cfg' file installed.\MessageBreak I will assume you are using
322 `thickspace' and `thickqspace'} \ExecuteOptions{thickspace,thickqspace}}
323 \let\ExecuteOptions\SIunits@origExecuteOptions
324 \ProcessOptions
325 \endinput

326 ⟨/package⟩

Copyright \begin{matrix}c \\ ◯ \end{matrix}1998 by Marcel HeldoornM.H.