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Subject: Metric System FAQ

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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