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From: [email protected] (Markus Kuhn)
Newsgroups: misc.metric-system,misc.answers,news.answers
Subject: Metric System FAQ
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Summary: Introductory information and references about the metric system
        as well as answers to common questions in the newsgroup
        misc.metric-system.
Keywords: metric system, international system of units, systeme international,
         SI, international standards, units of measurement, metrication
Xref: senator-bedfellow.mit.edu misc.metric-system:5893 misc.answers:20129 news.answers:324107

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URL: http://www.cl.cam.ac.uk/~mgk25/metric-system-faq.txt

Metric System FAQ
-----------------

This regular posting to the USENET group misc.metric-system provides a
brief introduction, collects useful references, and answers some
frequently asked questions.

A note on the character set: This file was written and distributed in
the Unicode UTF-8 encoding. If "©" does not show up as a copyright
sign, chances are that the encoding has been corrupted on the way to
you or that your news reader lacks support for the MIME or UTF-8
standards. If "Ω" does not show up as a Greek capital letter omega,
chances are that chosing a different font with a larger Unicode
repertoire to read this text may help.

Suggestions for improvement are welcome! ☺

Markus Kuhn
http://www.cl.cam.ac.uk/~mgk25/


Contents
--------

1  Basics

1.1  What is the International System of Units (SI)?
1.2  What is the history of the metric system?
1.3  Which countries have yet to fully adopt the metric system?
1.4  What are the advantages of the metric system?
1.5  How can I make myself more familiar with the metric system?
1.6  Where are good web sites related to the metric system?
1.7  Are there any good books or newsletters on the metric system?
1.8  What are the SI base units and how are they currently defined?
1.9  What are the SI derived units with a special name?
1.10 Who were the SI units named after?
1.11 What are the SI prefixes?
1.12 What is the correct way of writing metric units?

2  Metric product specifications

2.1  What are preferred numbers or Renard numbers?
2.2  How do metric paper sizes work?
2.3  How do metric threads work?
2.4  How do metric clothes sizes work?
2.5  What inch-based standards are widely used in metric countries?
2.5.1  Metric water-pipe thread designations
2.5.2  Metric bicycle tire and rim designations
2.5.3  Shotgun gauge sizes
2.6  What metric standards are commonly known under an inch name?

3  Misc

3.1  Why is there a newsgroup on the metric system?
3.2  Where can I look up unit conversion factors?
3.3  What is the exact international definition of some non-SI units?
3.4  What are calories?
3.5  What are FFUs and WOMBAT units?
3.6  Does kilo mean 1024 in computing?
3.7  What are the official short symbols for bit and byte?
3.8  What does the "e" symbol found on many packaged goods mean?
3.9  How are metric units used in the kitchen?
3.10 How to convert US customary recipes into metric?


1  Basics
=========


1.1 What is the International System of Units (SI)?
---------------------------------------------------

The "International System of Units" is the modern definition of what
is colloquially known in the English-speaking world as the "metric
system". Its name is commonly abbreviated as "SI", short for the
French "Le Système International d'Unites".

The SI is built on the seven base units metre, kilogram, second,
ampere, kelvin, mole, and candela for measuring length, mass, time,
electric current, thermodynamic temperature, amount of substance and
luminosity.

Units for measuring all other quantities are derived in the SI by
multiplying and dividing these base units. This leads to a "coherent"
system of units that almost eliminates the need for unit conversion
factors in calculations. A list of 22 derived SI units have names of
their own, for example newton, pascal, joule, volt, ohm, and watt.

In order to provide conveniently sized units for all applications, the
SI defines a set of prefixes -- such as milli, micro, nano, kilo,
mega, and giga -- that can be used to derive decimal multiples or
submultiples of units.  The use of SI prefixes introduces conversion
factors in calculations, but these are all powers of ten, which are
trivial to apply in mental arithmetic by shifting the decimal point.


1.2  What is the history of the metric system?
----------------------------------------------

A very brief scientific history of the metric system:

The origin of the SI dates back to the early 1790s, when a coherent
system of weights and measures with decimal multiples and fractions
was proposed in France. On 22 June 1799, two platinum standards
representing the metre and the kilogram were manufactured in London
and deposited in Paris. In 1832, the German astronomer Gauss made a
strong case for the use of the metric system in the physical sciences
and proposed extensions for measuring magnetic fields. The British
physicists Maxwell and Thomson led in 1874 the extension of Gauss'
proposal to the CGS. This system of units for electromagnetic theory
was derived from the base units centimetre, gram and second and found
some use in experimental physics. However, the sizes of some of the
CGS units turned out to be inconvenient. This lead in the 1880s in
British and international scientific organizations to the development
of a variant system with the base units metre, kilogram and second,
known as MKS. This system introduced the modern electricity units
volt, ampere, and ohm. In 1901, the Italian physicist Giorgi proposed
a minor modification of the MKS system, turning the ampere into a
fourth base unit, leading to the MKSA system of units that finally
became internationally accepted after long discussions in 1946. In
1954, two more base units for temperature (kelvin) and luminosity
(candela) were added to the MKSA system, which was renamed in 1960
into the International System of Units (SI). Finally, in 1971, the SI
as it is used today was completed by adding the mole as the base unit
for amount of substance.

A very brief legal history of the metric system:

Metric units became the only legally accepted weights and measures in
Belgium, the Netherlands, and Luxembourg in 1820, followed by France
in 1837. They were rapidly adopted between 1850 and 1900 across
Continental Europe and Latin America. The metric system became the
subject of an international treaty, the Metre Convention of 1875. This
created the International Bureau of Weights and Measures (Bureau
International des Poids et Mesures, BIPM) in Paris, the body in charge
of maintaining the metric system. Its exact definition has since then
been periodically reviewed and revised by the International Conference
of Weights and Measures (Conférence Générale des Poids et Mesures,
CGPM). It continued to spread around the world during the first half
of the 20th century. Among the last developed countries to convert
were South Africa, Australia, New Zealand and Canada in the early
1970s.

More information:

 - http://www.bipm.org/en/si/history-si/
 - http://lamar.colostate.edu/~hillger/#metric
 - Pat Naughtin's articles
   http://metricationmatters.com/who-invented-the-metric-system.html
   http://metricationmatters.com/docs/USAMetricSystemHistory.pdf
   elaborate some of the early intellectual history of the metric system.


1.3  Which countries have yet to fully adopt the metric system?
---------------------------------------------------------------

British industry converted successfully to the metric system in the
1960s. But with continued legal validity of inch-pound units, takeup
of the metric system by the British public remained a slow process for
three decades, which is still in progress. The pound finally lost its
status as a legal unit of weight in the United Kingdom on 1 January
2000. The legal use of non-metric units is now limited in Britain to a
few special fields, which have been summed up jokingly as "drinking
and driving":

 - mile, yard, foot or inch for road traffic signs, distance
   and speed measurement

 - pint for dispensing draught beer and cider

 - pint for milk in returnable containers

 - acre for land registration
   (actually no longer used today by UK land registries)

 - troy ounce for transactions in precious metals

 - units used in international conventions for air and sea transport

[http://www.legislation.hmso.gov.uk/si/si1995/Uksi_19951804_en_1.htm]

British media coverage continues to use non-metric units frequently
alongside metric units, in particular feet and inches for the size of
humans and stones for their weight. Weather reports add the occasional
Fahrenheit temperature as a courtesy to the older generation, but air
temperature is predominantly reported in degrees Celsius today.

The report "A very British mess", prepared in 2004 by the UK metric
association, gives a more detailed picture of the mixed use of units
in British legislation and everyday life:

 http://www.ukma.org.uk/Docs/VBM.pdf

Progress in the Republic of Ireland has been somewhat faster than in
Britain. For example, speed limits on Irish road signs became fully
metric in January 2005.

The United States is today the last country in which the use of
inch-pound units is required by law in many areas. Most other
countries do not even legally recognize inch-pound units. US media
coverage still uses almost exclusively inch-pound-fahrenheit units. A
dual labeling requirement for retail products was introduced in
1992. A lobbying campaign "Coalition for Permissible Metric-Only
Labeling" supported by several large US manufacturers is now underway
to make the use of inch-pound units in consumer products optional in
federal law. The proposed change would allow manufacturers to simplify
US labels such as "24 fl. oz. (1 Pint 8 fl. oz.) 710 mL" to something
as neat and globally acceptable as "710 mL". US manufacturers suffer
at the moment the problem that the US customary units for volume,
which are mandatory in the US, differ from the Imperial units of the
same name and are therefore illegal for use in the United
Kingdom. This leads to separate labels and causes additional costs for
US manufacturers who want to export to Britain.

Canada has switched to the metric system in the late 1970s, but
inch-pound units remain some part of daily life in Canada due to its
close economic ties with the US. For example, Canada is the only other
country in the world that uses the US "Letter" paper size instead of
the international standard A4 format.

If your teacher has asked you to find out, which three countries have
not yet introduced the metric system, chances are that the expected
answer is "United States, Liberia and Burma" (the last of these is
called Myanmar today). This answer is almost certainly out of
date. The widely-quoted statement that these are the last three
countries not to have introduced the metric system may have originated
in some 1970s US government report and appears to have been mentioned
for a while in the CIA World Factbook. Although the introduction of
the metric system is clearly slowest in the US, compared to any other
developed country, it is widely used today in the US in selected
areas. Little authoritative information can be found on what the legal
or customary units are in Liberia and Burma today. Anecdotal evidence
from visitors and trading partners suggests that both are essentially
metric. The misc.metric-system readers are still eagerly awaiting
knowledgeable first-hand reports from people living in these
countries.

More information:

 http://en.wikipedia.org/wiki/Metrication


1.4 What are the advantages of the metric system?
-------------------------------------------------

This question comes up in misc.metric-system usually in discussions
with US Americans who see no compelling reason for why the United
States should make a serious effort to abandon their customary
inch-pound units and move on to the metric system.

The most frequently given answers include:

 - Because practically everyone uses it

   Americans who have never left their country may not realize that
   their customary system of inch-pound units is today practically
   unknown in most countries. For more than 95% of the world
   population, the metric system is the customary system of units,
   and for more than half of the industrialized world, it has been
   for at least a century. Products designed in non-metric units or
   using non-metric standards can cause serious maintenance and
   compatibility problems for customers in major world markets and do
   place a manufacturer at a disadvantage.

 - Because using two incompatible systems causes unnecessary friction

   The United States lacks a coherent system of units. Economic
   realities, international standards, and the short-comings of the
   inch-pound system (e.g., lack of electrical and chemical units,
   lack of small subunits) force it already to use the metric system
   alongside its customary inch-pound units. American students waste
   at least half a year of mathematics education with developing
   unit-conversion skills (both within the inch-pound system and
   between inch-pound and metric) that are utterly irrelevant in the
   metric-only rest of the world. [The study "Education System
   Benefits of U.S. Metric Conversion", by Richard P. Phelps,
   published in Evaluation Review, February 1996, claimed that
   teaching solely metric measurements could save an estimated 82
   days of mathematics instruction-time annually, worth over 17
   billion dollars.]

 - Because it dramatically reduces conversion factors in calculations

   In spite of a significant amount of secondary school time being
   wasted in the United States in science and math education with
   training the use of conversion factors between the bewildering set
   of units in use there, only few educated Americans know by heart
   how to convert between gallons and cubic feet or inches and miles.
   The inch-pound system suffers from a bewildering, random and
   completely unsystematic set of conversion factors between units
   for the same quantity, for instance 1 mile = 1760 yards and 1 US
   gallon = 231 cubic inches. It also suffers from the use of too
   many different units for the same quantity. Energy alone, for
   example, is measured in the US in calories, british thermal units,
   ergs, feet pound-force, quads, therms, tons of TNT,
   kilowatt-hours, electron volts, and joules, and power is measured
   in ergs per second, foot pound-force per second, several types of
   horsepowers, and watts.

   Users of the metric system, on the other hand, have to use
   conversion factors only where there are significant physical
   reasons for using alternative units to express some situation.  An
   example is the choice between molar concentration (a count of
   molecules better describes a chemical reaction balance) and a mass
   concentration (which describes better how a pharmacist prepares
   medication) in medicine. The main other reason for using
   conversion factors in the metric world is the continued use of
   non-decimal multiples of the second (hour, day, year).

 - Because metric dimensions are easier to divide by three

   A commonly brought up -- but misleading -- claim is that the
   inch-pound system supports division by three. While it is true
   that the factor three appears in the inch-foot and foot-yard
   conversion factors, this argument fails for the rest of the
   system. In practice, people find that metric dimensions are far
   easier to subdivide by various factors, as it is easier to move to
   smaller subunits and as it is more common in the metric world to
   use standardized preferred number sequences. For example, in the
   British building industry (see British Standard BS 6750), it is
   customary to chose major design dimensions (e.g., grid lines on a
   building plan) as multiples of 300, 600, or 1200 mm. As a result,
   common building dimensions can be divided by 2, 3, 4, 5, 6, 8, 10,
   12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, and
   300, without having to resort to millimetre fractions. Even
   without such precautions, it is instantly obvious that one
   kilometre divided by three is 333 1/3 metres and 1/3 L = 333 1/3
   mL. On the other hand, even inch-pound enthusiasts are a bit
   pressed when asked what 1/3 mile is in yards (answer: 586 2/3) or
   what 1/3 lb is in ounces (5 1/3). Although the use of decimal
   fractions is preferred in the metric system, because this
   simplifies the mental conversion between different unit prefixes,
   there is no reason why vulgar fractions cannot be used where it
   seems appropriate.

 - Because it is the only properly maintained system

   The inch-pound system used in the United States has essentially
   stopped evolving more than 200 years ago when the metric system
   emerged. Although it would, in principle, have been possible to
   extend the inch-pound system into a coherent and even decimal
   system of units, this never happened. The US customary system of
   units uses the inch and pound only for mechanical quantities. It
   had to copy, for example, all its electrical units (volt, ampere,
   watt, ohm) from the metric system. The length of the inch still
   differed noticeably between several English-speaking countries as
   late as World War II, which interfered with the exchange of
   precision equipment. It had to be redefined in 1959, when 1 inch
   finally became 25.4 mm. At this point, industries in all
   English-speaking countries -- apart from the United States --
   decided to abandon the inch entirely for precision work, and later
   also for general use.


1.5  How can I make myself more familiar with the metric system?
----------------------------------------------------------------

The metric system is today widely used in Britain. In the United
States, it clearly dominates so far at least in science, medicine, and
in many industries (electronics, automobile, etc.). But as long as
inch-pound units appear in the media and in consumer communication
(advertisement, product labels), many people will end up feeling more
familiar with them, in particular the generation that went through
secondary education before the 1970s.

Good knowledge of a few important reference values make units easy to
visualize, even where they are not yet encountered in daily life. This
list is a suggestion of approximate metric values that every educated
adult may want to be familiar with. Also useful for trivial-pursuit
type games.


A) Humans

 Typical height of an adult:          1.60-1.90 m
 Typical weight of an adult:              50-90 kg

   [The "body mass index (BMI)" is the weight in kilograms divided by
   the height in metres squared. BMI values of 18-25 kg/m² are
   considered normal, values outside this range can mean an increased
   disease risk.]

 Keeping in mind that the size of most adults varies by about 20%,
 the following are easy to remember estimates for typical values:

 Width of an adult hand or foot:               10 cm

 Width of the nail of the little finger:        1 cm

 Maximum distance between elbows:               1 m

 Height of the hip above ground:                1 m

 Length of a moderately large step:             1 m

 Foot length:                                  25 cm

 Daily energy needed:                          10 MJ  (men)
                                                8 MJ  (women)

 Energy of a healthy meal:                      2 MJ

 Daily water needed:                            2 L

 Blood volume:                                  5 L

 Lung capacity:                                 5 L

B) General Physics

 Speed of sound (in air):                     340 m/s

 Speed of light (in air or vacuum):       300 000 km/s

 Acceleration of free fall (Earth):            10 m/s²

 Atmospheric pressure (Earth):                100 kPa

 Density of water:                           1000 kg/m³ = 1 kg/L

C) Geology and Astronomy

 Distance pole to equator (Earth):         10 000 km = 10 Mm

 Length of the Earth equator:              40 000 km = 40 Mm

 Altitude of geostationary Earth orbit:    36 000 km = 36 Mm

 Distance Earth-Sun:                          150 Gm

 Diameter of solar system:                     12 Tm

 Diameter of our galaxy:                        1 Zm

 Distance to most distant visible objects:  100 Ym

D) Traffic

 Walking speed                                  5 km/h

 Cycling speed                                 20 km/h

 Speed limit in traffic-calmed areas:          30 km/h

 Speed limits on urban roads:               50-60 km/h

 Speed limits on rural roads:               60-80 km/h

 Speed limits on highways:                 90-130 km/h

 Long-distance average car speed:             100 km/h

 Cruise speed of passenger planes:        600-800 km/h

 Cruise altitude of passenger planes:          10 km

 Official altitude boundary between Earth's
 atmosphere and space ("Karman line"):        100 km

E) Temperatures

 Lowest possible temperature:             -273.15 °C = 0 K

 Typical freezer temperature:                 -18 °C

 Freezing water/melting ice:                    0 °C

 Drink with many ice cubes:                     0 °C

 Temperature of highest density of water:       4 °C

 Typical refrigerator temperature:            4-8 °C

 Comfortable office room temperature:       20-25 °C
 (same for swimming-pool water)

 Hot day (for Britain):                     25-35 °C
 (same for baby bath water)

 Body temperature:                             37 °C

 Fever temperatures:                        38-40 °C

 Deadly fever:                              41-42 °C

 Proteins denaturate starting from:         45-50 °C
 (in cooking: egg becomes solid)

 Food poisoning bacteria might grow:         5-55 °C

 Food poisoning bacteria die:                  60 °C

 Flour absorbs most water starting at:         70 °C
 (minimum temperature dough/batter needs
 to reach in any kind of baking)

 Alcohol boils:                                78 °C

 Best temperature for green tea (Japan):       80 °C

 Water boils (at sea level):                  100 °C

 Typical baking-oven air temperature:     150-220 °C

 Washing machine settings:     30, 40, 50, 60, 95 °C

F) Angles

 While degrees remain popular and useful for large angles (30°, 45°,
 60°, 90°, etc.), the radian is extremely convenient and intuitive
 for small angles, for example those covered by a pixel of a digital
 camera.

 1 mm seen from 1 m distance:                   1 mrad
 1 mm seen from 1 km distance:                  1 µrad
 1 m at the "end of the universe" (100 Ym):  0.01 yrad

 The steradian is used mostly in the context of describing the
 intensity of radiation.

 1 mm² seen from 1 m distance:                  1 µsr
 1 mm² seen from 1 km distance:                 1 psr


1.6  Where are good web sites related to the metric system?
-----------------------------------------------------------

The Bureau International des Poids et Mesures (BIPM) is the
international organization in charge of maintaining the International
System of Units:

 http://www.bipm.org/

The BIPM's "SI Brochure" is the official 72-page in-depth description
of the International System of Units:

 http://www.bipm.org/en/publications/brochure/

The Physics Laboratory of the US National Institute of Science and
Technology (NIST) maintains an excellent web site on SI units:

 http://physics.nist.gov/cuu/Units/

In particular, NIST has published three highly recommendable guides to
the SI:

 - The first focuses on the practical use of the SI in the United
   States, and features a very comprehensive conversion table for all
   units used in the United States, as well as detailed guidelines
   for the correct (US) spelling, abbreviation and typesetting of SI
   unit names:

     Guide for the Use of the International System of Units (SI)
     NIST Special Publication 811, 1995 Edition, by Barry N. Taylor.
     http://physics.nist.gov/Pubs/SP811/

 - The second is simply the official United States version of the
   English SI brochure, which provides more information on the
   history of the SI:

     The International System of Units (SI)
     NIST Special Publication 330, 2001 Edition, Barry N. Taylor, Editor.
     http://physics.nist.gov/Pubs/SP330/

 - Finally, for those looking for the legal definition of the SI in
   US legislation, there is:

     Interpretation of the International System of Units for
     the United States, Federal Register notice of July 28, 1998,
     63 FR 40334-40340
     http://physics.nist.gov/Document/SIFedReg.pdf

The Laws & Metric Group of NIST's Weights and Measures Division also
maintains a comprehensive site on the metric system, with a particular
focus on its legal role and history in the United States:

 http://www.nist.gov/metric

The National Physical Laboratory (NPL) in Britain has some SI
information:

 http://www.npl.co.uk/reference/

The unit-of-measurement laws of all European Union member states are
based on

 http://europa.eu.int/eur-lex/en/consleg/pdf/1980/en_1980L0181_do_001.pdf

The U.S. Metric Association (USMA) is a non-profit organization
founded in 1916 that advocates US conversion to the International
System of Units:

 http://lamar.colostate.edu/~hillger/

Its British counterpart, the UK metric association (UKMA), was founded
in 1999:

 http://www.metric.org.uk/

Two excellent online dictionaries of units are:

 http://www.unc.edu/~rowlett/units/
 http://www.sizes.com/units/

Wikipedia contains a number of related articles, for example:

 http://en.wikipedia.org/wiki/Metrication
 http://en.wikipedia.org/wiki/Metric_system
 http://en.wikipedia.org/wiki/SI
 http://en.wikipedia.org/wiki/SI_prefixes
 http://en.wikipedia.org/wiki/SI_derived_units
 http://en.wikipedia.org/wiki/ISO_31

Other interesting web sites related to the metric system:

 http://www.metrication.com/
 http://www.metricationmatters.com/  (with monthly newsletter)
 http://www.metre.info/


1.7  Are there any good books or newsletters on the metric system?
------------------------------------------------------------------

A fascinating book on the history of the metre and the considerations
that led to its creation is:

 Ken Alder: The Measure of All Things. Free Press, October 2003,
 ISBN 0743216768.

 In June 1792, amidst the chaos of the French Revolution, two intrepid
 astronomers set out in opposite directions on an extraordinary
 journey. Starting in Paris, Jean-Baptiste-Joseph Delambre would make
 his way north to Dunkirk, while Pierre-François-André Méchain voyaged
 south to Barcelona. Their mission was to measure the world, and their
 findings would help define the metre as one ten-millionth of the
 distance between the pole and the equator -- a standard that would be
 used "for all people, for all time."

A very useful reference not only on the correct use of SI units, but
on international standard conventions for mathematical and scientific
notation in general is:

 ISO Standards Handbook: Quantities and units. 3rd ed., International
 Organization for Standardization, Geneva, 1993, 345 p.,
 ISBN 92-67-10185-4, 188.00 CHF
 http://www.iso.org/iso/en/prods-services/popstds/quantitiesandunits.html

 This unfortunately rather expensive book contains the full text
 of the following ISO standards:

   ISO 31:1992    Quantities and units

                  Part 0:  General principles
                  Part 1:  Space and time
                  Part 2:  Periodic and related phenomena
                  Part 3:  Mechanics
                  Part 4:  Heat
                  Part 5:  Electricity and magnetism
                  Part 6:  Light and related electromagnetic radiations
                  Part 7:  Acoustics
                  Part 8:  Physical chemistry and molecular physics
                  Part 9:  Atomic and nuclear physics
                  Part 10: Nuclear reactions and ionizing radiations
                  Part 11: Mathematical signs and symbols for use in
                           the physical sciences and technology
                  Part 12: Characteristic numbers
                  Part 13: Solid state physics

  ISO 1000:1992   SI units and recommendations for the use of their
                  multiples and of certain other units

 ISO 31 standardizes a significant part of the mathematical notation
 used in physical sciences and technology worldwide. Its various
 parts contains a pretty comprehensive table of physical quantities
 (e.g., speed, mass, frequency, resistance), and defines for each the
 standard variable name (e.g., v, m, f, R) that is normally used in
 textbooks, together with the appropriate SI unit and a brief
 explanation of the meaning of the quantity. ISO 31-0 contains
 detailed guidelines on how to use and write SI units in mathematical
 formulas and ISO 31-11 defines all the commonly used mathematical
 symbols and operators.

 ISO 1000 is a brief summary of the SI (shorter than ISO 31-0), plus
 an appendix that lists for some selected quantities and units the
 more commonly used prefixes.

 Especially authors and editors of scientific textbooks, teaching
 material and reference works that use SI units should make sure that
 they have easy access to a copy of ISO 31 or an equivalent national
 standard (e.g., BS 5775 in Britain).

The unfortunately not less expensive German equivalent is:

 DIN-Taschenbuch 22: Einheiten und Begriffe für physikalische
 Größen. Deutsches Institut für Normung, 1999-03,
 ISBN 3-410-14463-3, 98.90 EUR

A list of books on metrication is on:

 http://www.metrication.com/products/books.htm

If you join the U.S. Metric Association, you will receive six times a
year the "Metric Today" newsletter, with detailed updates on the
progress of metrication in the US. Membership costs 30 USD anually (35
USD abroad).

 http://lamar.colostate.edu/~hillger/mtoday.htm
 http://lamar.colostate.edu/~hillger/member.htm

A very comprehensive book on current and historic units from all over
the world is

 François Cardarelli: Encyclopaedia of scientific units,
 weights and measures: their SI equivalences and origins.
 Springer, 2003, 872 pages, ISBN 1-85233-682-X.


1.8  What are the SI base units and how are they currently defined?
-------------------------------------------------------------------

length:  metre (m)

 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.

 [Originally, the metre was chosen to approximate the distance
 between the north pole and the equator divided by ten million, such
 that a unit that is roughly the size of a step can also help to
 visualize large distances on the surface of the earth easily.]

mass: kilogram (kg)

 The kilogram is the unit of mass; it is equal to the mass of the
 international prototype of the kilogram.

 [No independent lab experiment is known yet that provides a more
 stable reference for mass than the regular comparison with a lump of
 platinum-iridium alloy kept in a safe at the BIPM in Paris.]

 [Originally, the kilogram was chosen to approximate the mass of one
 litre (1/1000 m³) of water. This choice, combined with the second,
 also led to very convenient numbers for the Earth's gravity (about
 10 m/s²) and atmospheric pressure (about 100 kPa).]

time:  second (s)

 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 caesium 133 atom.

 [In other words: if you want to know how long a second is, buy an
 atomic clock that uses caesium, such as the classic Agilent/HP 5071A.]

 [Originally, the SI second was chosen to approximate the length of
 the astronomical second (1 day divided by 60 × 60 × 24) around 1820.]

electric current: ampere (A)

 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 m apart in vacuum, would
 produce between these conductors a force equal to 2 × 10^-7 newton
 per metre of length.

 [In other words, the ampere is defined by setting the magnetic
 permeability of free space to 4π × 10^-7 H/m. This way,
 electromagnetic equations concerning spheres contain 4π, those
 concerning coils contain 2π and those dealing with straight wires
 lack π entirely.]

thermodynamic temperature: kelvin (K)

 The kelvin, unit of thermodynamic temperature, is the fraction
 1/273.16 of the thermodynamic temperature of the triple point of
 water.

 [The celsius temperature scale divides the temperature interval of
 liquid water into 100 steps. The kelvin has the same size as the
 degree celsius, but its origin is moved to the lowest possible
 temperature (0 K = -273.15 °C) to simplify gas calculations and
 avoid negative numbers. The triple point of water at 0.01 °C is a
 more well-defined reference temperature than its melting temperature
 at some arbitrarily chosen pressure.]

amount of substance: mole (mol)

 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 particles.

 [No technique is known yet to accurately count the number of
 molecules in a macroscopic amount of matter, therefore the current
 definition of the mole is no better than the definition of the
 kilogram.]

luminous intensity: candela (cd)

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

 [This is a psychophysical unit for describing how bright an average
 human eye perceives some electromagnetic radiation in the optical
 frequency bands. As such, it differs very much from the purely
 physical nature of the other units. The definition of the SI base
 unit for luminous intensity provides merely a calibration value that
 replaces an older one based on a reference candle. It has to be used
 together with sensitivity models of an average human eye that have
 been standardized by CIE. Many other physiological units are in use,
 such as the "phon" for perceived loudness and the "bark" for
 perceived audio frequency in acoustics, but none of these have made
 it into the SI, possibly because it is much more difficult to reach
 a consensus in audiology.]

See also:

 http://www1.bipm.org/en/si/base_units/


1.9  What are the SI derived units with a special name?
-------------------------------------------------------

 Derived quantity        unit name    symbol    in terms of base or
                                                other derived units

 plane angle             radian        rad      1 rad = 1 m/m = 1
 solid angle             steradian     sr       1 sr = 1 m²/m² = 1
 frequency               hertz         Hz       1 Hz = 1 1/s
 force                   newton        N        1 N = 1 kg·m/s²
 pressure, stress        pascal        Pa       1 Pa = 1 N/m²
 energy, work, heat      joule         J        1 J = 1 N·m
 power                   watt          W        1 W = 1 J/s
 electric charge         coulomb       C        1 C = 1 A·s
 electric potential      volt          V        1 V = 1 W/A
 capacitance             farad         F        1 F = 1 C/V
 electric resistance     ohm           Ω        1 Ω = 1 V/A
 electric conductance    siemens       S        1 S = 1 1/Ω
 magnetic flux           weber         Wb       1 Wb = 1 V·s
 magnetic fluc density   tesla         T        1 T = 1 Wb/m²
 inductance              henry         H        1 H = 1 Wb/A
 Celsius temperature     deg. Celsius  °C       1 °C = 1 K
 luminous flux           lumen         lm       1 lm = 1 cd·sr
 illuminance             lux           lx       1 lx = 1 lm/m²
 catalytic activity      katal         kat      1 kat = 1 mol/s

Note: We have 0 °C = 273.15 K and temperature differences of 1 °C and
1 K are identical. Kelvin and degrees Celsius values can be converted
into each other by adding or subtracting the number 273.15. The origin
of the degrees Celsius scale is set 0.01 K below the triple-point
temperature of water (273.16 K) and approximates the freezing
temperature of water at standard pressure.

Three more SI derived units have been defined for use in radiology and
radioactive safety:

 radioactivity           becquerel     Bq       1 Bq = 1 1/s
 absorbed dose           gray          Gy       1 Gy = 1 J/kg
 dose equivalent         sievert       Sv       1 Sv = 1 J/kg

Note: Different types of radiation (α, β, γ, X-rays, neutrons, etc.)
vary in the amount of damage they cause in biological tissue, even
when the same energy is absorbed. While the physical unit gray is used
to describe just the energy absorbed, the medical unit sievert is used
where the absorbed energy has been multiplied with a quality factor to
quantify the health risk better. This quality factor is 1 for X-rays,
γ-rays, electrons, and muons. It goes up to 20 for heavier
particles. [Details in ICRU Report 51 from http://www.icru.org/.]

Note: only those unit symbols start with an uppercase letter where the
name of the corresponding unit was derived from the name of a person.

The following eight units are not SI units, but are accepted to be
commonly used with or instead of SI units:

 time                    minute        min      1 min = 60 s
                         hour          h        1 h = 60 min
                         day           d        1 d = 24 h
 plane angle             degree        °        1° = (π/180) rad
                         minute        '        1' = (1/60)°
                         second        "        1" = (1/60)'
 volume                  litre         l, L     1 l = 1 dm³
 mass                    tonne         t        1 t = 1000 kg

Note: The litre would normally be abbreviated with a lowercase l, as
it is not named after a person. However, the US interpretation of the
SI prefers the capital letter L instead, to avoid confusion between l
and 1.

Note: The tonne (1000 kg) is also called "metric ton" in English, or
often simply just "ton". The short form "ton" remains ambiguous
though, because there are also a "short ton" of 907.18474 kg and a
"long ton" of 1016.046909 kg still in use in the US.

The following two units acceptable for use with or instead of SI
units have values that are obtained experimentally:

 energy                  electron volt eV       1 eV = energy acquired by
                                                       an electron passing
                                                       through 1 V potential
                                                       difference
 mass                    atomic unit   u        1 u  = 1/12 of the mass of
                                                       one carbon-12 atom


1.10  Who were the SI units named after?
----------------------------------------

The SI units whose symbols start with a capital letter are named after
the following scientists:

 André Marie Ampère                      France   1775-1836
 Lord Kelvin (Sir William Thomson)       Britain  1824-1907
 Sir Isaac Newton                        Britain  1643-1727
 Heinrich Hertz                          Germany  1857-1894
 Blaise Pascal                           France   1623-1662
 James Prescott Joule                    Britain  1818-1889
 James Watt                              Britain  1736-1819
 Charles Augustin de Coulomb             France   1736-1806
 Alessandro Volta                        Italy    1745-1827
 Michael Faraday                         Britain  1791-1867
 Georg Simon Ohm                         Germany  1787-1854
 Werner von Siemens                      Germany  1816-1892
 Wilhelm Eduard Weber                    Germany  1804-1891
 Nikola Tesla                            USA      1856-1943
 Joseph Henry                            USA      1797-1878
 Anders Celsius                          Sweden   1701-1744
 Antoine Henri Becquerel                 France   1852-1908
 Louis Harold Gray                       Britain  1905-1965
 Rolf Maximilian Sievert                 Sweden   1896-1966

There has been at least one attempt to add a fictious character to
this list:

In many English-speaking countries, the digit 1 lacks an upstroke in
handwriting and is therefore difficult to distinguish from the letter
l. In the 1970s, the CGPM received suggestions to change the symbol of
the litre from the lowercase l to the uppercase L, to avoid such
confusion.  This would, of course, violate the rule that only symbols
for units named after a person are capitalized in the SI, whereas the
word litre derives from the Greek and Latin root litra. It took not
long, before someone invented a hoax scientist, to help justify the
capital L. The April 1978 issue of "CHEM 13 NEWS", a newsletter for
Canadian high-school teachers, carried an article by Prof. Ken
A. Woolner (University of Waterloo), that elaborated on the made-up
biography of Claude Émile Jean-Baptiste Litre (1716-1778), an alleged
French pioneer in chemical glassware and volumetric measurement, son
of a family with a long tradition in wine-bottle manufacturing.
Details of this story have been compiled in

 http://www.student.math.uwaterloo.ca/~stat231/stat231_01_02/w02/section3/fi1.2.pdf


1.11  What are the SI prefixes?
-------------------------------

 10       deca    da    |   0.1      deci    d
 100      hecto   h     |   0.01     centi   c
 1000     kilo    k     |   0.001    milli   m
 10^6     mega    M     |   10^-6    micro   µ
 10^9     giga    G     |   10^-9    nano    n
 10^12    tera    T     |   10^-12   pico    p
 10^15    peta    P     |   10^-15   femto   f
 10^18    exa     E     |   10^-18   atto    a
 10^21    zetta   Z     |   10^-21   zepto   z
 10^24    yotta   Y     |   10^-24   yocto   y

Some rules about writing and using SI prefixes are worth remembering:

 - The symbols for the prefix kilo and everything below start with a
   lowercase letter, whereas mega and higher use an uppercase
   letter.

   [The reason why the boundary between lowercase and uppercase has
   been moved between kilo and mega is the fact that that kilo also
   appears in the unit kilogram, whose symbol must start with a
   lowercase letter to follow the rule that only units named after
   people are abbreviated with an uppercase symbol.]

 - SI prefixes bind to a unit stronger than any mathematical
   operator, that is 1 km² means a kilometre squared (as in 1 (km)²)
   and not one kilosquaremeter (as in 1 k(m²)).

 - SI prefixes are not allowed to be used on anything other than an
   unprefixed unit, in other words there is no such thing as a
   megakilometre or a kilosquaremetre.

Note: Prefixes "myria" for 10^4 and "myrio" for 10^-4 are occasionally
quoted in US dictionaries. These were never part of the SI nor are
they mentioned in any BIPM or ISO document, and therefore should not
be used today. They appear to date back to the earliest proposals for
a metric system in the 1790s in France, but did not make it into the
modern international system of units. The myria prefix survives to
this day in the form of the myriameter (10 km) and myriagram (10 kg)
that are listed in US law (15USC205). There is no official symbol
defined today for either prefix, though "ma" and "mo" have been quoted
as having been used in the past.


1.12  What is the correct way of writing metric units?
------------------------------------------------------

Each unit and prefix in the International System of Units has an
official symbol (abbreviation) assigned to it. This symbol is
identical in all languages. When writing down numeric quantities,
especially in the more formal context of product descriptions,
documentation, signs, scientific publications, etc., it is important
to pay some attention to the accurate writing of the unit symbol.

Here are the most important rules for abbreviating SI units:

 - Use exactly the standard symbols for prefixes and units listed
   in the tables above. Do not invent your own abbreviations.

 - Remember that there is a simple system for deciding which letters
   are uppercase or lowercase:

     - Symbols of units named after a person start uppercase.
       (E.g., newton, volt, weber use N, V, Wb.)
     - Other units start lowercase.
       (E.g., metre, second, lux use m, s, lx.)
     - Symbols of prefixes greater than 10³ (kilo) start uppercase.
     - All other prefix symbols start with a lowercase letter.
     - Further letters in a unit or prefix are always lowercase.

   (Correct examples: kHz, MHz)

 - Unit symbols are never used with a plural s.

 - Units symbols are never used with a period to indicate
   an abbreviation.

 - Division can be indicated by either a stroke (slash) or by a
   negative exponent, but never by a "p" for "per".

 - Square and cube are indicated by exponents 2 and 3, respectively.

 - The unit symbol is separated from the preceding number by a space
   character (with the exception of degrees, minutes and seconds of
   plane angle: 90° 13' 59").

 - There is no space between a prefix and a unit.

 - In mathematical and technical writing, SI unit symbols should be
   typeset in an upright font, in order to distinguish them from
   variables, which are usually set in an italic font.

Examples:

 Good: 60 km/h, 3.2 kHz, 40 kg, 3.6 mm, 80 g/m²

 Bad:  60 kph, 3.2 Khz, 40 kgs, 3.6mm, 80-grms./sq.mtr.

Whether a decimal comma (French, German, etc.) or decimal point
(English) is used depends on the language. Either is valid for use
with SI units. To avoid confusion, neither the comma nor the dot
should be used to group digits together. Better use a space or
thin-space character, if necessary.

 Good: 12 000 m
 Bad:  12,000 m   (might be read as 12 m in France and 12 km in the US)

Hints for word processing users:

 - The degree sign (° as in °C and 360°, Unicode U+00B0) is in some
   fonts easily confused with the Spanish masculine ordinal indicator
   sign (º, a raised little letter "o", as in 1º for "premiero",
   Unicode U+00BA). In other fonts, the Spanish raised o is clearly
   distinguishable because it is underlined. It is therefore
   important, especially where the author has no control over the
   font used by the reader (email, web, etc.), to pick the correct
   character.

     Good: °C
     Bad:  ºC

 - The micro sign (µ) is at Unicode position U+00B5 (decimal: 181)
   and can be entered under Microsoft's Windows by pressing 0181 on
   the numeric keypad while pressing the Alt key.

   Other characters not found on every keyboard can be entered as
   well by entering the decimal Unicode value preceded by zero on the
   numeric keypad, while holding down the Alt key:

      Character       Unicode value   Unicode value  Character
        name           hexadecimal       decimal

      no-break space      U+00A0           160            
      degree sign         U+00B0           176           °
      superscript 2       U+00B2           178           ²
      superscript 3       U+00B3           179           ³
      micro sign          U+00B5           181           µ
      ohm sign            U+2126          8486           Ω

   Some keyboards with AltGr key provide these characters also via
   AltGr-d, AltGr-2, AltGr-3, AltGr-m, or similar combinations.

While the short symbols for SI units are internationally standardized,
at least for all languages that use the Latin alphabet, the spelling
of unit names varies between languages and even countries.  In
English, unabbreviated unit names are not capitalized, even where they
are named after people, and both the French -re and the Germanic -er
ending of metre and litre are commonly used.

Examples:

       French          German        English (GB)    English (US)

       litre           Liter           litre           liter
       metre           Meter           metre           meter

This FAQ uses the British English spellings of metre and litre, as
they are used in ISO and BIPM documents.

Some countries that do not use the Latin alphabet have standardized
their own short symbols for SI units. The Russian standard GOST
8.417:1981, for example, specifies Cyrillic symbols м (m), кг (kg),
с (s), А (A), К (K), моль (mol), кд (cd), etc. (Full list on
<http://www.unics.uni-hannover.de/ntr/russisch/si-einheiten.html>.)

There used to exist an international standard ISO 2955:1983
("Presentation of SI and other units in systems with limited character
sets") that defined a list of unambiguous SI symbols for use with
computers that can only display ASCII, or even only uppercase
letters. This standard was withdrawn 2001. The ISO 8859-1 and ISO
10646 character sets are today widely enough available to make using
the original SI symbols on computers feasible.

There is no international standard for pronouncing the names of
units. In particular, in English both KILL-o-metr and ki-LO-metr are
commonly used. The former seems to be more common in Britain (short
stress on the first syllable) and may have the slight advantage of
being consistent with the English pronunciation of kilogram and
kilohertz.  (It is also the pronunciation of kilometre in other
Germanic languages.)

In spoken language, various colloquial short forms have evolved for SI
units. For example, "kilo", "hecto" and "deca" are used in various
countries for 1 kg, 100 g and 10 g when buying groceries. In the US
military, a "klick" is 1 km or 1 km/h, depending on the context, and
in the semiconductor industry a "micron" is 1 µm. A "kay" can be heard
in some English-speaking countries referring to any of 1 km, 1 km/h, 1
kg, 1 kHz, 1 kB, 1 kbit/s, again depending on the context. A "pound"
refers to 500 g in many European countries, but it is less commonly
used today than a decade or two ago. But none of these colloquial
forms should be used in writing.


2  Metric product specifications
================================


2.1  What are preferred numbers or Renard numbers?
-------------------------------------------------

Product developers need to decide at some point, how large various
characteristic dimensions of their design will be exactly. Even after
taking into account all known restrictions and considerations, the
exact choice of lengths, diameters, volumes, etc. can often still be
picked quite randomly within some interval.

Wouldn't it be nice if there were some recipe or guideline for making
the choice of product dimensions less random? If there were one
generic standard for a small set of preferred numbers, it would be
more likely that a developer working in a different company made the
same choice. Products would more frequently become compatible by
chance. Say you design a gadget that will be fixed on a wall with two
screws. A small set of preferred distances between mounting screws
would make it less likely that new holes have to be drilled if your
customer replaces an older gadget of similar size, whose designer
hopefully chose the same distance.

The French army engineer Col. Charles Renard proposed in the 1870s
such a set of preferred numbers for use with the metric system, which
became in 1952 the international standard ISO 3. Renard's preferred
numbers divide the interval from 1 to 10 into 5, 10, 20, or 40
steps. The factor between two consecutive numbers in a Renard series
is constant (before rounding), namely the 5th, 10th, 20th or 40 root
of 10 (1.58, 1.26, 1.12, and 1.06, respectively), leading to a
geometric series. This way, the maximum relative error is minimized if
an arbitrary number is replaced by the nearest Renard number
multiplied by the appropriate power of 10.

The most basic R5 series consists of these five rounded numbers:

  R5: 1.00        1.60        2.50        4.00        6.30

Example: If our design constraints tell us that the two screws in our
gadget can be spaced anywhere between 32 mm and 55 mm apart, we make
it 40 mm, because 4 is in the R5 series of preferred numbers.

Example: If you want to produce a set of nails with lengths between
roughly 15 and 300 mm, then the application of the ISO 3 R5 series
would lead to a product repertoire of 16 mm, 25 mm, 40 mm, 63 mm, 100
mm, 160 mm and 250 mm long nails.

If a finer resolution is needed, another five numbers are added and we
end up with the R10 series:

 R10: 1.00  1.25  1.60  2.00  2.50  3.15  4.00  5.00  6.30  8.00

If you design several prototypes of a product that may later have to
be offered in several additional sizes, choosing characteristic
dimensions from the Renard numbers will make sure that your prototypes
will later fit nicely into an evenly spaced product repertoire.

Where higher resolution is needed, the R20 and R40 series can be
applied:

 R20: 1.00 1.12 1.25 1.40 1.60 1.80 2.00 2.24 2.50 2.80
      3.15 3.55 4.00 4.50 5.00 5.60 6.30 7.10 8.00 9.00

 R40: 1.00 1.06 1.12 1.18 1.25 1.32 1.40 1.50 1.60 1.70
      1.80 1.90 2.00 2.12 2.24 2.36 2.50 2.65 2.80 3.00
      3.15 3.35 3.55 3.75 4.00 4.25 4.50 4.75 5.00 5.30
      5.60 6.00 6.30 6.70 7.10 7.50 8.00 8.50 9.00 9.50

In some applications more rounded values are desirable, either
because the numbers from the normal series would imply an
unrealistically high accuracy, or because an integer value is needed
(e.g., the number of teeth in a gear). For these, the more rounded
versions of the Renard series have been defined:

 R5': 1           1.5         2.5         4           6

R10': 1     1.25  1.6   2     2.5   3.2   4     5     6.3   8

R10": 1     1.2   1.5   2     2.5   3     4     5     6     8

R20': 1    1.1  1.25 1.4  1.6  1.8  2    2.2  2.5  2.8
      3.2  3.6  4    4.5  5    5.6  6.3  7.1  8    9

R20": 1    1.1  1.2  1.4  1.6  1.8  2    2.2  2.5  2.8
      3    3.5  4    4.5  5    5.5  6    7    8    9

R40': 1    1.05 1.1  1.2  1.25 1.3  1.4  1.5  1.6  1.7
      1.8  1.9  2    2.1  2.2  2.4  2.5  2.6  2.8  3
      3.2  3.4  3.6  3.8  4    4.2  4.5  4.8  5    5.3
      5.6  6    6.3  6.7  7.1  7.5  8    8.5  9    9.5

Other more specialized preferred number schemes are in use in various
fields. For example:

 - IEC 63 standardizes a preferred number series for resistors and
   capacitors, a variant of the Renard series that subdivides the
   interval from 1 to 10 into 6, 12, 24, etc. steps. These
   subdivisions ensure that when some random value is replaced with
   the nearest preferred number, the maximum error will be in the
   order of 20%, 10%, 5%, etc.:

     E6 (20%): 10    15    22    33    47    68

    E12 (10%): 10 12 15 18 22 27 33 39 47 56 68 82

    E24 ( 5%): 10 11 12 13 15 16 18 20 22 24 27 30
               33 36 39 43 47 51 56 62 68 75 82 91

 - Paper sizes commonly use factors of sqrt(2), sqrt(sqrt(2)), or
   sqrt(sqrt(sqrt(2))) as factors between neighbor dimensions
   (Lichtenberg series, see next section). The sqrt(2) factor also
   appears between the standard metric pen thicknesses for technical
   drawings (0.13, 0.18, 0.25, 0.35, 0.50, 0.70, 1.00, 1.40, and 2.00
   mm). This way, the right pen size is available to continue a
   drawing that has been magnified to a different metric paper size.

 - In the building industry, major dimensions (e.g., grid lines on
   plans, distances between wall centers or surfaces) are multiples
   of 100 mm. This size is called the "basic module" and represented
   by the letter M. Preference is given to the multiples of 3 M (=
   300 mm) and 6 M (= 600 mm) of the basic module. For larger
   dimensions, preference is also given to the multimodules 12 M (=
   1.2 m), 15 M (= 1.5 m), 30 M (= 3 m), and 60 M (= 6 m). For
   smaller dimensions, the submodular increments 50 mm or 25 mm are
   used. (For details, see ISO 2848 or BS 6750.)

 - In computer engineering, the powers of two (1, 2, 4, 8, 16, ...)
   multiplied by 1, 3 or 5 are frequently used as preferred numbers.
   These correspond to binary numbers that consist mostly of trailing
   zero bits, which are particularly easy to add and subtract in
   hardware. [Software developers should keep in mind though that
   using powers of 2 in software, especially with array sizes, may
   also have disadvantages, such as reduced CPU cache efficiency.]


2.2  How do metric paper sizes work?
------------------------------------

The international standard paper formats defined in ISO 216 in the A,
B and C series are used today in all countries worldwide except for
the US and Canada.

The formats have been defined as follows:

 - The width divided by the height of all ISO A, B, and C formats
   is the square root of 2 (= 1.41421...)

 - The A0 paper size has an area of one square metre.

 - You get the next higher format number by cutting the paper in two
   equal pieces (cutting parallel to the shorter side). The result will
   again have a 1 : sqrt(2) format (that's the big advantage of this format).

 - The size of a B-series paper is the geometric mean between the size of
   the corresponding A-series paper and the next bigger A-series paper.
   For example, the same magnification factor converts from A1 to B1
   and from B1 to A0.

 - The size of a C-series paper is the geometric mean between the size of
   the A-series and B-series paper with the same number.

This means that the following formulas give the dimensions in metres:

                     Width                   Height
     A-series        2 ^ (- 1/4 - n/2)       2 ^ (1/4 - n/2)
     B-series        2 ^ (      - n/2)       2 ^ (1/2 - n/2)
     C-series        2 ^ (- 1/8 - n/2)       2 ^ (3/8 - n/2)

Larger sizes have smaller numbers.

The official definitions of the ISO paper formats are obtained by
rounding down to the next lower integer millimetre after each
division:

     4 A0 1682 × 2378
     2 A0 1189 × 1682
       A0  841 × 1189       B0 1000 × 1414       C0  917 × 1297
       A1  594 × 841        B1  707 × 1000       C1  648 × 917
       A2  420 × 594        B2  500 × 707        C2  458 × 648
       A3  297 × 420        B3  353 × 500        C3  324 × 458
       A4  210 × 297        B4  250 × 353        C4  229 × 324
       A5  148 × 210        B5  176 × 250        C5  162 × 229
       A6  105 × 148        B6  125 × 176        C6  114 × 162
       A7   74 × 105        B7   88 × 125        C7   81 × 114
       A8   52 × 74         B8   62 × 88         C8   57 × 81
       A9   37 × 52         B9   44 × 62         C9   40 × 57
       A10  26 × 37         B10  31 × 44         C10  28 × 40

The most popular sizes are perhaps:

       A0          technical drawings
       A4          letters, forms, faxes, magazines, documents
       A5, B5      books
       C4, C5, C6  envelopes
       B4, A3      supported by many copy machines, newspapers

There are also strip formats possible for tickets, compliment cards,
etc.:

   1/3 A4   99 × 210
   2/3 A4  198 × 210
   1/4 A4   74 × 210
   1/8 A4   37 × 210
   1/4 A3  105 × 297
   1/3 A5   70 × 148
   etc.

All these formats are end formats, i.e. these are the dimensions of
the paper delivered to the user/reader. Other standards define
slightly bigger paper sizes for applications where the paper will be
cut to the end format later (e.g., after binding).

The A4 format used in almost all countries is 6 mm narrower and 18 mm
taller than the US Letter format used exclusively in the US and
Canada. This difference causes an enormous amount of havoc every day
in document exchange with these countries. The introduction of A4
paper as the general office format in the United States would be a
very significant simplification and an enormous improvement. Only a
top-level US government decision is likely to make this happen.

For much more information, for example on how the Japanese JIS B sizes
differ from the ISO ones, see

 http://www.cl.cam.ac.uk/~mgk25/iso-paper.html


2.3  How do metric threads work?
--------------------------------

The preferred ISO metric thread sizes for general purpose fasteners
(coarse thread) are

 designation     pitch     tapping drill        clearance holes
                                             close   medium   free

   M1.6           0.35         1.25           1.7      1.8     2.0
   M2             0.4          1.6            2.2      2.4     2.6
   M2.5           0.45         2.05           2.7      2.9     3.1
   M3             0.5          2.5            3.2      3.4     3.6
   M4             0.7          3.3            4.3      4.5     4.8
   M5             0.8          4.2            5.3      5.5     5.8
   M6             1.0          5.0            6.4      6.6     7.0
   M8             1.25         6.8            8.4      9.0    10.0
   M10            1.5          8.5           10.5     11.0    12.0
   M12            1.75        10.2           13.0     14.0    15.0
   M16            2.0         14.0           17.0     18.0    19.0
   M20            2.5         17.5           21.0     22.0    24.0
   M24            3.0         21.0           25.0     26.0    28.0
   M30            3.5         26.5           31.0     33.0    35.0
   M36            4.0         32.0           37.0     39.0    42.0
   M42            4.5         37.5           43.0     45.0    48.0
   M48            5.0         43.0           50.0     52.0    56.0

The number naming the thread is the major diameter of the screw thread
in millimetres. The thread angle is 60°. The pitch is the distance, in
millimetres, that the screw will travel forward or backward during one
rotation.

The preferred standard pitch defined for each M-series thread is
called the "coarse pitch". For special applications (e.g., thin wall
tubes), there are also "fine pitch" variants defined. In their
designation, the pitch is added after a cross (×), as in

   M8×1, M10×1, M12×1.5, ...

[This section is work in progress ... contributions welcome.]

http://en.wikipedia.org/wiki/ISO_metric_screw_thread
http://www.metrication.com/engineering/threads.htm
http://www.efunda.com/DesignStandards/screws/screwm_coarse.cfm


2.4  How do metric clothes sizes work?
--------------------------------------

Even in Europe, most clothes are currently still labelled using some
ad-hoc dress size number that has no obvious or even well-defined
relation with actual body dimensions. Ad-hoc dress sizes vary
significantly between countries, many are inadequate because they are
based on obsolete 1950s data of typical body dimensions, and some
manufacturers have started to inflate women's dress sizes to
compensate for the average weight gain of middle aged adults. As a
result, dress sizes have lost much of their usefulness. The situation
is particularly problematic for mail and online ordering.

Therefore, the European standards committee CEN TC 248 WG 10 has set
out to develop a new system of metric cloth sizes. The system is still
being developed, but the first three parts of the resulting European
Standard EN 13402 have already been published.

The core idea is this:

Under the EN 13402 system, clothes will be labelled based on the body
dimensions, in centimetres, of the wearer for whom they are
suitable. This differs from the existing practice, in some countries,
of labeling clothes based on dimensions measured on the article. For
example, there is a significant difference between the length of a
foot, and the inside length of the shoe that best fits that foot. In
fact, the most suitable inside length of a shoe for a given foot can
vary significantly for different types of shoes. If shoes are labeled
based on the length of the feet for which they were designed, I will
only ever have to remember that my feet are 28 cm.

The standard consists of several parts:

EN 13402-1 defines the list of body dimensions that can be used in
clothes labels, together with an anatomical explanation and
measurement guidelines. This list includes head, neck, chest, bust,
underbust, waist, hip and girth, as well as the inside leg, arm, and
foot length along with height and body bass. It also defines a
standard pictogram that can be used on language-neutral labels to
indicate one or several of these body dimensions. [See
http://www.cl.cam.ac.uk/~mgk25/download/bodydim.pdf for some software
to draw such pictograms.]

EN 13402-2 defines for each type of garment a "primary dimension"
according to which it should be labelled (e.g., head girth for a
bicycle helmet or chest girth for a pyjama). For some types of
garnment, a single size is not adequate to select the right product,
so a "secondary dimension" is added (e.g., inside leg length in
addition to waist girth for trousers).

EN 13402-3 defines, for each type of garnment, preferred numbers of
primary and secondary body dimensions. Manufacturers and national
standards bodied can then chose a subset of these. Several large
anthropometric studies have recently been performed to find the best
set of dimension ranges and step sizes for this part of the standard.

EN 13402-4 is still under review and describes a compact alphanumeric
coding system for clothes sizes. It is mostly intended for industry to
use in databases and as a part of stock-keeping identifiers and
catalogue ordering numbers. It is expected to be available in late
2007.

For a more detailed summery of EN 13402, go to

 http://en.wikipedia.org/wiki/EN_13402

Two related press releases by the British Standards Institute:

 http://www.bsi-global.com/News/Releases/2002/March/n3f02c7044524a.xalter
 http://www.bsi-global.com/News/Releases/2003/October/n3f9953e58c3df.xalter

Professional dress and personal protection equipment has for many
years been labelled with metric body dimensions, based on ISO
standards very similar to EN 13402-1. It can be hoped that the
completion of the remaining parts of EN 13402 will boost the use of
metric clothes sizes also on the high street. However, like with any
other successful standard, it will take three to five years from the
completion of the standard until the new system is widely used in the
market.

[The British retailer Marks & Spencer has dual-labeled clothes for
some time in both inches and centimeters. However, the centimetre
figures used are in some cases simply converted equivalents of the
traditional inch-based designations. They are not always equivalent to
the corresponding EN 13402 body dimensions.]


2.5  What inch-based standards are widely used in metric countries?
-------------------------------------------------------------------

2.5.1  Pipe threads:

The ISO 7 and ISO 228 pipe threads used all over the world in domestic
water and heating systems are based on the British Standard pipe (BSP)
threads. They use a Whitworth (55°) thread with an integral number of
threads per inch (i.e., the thread pitch divides 25.4 mm evenly). The
standard specifies today the exact thread parameters in millimetres,
but the threads are still named after the number of inches of the
nominal bore (inner) diameter of the pipe, which defines its flow
capacity. In the current standards, this thread size is just one of 15
dimensionless numbers, in the range 1/16 to 6. It is no longer treated
as an inch measure, because no such inch measure appears anywhere on
the thread profile.

The standards for steel pipes that are suitable for use with ISO 7
threads (ISO 65, etc.) no longer quote any inch dimensions. The
British Standard Pipes are defined today by their outer diameter (OD)
and wall thickness in millimeters. They can also be referred to by
their "DN designation", which is essentially a crudely downwards
rounded millimetre figure that approximates the inner diameter
(historically a round inch figure). Like the thread size, the DN
designation should only be used as a dimensionless type number and not
as a millimeter measure, because the actual inner diameter of the
standard pipes is slightly larger. The preferred way to refer to a
standard steel pipe today is to specify the actual outer diameter of
the pipe in millimeters.

 Thread size  DN designation  Outer diameter  Wall thickness
   number        of pipe       of pipe [mm]    of pipe [mm]

    1/16
     1/8            6             10.2            2.0
     1/4            8             13.5            2.3
     3/8           10             17.2            2.3
     1/2           15             21.3            2.6
     3/4           20             26.9            2.6
       1           25             33.7            3.2
   1 1/4           32             42.4            3.2
   1 1/2           40             48.3            3.2
       2           50             60.3            3.6
   2 1/2           65             76.1            3.6
       3           80             88.9            4.0
       4          100            114.3            4.5
       5          125            139.7            5.0
       6          150            165.1            5.0


2.5.2  Metric bicycle tire and rim designations:

Many of the bicycle tires and rims used all over the world are based
on older British inch-based standards. However, their dimensions are
defined and labelled today in millimetres according to the
international standard format defined in ISO 5775.

For example, a normal "wired edge" tire (for straight-side and
crotchet-type rims) with a "nominal section width" of 32 mm, a
"nominal rim diameter" of 597 mm, and a "recommended inflation
pressure" of 400 kPa is marked according to ISO 5775-1 as:

   32-597 inflate to 400 kPa

The first number (nominal section width) is essentially the width of
the inflated tire (minus any tread) in millimetres. The inner width of
the rim on which the tire is mounted should be about 65% of the tire's
nominal section width for tires smaller than 30 mm and 55% for those
larger. The second number (nominal rim diameter) is essentially the
inner diameter of the tire in millimetres when it is mounted on the
rim. The corresponding circumference can be measured with a suitably
narrow tape inside the rim.

The minimum inflation pressure recommended for a "wired edge" tire is
300 kPa for narrow tires (25 mm section width or less), 200 kPa for
other sizes in normal highway service, and 150 kPa for off-the-road
service.

More information:

 http://www.cl.cam.ac.uk/~mgk25/iso-5775.html
 http://en.wikipedia.org/wiki/ISO_5775

2.5.3  Shotgun gauge sizes

Shotgun barrel diameters are in many countries still named using a
historic "gauge" scale.  An n-gauge diameter means that n balls of
lead (density 11.352 g/cm³) with that diameter weigh one pound
(453.5924 g). Therefore an n-gauge shotgun has a barrel diameter

 d = [6 × 453.59237 g / (11.352 g/cm³ × n × π)] ^ 1/3
   = 42.416 mm / (n ^ 1/3)


2.6  What metric standards are commonly known under an inch name?
-----------------------------------------------------------------

 - The so-called "3.5 inch floppy disk" (ISO 9529) is in fact a fully
   metric design, originally developed by Sony in Japan. It was first
   introduced on the market as the "90 mm floppy disk", and it is
   exactly 90 mm wide, 94 mm long, and 3.3 mm thick. The disk inside
   has a diameter of 85.8 mm. Not a single dimension of this disk
   design is 3.5 in (88.9 mm).

   [The older 5 1/4 and 8 inch floppies, on the other hand, are
   inch-based designs by IBM.]

 - The standard silicon wafers known in the US as 6, 8, or 12 inch
   wafers are actually 150 mm, 200 mm and 300 mm in diameter (SEMI
   M1-1103).

 - People unfamiliar with the ISO 3 preferred number system sometimes
   suspect wrongly that a -- to them -- unusual looking measured
   millimetre dimension is actually an inch dimension, whereas the
   designer chose in fact a metric length from a Renard series:

     Renard dimension       popular inch dimension

          25 mm (R5)          1 inch = 25.4 mm
          12 mm (R5)        1/2 inch = 12.7 mm
         6.3 mm (R5)        1/4 inch = 6.35 mm
        3.15 mm (R10)       1/8 inch = 3.175 mm


3  Misc
=======


3.1  Why is there a newsgroup on the metric system?
---------------------------------------------------

The USENET newsgroup was created in December 2003 after a ballot for
its creation had passed on 25 November 2003 with 211 yes votes against
25 no votes. The charter of this worldwide unmoderated electronic
discussion forum sums up its scope:

 This newsgroup is for discussion about the International System of
 Units (SI) or metric system, including its use in scientific,
 technical, and consumer applications, its history and definition, and
 its adoption in fields and regions where other units of measurement
 are still prevalent (metrication). Included within its scope are
 related global standards and conventions, for example metric product
 specifications and consumer-product labelling practice.

The proposal to create the group noted:

Units of measurement and related standards affect many aspects of our
daily lives. The global standardization of a single consistent
International System of Units was a major breakthrough for human
civilization and significantly simplified communication, learning,
work and trade all over the planet.

The introduction of the metric system still faces delays in some
areas. Notable examples are consumer communication and traffic
regulations in the United States and United Kingdom, as well as parts
of the aeronautical and typographic industry. It is therefore no
surprise that discussions about the metric system flare up regularly
in many different newsgroups. In particular the slow progress with
metrication in the United States promises to fuel such debates for
many years to come.

A dedicated newsgroup will focus expertise and will provide a medium
for professionals and hobbyists to find advice and suggestions on
metric product standards and conventions.


3.2  Where can I look up unit conversion factors?
-------------------------------------------------

The popular Web search service http://www.google.com/ has a powerful
built-in calculator function and knows a comprehensive set of unit
conversions.

Usage examples:

 4 inches
   => 10.16 centimetres

 c in furlongs per fortnight
   => the speed of light = 1.8026175 × 10^12 furlongs per fortnight

Another unit converter website:

 http://www.convertit.com/Go/ConvertIt/Measurement/Converter.ASP

There is various unit-conversion software available, such as:

 http://www.gnu.org/software/units/

A very comprehensive list of conversion factors for units used in the
United States can be found in

 Guide for the Use of the International System of Units (SI)
 NIST Special Publication 811, 1995 Edition, by Barry N. Taylor.
 Appendix B: Conversion Factors
 http://physics.nist.gov/Pubs/SP811/


3.3  What is the exact international definition of some non-SI units?
---------------------------------------------------------------------

 unit name             symbol           exact definition

 inch                    in             1 in = 25.4 mm
 foot                    ft             1 ft = 12 in = 0.3048 m
 yard                    yd             1 yd = 3 ft = 0.9144 m
 mile                                   1 mile = 5280 ft = 1609.344 m
 nautical mile                          1 nautical mile = 1852 m
 knot                                   1 knot = 1.852 km/h

 are                     a              1 a = 100 m² = 10 m x 10 m
 hectare                 ha             1 ha = 10000 m² = 100 m x 100 m

 pint (GB)               pt (GB)        1 pt (GB) = 0.56826125 L
 gallon (US)             gal (US)       1 gal (US) = 231 in³ = 3.785411784 L

 pound                   lb             1 lb = 0.45359237 kg
 kilogram force          kgf            1 kgf = 9.80665 N
 kilopond                kp             1 kp = 1 kgf

 bar                     bar            1 bar = 100 kPa
 standard atmosphere     atm            1 atm = 101.325 kPa
 torr                    Torr           1 Torr = 1/760 atm
 technical atmosphere    at             1 at = 1 kgf/cm² = 98.0665 kPa
 millimetre of water     mmH₂O          1 mmH₂O = 10^-4 at = 9.80665 Pa

 rad                     rad            1 rad = 0.01 Gy
 rem                     rem            1 rem = 0.01 Sv
 curie                   Ci             1 Ci = 3.7 × 10^10 Bq
 röntgen                 R              1 R = 2.58 × 10^-4 C/kg

Use of all these non-SI units is deprecated, except for use in fields
where they are still required by law or contract.

[All values and definitions taken from ISO 31:1992 and ISO 1000:1992.]


3.4  What are calories?
-----------------------

One calorie (cal) is the amount of heat required to warm 1 g of
air-free water from 14.5 °C to 15.5 °C at a constant pressure of 1
atm. It is defined as 1 cal = 4.1855 J, but this value has an
uncertainty of 0.5 mJ. There is also an "International Table calorie"
with 1 cal = 4.1868 J, as well as a "thermochemical calorie" with 1
cal = 4.184 J.

In the United States, the kilocalorie (kcal) is often abbreviated as
"Cal".

The kilocalorie is still widely used all over the world to measure the
nutritional energy of food products (usually per 100 g). Perhaps it is
the fact that the term "calories" has become a common synonym for
"nutritional energy" that makes it somewhat difficult for the SI unit
for energy, the joule, to become popular in this area.

("Low-calorie food" may be easier to sell than "low-energy food".)


3.5  What are FFUs and WOMBAT units?
------------------------------------

The collection of units used in the United States lacks a defining
formal name. The term "imperial units" does not quite fit, because
although many of the US units are derived from those of the British
Empire, they are not all identical. Most notably, 1 US pint = 473.1765
mL, whereas 1 Imperial pint = 568.2615 mL. The term "US customary
units" seems to be preferred in government documents.

Two alternative and somewhat less diplomatic names for these units
emerged on the US Metric Association mailing list:

 - Flintstone Units or Fred Flintstone Units (FFUs)

 - Way Of Measuring Badly in America Today (WOMBAT)
   (also: Waste Of Money, Brains And Time)


3.6  Does kilo mean 1024 in computing?
--------------------------------------

Powers of two occur naturally as design dimensions in computer
hardware, in particular for the size of address spaces. It has
therefore become customary in some areas (most notably memory chips)
to use the SI prefixes kilo, mega and giga as if they stood for the
factors 2^10, 2^20 and 2^30 instead of 10^3, 10^6, and 10^9,
respectively. For example, a RAM chip with 65536 bits capacity is
commonly referred to as a "64-kbit-chip".

While such use may be acceptable when it occurs in the names of
product classes (e.g., a "megabit chip" is the smallest chip model
that can contain one million bits), it must not be extended into
formal language, such as parameter tables in product datasheets or
messages generated by software.

The BIPM has clarified that the SI prefixes must unambiguously stand
for the exact powers of ten.

Even in the field of computer design, the prefixes kilo, mega and giga
are very commonly used to refer to powers of ten. For example a 64
kbit communication line transmits exactly 64 000 bits per second and a
200 MHz processor operates with exactly 200 000 000 clock cycles per
second. Bizarre mixtures between binary and decimal interpretations of
the SI prefixes have been spotted in the wild as well. For example,
the 90 mm floppy disk that is sometimes labelled with a capacity of
"1.44 megabytes" has a formatted capacity of 512 × 80 × 18 × 2 = 1.44
× 1000 × 1024 bytes.

In order to help eliminate such abuse of SI prefixes, the
International Electrotechnical Commission in 1999 amended the standard
IEC 27-2 (Letter symbols to be used in electrical technology, Part 2:
Telecommunications and electronics). It now defines new unit prefixes
for powers of two:

 1024   = 2^10 = 1 024                         kibi    Ki
 1024^2 = 2^20 = 1 048 576                     mebi    Mi
 1024^3 = 2^30 = 1 073 741 824                 gibi    Gi
 1024^4 = 2^40 = 1 099 511 627 776             tebi    Ti
 1024^5 = 2^50 = 1 125 899 906 842 624         pebi    Pi
 1024^6 = 2^60 = 1 152 921 504 606 846 976     exbi    Ei

This way, the 90 mm floppy disk has now unambiguously a capacity of
1400 kibibytes (KiB). The standard crystal-oscillator frequency in
wrist watches is 32768 Hz = 32 KiHz.

Note that the symbol for kibi (Ki) starts with an uppercase letter, in
contrast to the symbol for kilo (k).

These new binary prefixes were recently equally defined in IEEE Std
1541-2002 (IEEE trial-use standard for prefixes for binary multiples).

More information:

 http://physics.nist.gov/cuu/Units/binary.html
 http://www.cofc.edu/~frysingj/binprefixes.html


3.7  What are the official short symbols for bit and byte?
----------------------------------------------------------

The SI currently does not cover units for information. The conventions
in this field are still somewhat less well defined than they are for
SI units. There are some other standards, such as IEC 27, that define
various computer, telecommunication and psychophysics units that can
be used with the SI. These include bit (bit), byte (B), neper (Np),
shannon (Sh), bel (B), octave, phon, sone, baud (Bd), erlang (E), and
hartley (Hart).

Note: The abbreviation B for byte is slightly problematic for two
reasons. Firstly, the B is also the symbol for the unit bel (used for
the decimal logarithm of the quotient between two power values), but
as the latter is in practice mostly used with the prefix deci (decibel
= dB), there is little chance of confusion. Secondly, it breaks the
tradition of using an uppercase letter only if the unit was named
after a person.

In French, the unit octet (o) is commonly used instead of byte. In
English, "octet" is commonly used at least in telecommunication
specifications, to unambiguously refer to a group of eight bits.

[IEEE Std 260.1-2004 defines the units and symbols bit (b) and byte
(B). In practice, the lowercase b as a symbol for bit seems less
frequently used since "bit" itself is already an abbreviation (for
"binary digit").]


3.8  What does the "e" symbol found on many packaged goods mean?
----------------------------------------------------------------

Prepackaged supermarket goods bought in Europe show, next to the
weight or volume indication, a symbol that looks like a slightly large
and bold lowercase letter "e". With this symbol, the manufacturer
guarantees that the tolerance of the indicated weight or volume meets
the requirements of European Union legislation, namely:

 Council Directive 75/106/EEC on the approximation of the laws of the
 Member States relating to the making-up by volume of certain
 prepackaged liquids, 1974-12-19, (Official Journal L 324, 1975-12-16).
 http://europa.eu.int/eur-lex/en/consleg/pdf/1975/en_1975L0106_do_001.pdf

 Council Directive 76/211/EEC on the approximation of the laws of the
 Member States relating to the making-up by weight or by volume
 of certain prepackaged products, 1976-01-20, (Official Journal L 046,
 1976-02-21, p. 1)
 http://europa.eu.int/eur-lex/en/consleg/pdf/1976/en_1976L0211_do_001.pdf

These EU regulations define the maximally allowed negative error of
the packaged content in relation to the label, as well as statistical
tests that manufactured packages must be able to pass.

The exact shape of the "e" is defined, along with various other far
less frequently used symbols, in:

 Council Directive 71/316/EEC on the approximation of the laws of the
 Member States relating to common provisions for both measuring
 instruments and methods of metrological control, 1971-07-26,
 (Official Journal L 202, 1971-09-06, p. 1).
 http://europa.eu.int/eur-lex/en/consleg/pdf/1971/en_1971L0316_do_001.pdf

The Unicode and ISO 10646 character-set standards call this "e" the
ESTIMATED SYMBOL and encode it at position U+212E.


3.9  How are metric units used in the kitchen?
----------------------------------------------

In metric countries, cook-book recipes traditionally list

 - liquid ingredients by volume (mL)

 - solid and powder ingredients by weight (g)

In addition, small amounts (< 50 mL) of both liquid and powder
ingredients are measured in "tea spoons", "table spoons", or
"pinches". Ingredients sold as items are simply listed by number or
fraction (e.g., 3 eggs, 1/2 medium-sized apple).

Practically every well-equipped kitchen in metric countries features:

 - a measuring cup, suitable for measuring volumes of 50-500 mL

 - a scale, suitable for measuring weights of 20-2000 g

While integer multiples of subunits (125 mL milk, 250 g flour) are
more common, fractions of larger units (1/8 L milk, 1/4 kg flour) are
frequently encountered in metric recipes, entirely depending on the
author's personal preference. Some regions and disciplines have
evolved their own metric conventions. In Austrian or Polish kitchens,
for example, the decagram is commonly heard of. Bar tenders in many
countries use centilitres (cL) or decilitres (dL) and have measuring
spoons for these.

The metric practice of measuring powders by weight differs from the US
tradition of listing powders by volume (usually in "cups"). Weight
measures ensure somewhat more reproducible results, because the
density of fine powders (e.g., flour, powder sugar) can vary by as
much as 20%, depending on whether the powder was sifted, spooned or
dipped into the measuring cup, and on how heigh the resulting heap
became.


3.10  How to convert US customary recipes into metric?
------------------------------------------------------

When converting cooking recipies from US customary units to metric,
it is often not sufficient to merely convert the units. In the case of
powder ingredients (> 50 mL), the translator should also refer to the
typical density of the ingredient, in order to convert from volume to
weight.

Some example densities:

 wheat flour:      0.5  - 0.6  g/mL   (depending on it being sifted, spooned,
 powdered sugar:   0.4  - 0.5  g/mL    or dipped, as well as amount in heap)
 granulated sugar:        0.83 g/mL
 baking powder:    0.75 - 0.9  g/mL   (depending on composition)
 table salt:              1.2  g/mL

More detailed tables are available from:

 - USDA National Nutrient Database for Standard Reference,
   National Agricultural Library, United States Department
   of Agriculture.
   http://www.nal.usda.gov/fnic/foodcomp/

 - L. Fulton, E. Matthews, C. Davis: Average weight of a measured
   cup of various foods. Home Economics Research Report No. 41,
   Agricultural Research Service, United States Department of
   Agriculture, Washington, DC, 1977.

Some commonly used US kitchen measures are now defined by US law
(21CFR101.9(b)(5)(viii)) in terms of round metric volumes:

 1 tea spoon   =   5 mL
 1 table spoon =  15 mL
 1 fl oz       =  30 mL
 1 cup         = 240 mL

 http://edocket.access.gpo.gov/cfr_2004/aprqtr/21cfr101.9.htm

See also:

 Guidelines for determining metric equivalents of household measures,
 U.S. Food and Drug Administration, Center for Food Safety and
 Applied Nutrition Office of Food Labeling, October, 1993.
 http://www.cfsan.fda.gov/~dms/flmetric.html


Thanks to the many readers of misc.metric-system who provided
suggestions to improve this text.

--
Markus Kuhn, Computer Laboratory, University of Cambridge
http://www.cl.cam.ac.uk/~mgk25/ || CB3 0FD, Great Britain

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