The 7-bit US-ASCII character code is the greatest common denominator that can be expected to be available in any communication environment. Only very few units normally require symbols from the Greek alphabet and thus the cost of requiring Unicode does not outweigh the benefit. As explained above, the real issue about writing unit terms naturally is not the character set but the ability to write subscripts and superscripts and distinguish roman letters from italics.

Some computer systems or programming languages still have the requirement of case insensitivity and some humans who are not familiar with SI units tend to confuse upper and lower case or can not interpret the difference in upper and lower case correctly. For this reason the case insensitive symbols are defined. Although The Unified Code for Units of Measure does not encourage use of case insensitive symbols where not absolutely necessary, in some circumstances the case insensitive representation may be the greatest common denominator. Thus some systems that can handle case sensitivity may end up using case insensitive symbols in order to communicate with less powerful systems.

ISO 2955 and ANSI X3.50 call case sensitive symbols “mixed case” and case insensitive symbols “single case” and list two columns for “single case” symbols, one for upper case and one for lower case. In The Unified Code for Units of Measure all units can be written in mixed upper and lower case, but in the case insensitive variant the mixing of case does not matter.

White space is not recognized in a a unit term and should generally not occur. UCUM implementations may flag whitespace as an error rather than ignore it. Whitespace is not used as a separator of otherwise ambiguous parts of a unit term.

For example % “[abc+ef]”, “ab[c+ef]”, “[abc+]ef”, and “ab[c+ef]” % could all be valid symbols if defined in the tables. In “ab[c+ef]” either “a” or “ab” could be defined as a prefix, but not “ab[c”.

Square brackets take on one task of round parentheses in HL7's “ISO+” code, where one use of parentheses is to augment unit symbols with suffixes, as in “mm(Hg)”. Another use is to enclose one full unit symbol into parentheses, as “(ka_u)” (for the King-Armstrong unit of catalytic amount of phosphatase). Apparently, in a unit symbol such enclosed one is supposed not to expect a prefix. Thus, even if “a_u” would have been defined, “(ka_u)” should not be matched against kilo-a_u.

Parentheses, however, were also used for the nesting of terms since HL7 version 2.3. At this point it became ambiguous whether parentheses are part of the unit symbol or whether they are syntactic tokens. For instance, “(ka_u)” could mean a nested “ka_u” (where “k” could possibly be a prefix), but also the proper symbol “(ka_u)” that happens to have parentheses as part of the symbol. The Unified Code for Units of Measure uses parentheses for the usual meaning of term nesting and uses square brackets where HL7's “ISO+” assumes parentheses to be part of the unit symbol.

Curly braces are here because people want annotations and deeply believe that they need annotations. Especially in chemistry and biomedical sciences, there are traditional habits to write annotations at units or instead of units, such as “%vol.”, “RBC”, “CFU”, “kg(wet tis.)”, or “mL(total)”. These habits are hard to overcome. Any attempt of a coding scheme to restrict this perceived expressiveness will ultimately result in the coding scheme not being adopted, or just “half-way” adopted (which is as bad as not adopted).

Two alternative responses to this reality exist: either give in to the bad habits and blow up of the code with dimension- and meaningless unit atoms, or canalize this habit so that it does no harm. The Unified Code for Units of Measure canalizes this habit using curly braces. Nevertheless we do continuing efforts to upgrade doubtful units to genuine units of The Unified Code for Units of Measure by defining and linking them to the other units as good as possible. Thus, “g%” is a valid metric unit atom (so that “mg%” is a valid unit too.) A drops, although quite imprecise, is a valid unit of volume “[drp]”. Even HPF and LPF (the so called “high-” and “low power field” in the microscope) have been defined so that at least they relate to each other.

The use of the period instead of the asterisk (‘*’) as a multiplication operator continues a tradition codified in ISO 1000 and maintained in ISO 2955. Because floating point numbers may not occur in unit terms the period is not ambiguous. A period in a unit term has no other meaning than to be the multiplication operator.

Since Resolution 7 of the 9th CGPM in 1948 the myth of ambiguity being introduced by more than one solidus lives on and is quoted in all standards concerning the writing of SI units. However, when the strict left to right rule is followed there is no ambiguity, neither with one solidus nor with more than one solidus. However, in human practice we find the tendency to assign a lower precedence to the solidus which misleads people to write a/b·c when they really mean a/(b·c). When this is rewritten as a/b/c there is actually less ambiguity that in a/b·c. So the real source of ambiguity is when a multiplication operator follows a solidus, not when there is more than one solidus in a term. Hence, we remove the restriction for only one solidus and introduce parentheses which may be used to remove any perceived ambiguity.

For example, the string “123” is a positive integer number while “12a” is a symbol.

Note that the period is only used as a multiplication operator, thus “2.5” means 2 × 5 and is not equal to 5/2.

ISO 2955 and ANSI X3.50 actually do not allow a plus sign leading a positive exponent. However, if there can be any perceived ambiguities, an explicit leading plus sign may be of help sometimes. The Unified Code for Units of Measures therefore allows such plus signs at exponents. The plus sign on positive exponents can be used to delimit exponents from integer numbers used as simple units. Thus, 2+10 means 210 = 1024.

Up until revision 1.9 there was a third clause “Since a unit term in parenthesis can be used in place of a simple unit, an exponent may follow on a closing parenthesis which raises the whole term within the parentheses to the power.” However this feature was inconsistent with any BNF or other syntax description ever provided, was never used and seems to have no relevant use case. For this reason this clause has been stricken. This is a tentative change. Users who have used this feature in the past, should please comment on this deprecation. If we receive indication that this feature was used by anyone, we would undo the deprecation. If no comments are received, the deprecation continues to take effect.

The metric predicate accounts for the fact that there are units that are prefixed and others that are not. This helps to disambiguate the parsing of simple units into prefix and atom.

To determine whether a given unit atom is metric or not is not trivial. It is a cultural phenomenon, subject to change, just like language, the meaning of words and how words can be used. At one time we can clearly tell right or wrong usage of words, but these decisions may need to be revised with the passage of time.

Generally, metric units are those defined “in the spirit” of the metric system, that emerged in France of the 18th century and was rapidly adopted by scientists. Metric units are usually based on reproducible natural phenomena and are usually not part of a system of comparable units with different magintudes, especially not if the ratios of these units are not powers of 10. Instead, metric units use multiplier prefixes that magnify or diminish the value of the unit by powers of ten.

Conversely, customary units are in the spirit of the middle age as most of them can be traced back into a time around the 10th century, some are even older from the Roman and Babylonian empires. Most customary units are based on the average size of human anatomical or botanic structures (e.g., foot, ell, fathom, grain, rod) and come in series of comparable units with ratios 1/2, 1/4, 1/12, 1/16, and others. Thus all customary units are non-metric

Not all units from ISO 1000 are metric as degree, minute and second of plane angle are non-metric as well as minute, hour, day, month, and year. The second is a metric unit because it is a part of the SI basis, although it used to be part of a series of customary units (originating in the Babylonian era).

Furthermore, for a unit to be metric it must be a quantity on a ratio scale where multiplication and division with scalars are defined. The Comité Consultatif d'Unités (CCU) decided in February 1995 that SI prefixes may be used with the degree Celsius. This statement has not been made explicitly before. This is an unfortunate decision because difference-scale units like the degree Celsius have no multiplication operation, so that the prefix value could be multiplied with the unit. Instead the prefix at non-ratio units scales the measurement value. One dekameter is 10 times of a meter, but there is no meaning to 10 times of 1 °C in the same way as 30 °C are not 3 times as much as 10 °C. See §§21ff on how The Unified Code for Units of Measure finds a way to accommodate this different use of prefixes at units such as the degree Celsius, bel or neper.

Except for the rule on curly braces (§12), the rules on style govern the creation of the tables of unit atoms not their individual use. Users of The Unified Code for Units of Measure need not care about style rules (§§13–15) because users just use the symbols defined in the tables. Hence, style rules do not affect conformance to The Unified Code for Units of Measure. New submissions of unit atoms, however, must conform to the style rules.

For example one can write “%{vol}”, “kg{total}”, or “{RBC}” (for “red blood cells”) as pseudo-units. However, these annotations do not have any effect on the semantics, which is why these example expressions are equivalent to “%”, “kg”, and “1” respectively.

For example when distinguishing the International Table calorie from the thermochemical calorie, we would use 1 calIT or 1 calth in print. The Unified Code for Units of Measure defines the symbols “cal_IT” and “cal_th” with the underscore signifying that “IT” and “th” are subscripts. Other examples are the distinctions between the Julian and Gregorian calendar year from the tropical year or the British imperial gallon from the U.S. gallon (see §31 and §§37ff).

For example 1 m H2O is written as “m[H2O]” in The Unified Code for Units of Measure because the suffix H2O changes the meaning of the unit atom for meter (length) to a unit of pressure.

Customary units are defined in The Unified Code for Units of Measure in order to accommodate practical needs. However metric units are still preferred and the customary symbols should not interfere with metric symbols in any way. Thus, customary units are “stigmatized” by enclosing them into square brackets.

If unit symbols for the purpose of display and print are derived from The Unified Code for Units of Measure units, the square brackets can be removed. However, display units are out of scope of The Unified Code for Units of Measure.

For example, such legacy units called “Bodansky unit” or “Todd unit” have the unit symbols “[bdsk'U]”, and “[todd'U]” respectively.

The functions fs and fs-1 are applied as follows: let rs be the numeric measurement value expressed in the special unit s and let m be the corresponding dimensioned quantity, i.e., the measurement with proper unit u. Now, rs = fs(m/u) converts the proper measurement to the special unit and m = fs-1(rs) × u does the inverse.

Since prefixes have a scalar value that multiplies the unit atom, a unit must at least have a defined multiplication operation with a scalar in order to be a candidate for the metric predicate. All proper units are candidates for the metric property, special units are no such candidates.

The Comité Consultatif d'Unités (CCU) decided in February 1995 that any SI prefix may be used with degree Celsius. This statement has not been made explicitly before. This is an unfortunate decision because difference-scale units like the degree Celsius have no multiplication operation, so that the prefix value could be multiplied with the unit. Instead the prefix at non-ratio units scales the measurement value. One wonders why the CGPM keeps the Celsius temperature in the SI as it is superfluous and in a unique way incoherent with the SI.

The scale factor α is applied with the functions fs and fs-1 as follows: let rs be the numeric measurement value expressed in the special unit s and let m be the corresponding dimensioned quantity, i.e., the measurement with proper unit u. Now, rs = fs(m/u) / α converts the proper measurement to the special unit and m = fs-1(αrs) × u does the reverse.

Until version 1.6 The Unified Code for Units of Measure has dealt with arbitrary units as dimensionless, but as an effect the semantics of The Unified Code for Units of Measure made all arbitrary units commensurable. Since version 1.7 of The Unified Code for Units of Measure it is no longer possible to convert or compare arbitrary units with any other arbitrary unit.

The case insensitive prefix symbols are slightly different from those defined by ISO 2955 and ANSI X3.50, where “giga-,” “tera-,” and “peta-” have been “G,” “T,” and “PE.” The Unified Code for Units of Measure has a larger set of unit atoms and needs to prevent more name conflicts. Tera and giga have a second letter to be safe in the future. The change of “PE” to “PT” would be the way to go for ISO 2955 which currently has a name conflict (among others) with peta-volt and pico-electronvolt.

The new prefixes “yotta-,” “zetta-,” “yocto-,” and “zepto-” that were adopted by the 19th CGPM (1990) have a second letter ‘A’ and ‘O’ resp. to avoid current and future conflicts and to disambiguate among themselves. The other submultiples “micro-” to “atto-” are represented by a single letter to keep with the tradition.

As can be seen the base system used to define The Unified Code for Units of Measure is different from the system used by the Système International d'Unités (SI) The SI base unit kilogram has been replaced by gram and the mole has been replaced by the radian that is defined dimensionless in the SI. Because of the latter change The Unified Code for Units of Measure is not isomorphic with the SI.

The replacement of the kilogram is trivial. In order to bring syntax and semantics in line we can not have a unit with prefix in the base. We need a valid unit of mass before we can combine it with the prefix “kilo-” This change does not have any effect on the semantics whatsoever. The base unit kilogram is one of the oddities of the SI: if the gram would have been chosen as a base units the CGPM could have saved the rather annoying exception of the prefixing rules with the kilogram. At times where we have to multiply the wavelength of excited krypton-86 atoms by 1650763.73 to yield one meter, it seems trivial to divide the prototype of the kilogram by thousand to yield a base unit gram.

The rationale for removing the mole from the base is that the mole is essentially a count of particles expressed in a unit of very high magnitude (Avogadro's number). There is no fundamental difference between the count of particles and the count other things.

The radian has been adopted as the base unit of plane angle α to facilitate the distinction from the solid angle Ω by the relation Ω = α2 and to distinguish rotational frequency f from angular velocity ω = 2 π · rad · f.

The notation “10*” for powers of ten originated in the HL7 “ISO+“ extension of ISO 2955. In HL7 the character carat (‘^’) was thought as reserved. Since most people would expect to see “10^3” for the “third power of ten” and might in fact confuse “10*3” to mean “ten times 3”, the symbol using the carat was later added to The Unified Code for Units of Measure.

The case insensitive symbol for pascal is “PAL” which conforms to ISO 2955 and prevents the name conflict between pascal and pico-ampère.

Without reference to history, it is difficult to explain that the degree Celsius is part of the SI, because the degree Celsius is in a unique way incoherent with the SI, and is even superfluous since the base unit kelvin measures the same kind of quantity.

In the case sensitive variant the liter is defined both with an upper case ‘L” and a lower case ‘l’. NIST [63 FR 40338] declares the upper case ‘L’ as the preferred symbol for the U.S., while in many other countries the lower case ‘l’ is used. In fact the lower case ‘l’ was in effect since 1879. A hundred years later in 1979 the 16th CGPM decided to adopt the upper case ‘L’ as a second symbol for the liter. In the case insensitive variant there is only one symbol defined since there is no difference between upper case ‘L’ and lower case ‘l’.

The unit “are” competes with year for the symbol “a” not only in ISO 2955, and ANSI X3.50, but also in ISO 1000 as stating the official CGPM approved symbols. This is why the symbol for are is “ar” in The Unified Code for Units of Measure. ISO 2955 explicitly adds the unit atom “ha” for hectare, while “hectare” is just the correct spelling of the compositum of “hecto” and “are” and thus would not require a separate unit atom. Nevertheless, ISO 2955 in its case insensitive variant assigns “ARE” to the are and “har” to the hectare. This is obviously an anomaly which The Unified Code for Units of Measure will not follow. As a metric unit, “ar” can be prefixed with “h” to yield “har”

ANSI X3.50 had two different series of symbols for the units of time, the ones from ISO 2955 as adopted by The Unified Code for Units of Measure and the symbols “yr” “mo” “wk” “hr” and “sec” while “d” and “min” were defined twice. The Unified Code for Units of Measure does not define these synonyms of ISO 2955 symbols, but does adopt those units from ANSI X3.50 that are not part of ISO 2955, namely “mo” and “wk” Month and week are useful units mainly in business or clinical medicine.

The semantics of the units of time is difficult to capture. The difficulties start with the day: There is the sidereal and the solar day that depend on the earth's rotation. The earth's rotation is variable during one day and is continually slowing down in the long run. The usual subdivisions of the day in 24 hours of 60 minutes and 60 seconds originated in Babylonia. The earth's rotation was too inexact to measure time, which is why the 11th CGPM (1954) defined the second based on a standardized historical tropical year (see below) which was later (13th CGPM 1967-1968) replaced by frequency measurement. Thus the second came to be the base unit of time and the day is now 864000 s exactly with the Universal Coordinated Time (UTC) adding leap seconds every now and then.

For the year we have to distinguish the “tropical” (solar, sidereal) year from the calendar year. And both are difficult. The tropical year is the year defined by time the earth travels around the sun. This is difficult to measure and varies over time. Around 1900 it was 365.242196 d, currently it is 365.242190 d and around 2100 it will be 365.242184 d. In addition these durations are averages. The actual length of each year may vary by several minutes due to the gravitational influence of other planets. Thus there is quite a high uncertainty already in the fourth decimal digit.

The calendar year is also difficult because there is the Julian calendar (Sosigenes of Alexandria and Julius Caesar, 45 BC) with a slightly too long year of 365.25 d that causes the calendar to be one day ahead of the tropical year in 128 years. The Gregorian calendar (Christopher Clavius 1537-1612 and Pope Gregory XIII 1545-1563) leaves out three leap years in 400 years (let n be the year number, the leap year is dropped if n mod 100 = 0 but not n mod 400 = 0.) The Gregorian mean year is thus 365.2425 d. This leap year arithmetic seems to be too much even for astronomers, which is why the light year ends up being defined based on the Julian year [NIST Sp. Pub. 811, 1995 Edition]. For this reason The Unified Code for Units of Measure defines Tropical, Julian and Gregorian year by means of subscripts, but assigns the default year symbol to the Julian year.

The week is 7 days, this is a biblic truth we can count on (it is actually quite plausible that the week of seven days originated in Babylonia and entered Jewish tradition during the Babylonian exile.)

The difficulty continues with the month. The lunar (so called “synodal” month is variable. Around 1900 it was 29.5305886 d currently it is 29.5305889 d and in 2100 it will be 29.5305891 d, which we fixate in the 5th decimal digit with a considerable uncertainty. The calendar month is difficult because of the uneven distribution of days in a month over the year, and because of the two different calendar years. But we will usually use the mean calendar month, which is the Julian calendar year divided by 12.

As a conclusion, great care has to be taken when the “customary units” of time are used to measure time. The SI has fixated the second which should be used whenever accuracy is required. For business purposes the Julian calendar is sufficient especially since the notion of the Work-Day (vs. Holiday) is more important than the imprecision over 128 years. [Sources: “Calendar” Britannica Online.http://www.eb.com:180/cgi-bin/g?DocF=macro/5000/98/toc.html. Claus Tondering, Frequently asked questions about calendars. Part 1. 1998. http://www.pip.dknet.dk/~c-t/calendar.faq1.txt]

This list is not complete. It does not list all constants but only those that are fundamental and from which many other constants can be derived. The source of this table is The NIST Reference on Constants, Units, and Uncertainty Version 2.1, 21 May 1998. NIST Physics Laboratory. http://physics.nist.gov/cuu/Constants/index.html

In the base system of The Unified Code for Units of Measure, the general gas constant R is identical to the Boltzmann constant k. In the SI both are related through R = k × NA, where NA = 6.02214076 × 1023 /mol is the Avogadro constant. Because The Unified Code for Units of Measure defines the mole to be the dimensionless Avogadro number (number of particles in 1 g of 12C itself, there is no difference anymore if the Boltzmann constant is given as k = 1.380649 × 1023 J/K or R = 8.314511 J mol-1 K-1.

Although the CGPM “accepts” only very few CGS units “for use with the SI,” CGS units are proper metric units. CGS units are still used in many physiological laboratories and in clinical diagnostics (e.g., cardiology). In addition CGS units acquired a special dignity as this was the system of units used by the great physicists of the early 20th century, Albert Einstein, Max Planck, and many others who worked on the scientific revolution that had quite a cultural impact.

The CGS system defined electric and magnetic phenomena differently which is why the units named “oersted” and “maxwell” have no proper SI counterpart. This table was compiled from various sources and is not complete and not very systematic. We therefore welcome suggestions and advice as to how this table could be completed.

Customary units have once been used all over Europe. Units were taken from nature: anatomical structures (e.g., arm, foot, finger), botanical objects (e.g., grains of various sorts, rod), or processes of everyday life (e.g., amount of land one could plow in a morning, the length of 1000 steps, an hour of walking, etc.).

Many of these units can be traced back in history to the Romans (mile), Greeks (carat) and even more ancient times. It is thus no wonder that this heritage was in some way ordered. Indeed, one finds the same names for units used in different countries and most of these units where divided into smaller or multiplied to larger units in the same way.

For example, there was the foot (de. “Fuß” fr. “pied” nl. “voet”) that was divided into 12 inches (de. “Zoll” fr. “pouce”). An inch was divided into 12 lines (de. “Linie” fr. “ligne” ). Two feet was one ell (de. “Elle” da. “Alen” sv. “Aln”). The ell was, however, not very popular in England, as opposed to the rest of Europe. Conversely, the yard is hard to find elsewhere, aside from the Argentinian “vara.” But it is perhaps no accident that the meter ended up as the 40 × 10-6 of an earth's meridian, which is approximately one yard (43.7 × 10-6). The rod (de. “Rute” fr. “perche” nl. “roede” sv. “stång”) was very popular all over Europe and so was the fathom (de. “Klafter”).

The square rod (de. “Quadratrute” fr. “perche-carrée” nl. “vierkante-roede” was mainly used to measure land. The acre as the legendary land to sow in one morning (or day) is also widespread (de. “Morgen, Tagwerk, Acker” fr. “arpent” sv. “tunnland” , although the exact amount in square rod varies considerably from region to region. Interestingly, even the special purpose measures such as the “hand” for measuring horses have international equivalents (de. “faust”).

One can indeed say that there was once a “système international d'unités coutumières“ but the magnitudes of the units were not standardized internationally. Of course, Great Britain had the most impact in standardizing the customary system, because of its colonies, including its most important colony, America. However, after the customary units were established in the U.S. a major reform took place through the British Weights and Measures Act of 1824. For instance, Queen Anne's wine Gallon of 231 cubic inches, still used in the U.S., was discarded then, and the older bushel was standardized differently in Great Britain. Other deviations between the English and U.S. measures are due to various alignments with the metric system. Thus, in the U.S., the yard was standardized as 3600/3937 m and the inch was 2.540005 cm while in England the inch was still 2.539998 cm.

In 1959 major parts of the U.S. and British system of customary units were standardized internationally, again aligned to the metric system which is why the international yard is 0.9144 m exactly and the nautical mile became 1852 m exactly. However, traditional subdivisions and multiples have not been abolished in favor of the international standard. Furthermore the old U.S. standard for the yard is still legally used for land surveying.

Conclusively, there are different systems of customary units that are in use today. These systems use the same names for units that have different equivalents in the metric system, because the customary systems are based on different reference quantities but multiples and subdivisions of the reference quantities are very similar, though with notable exceptions.

In the following tables we tried to give the original definitions to the customary units. This means in general that the references to the metric system are as few as possible, with most of the units of one system defined as multiples and subdivisions of one reference unit.

We use the subscript notation to disambiguate units with same names in the different systems. Subscript notation means, for instance that if the print symbol for foot is “ft” we use subscripts to distinguish the international foot “fti” the U.S. survey foot “ftus” and the British Imperial foot “ftbr” We do not actually list print symbols for customary units, because there seems to be no standard for it, and because defining print symbols is out of scope of The Unified Code for Units of Measure. However, we presume that subscripts be used to disambiguate whatever print symbols are being used. According to §§13ff, The Unified Code for Units of Measure uses the underscore to denote those subscripts, and also encloses the entire unit atom into square brackets. Hence, the symbols for the international foot, the U.S. survey foot and the British Imperial foot are defined as “[ft_i],” “[ft_us],” and “[ft_br]” respectively.

Prospective users of The Unified Code for Units of Measure may be disappointed by the fact that there are many different symbols for foot and inch defined but all of them have a subscript and thus none of them are equal to the ANSI X3.50 symbols. We considered to define default symbols for customary units, where, e.g., the common units of length (foot, inch) would default to the international customary units, while mass units (pound, ounce) would default to the avoirdupois system. However, because the customary system is quite complex, and units by the same names can differ by more than 20%, defining defaults will probably cause even more confusion. There is no denial: a gallon is not just a gallon and a pound is not just a pound, this is the disadvantage of dealing with a unit system of medieval origin.

In general the international customary units are effective in the U.S. and in Great Britain since 1959. We are unsure, however, about this in countries that formerly or at present belong to the Commonwealth. We therefore appreciate advice and reference to original sources on this transition. Conceivably other countries may have made exceptions in the transition to the international definitions of customary units, such as the U.S. where the old definitions have been retained for the purpose of land surveying.

It is not quite clear exactly what units the international customary system comprises. According to the Encyclopedia Britannica [British Imperial System. Britannica Online], the rod was removed in Great Britain in 1963. Since the definition of the acre is based on the rod, we did not include rod and acre in the international customary system. In the U.S. the acre is still defined on the older U.S. customary system as of 1893.

In general, we did not include special customary units of area and volume in , since these are still used differently in the U.S. Special symbols such as square inch and cubic foot have been included according to ANSI X3.50. Generally the “square-” and “cubic-” prefixes are unnecessary in ISO 2955 and ANSI X3.50 and are deprecated by The Unified Code for Units of Measure. We placed the board foot, cord and circular mil into the international table because these units are suggested by ANSI X3.50 but we were not sure in what sense they are still used. We did, however, not include the square mile in the international table because in the U.S. measurements in square miles are most likely based on the survey mile that is part of the older system, see §35.

The circular mil is exactly the area of a circle with a diameter of one mil. One mil, in turn, equals 1/1000 inch (“mil” is the etymological equivalent of “milli-inch” ) The mil has been defined in to support the exact definition of the circular mil.

ANSI X3.50 does not define a symbol for the “hand,” but this unit is mentioned in the table given by the Encyclopedia Britannica. The hand is used in measuring the height of horses from foot to shoulder. It was probably not subject to the internationalization of customary units. Any advice as whether the hand is used based on an older British or U.S. definition is appreciated.

After the 1959 international agreement changed the definition of the yard in the US to be 0.9144 m exactly, surveyors and civil engineers complained that voluminous legacy surveys and so forth used the previous definition of (1200/3937) m and that this change would be disruptive. So, by statute, Congress created a survey foot of (1200/3937) m (the old 1893 Mendenhall Order definition). Thus, by statute, miles used in surveying are referred to as statute miles of 5280 survey feet each. The fathom, rod, and furlong are likewise based on the survey foot.

According to NIST, the acre as normally used in the U.S. is defined in terms of U.S. survey lengths, and not in terms of the international customary system. This older U.S. customary system of survey lengths is still used for geodesic measurements.

The older British Imperial system is predominantly of historical interest. However, it may be that some former members of the Commonwealth have retained this system after 1959, when the unified international definitions where established, and after 1963, when the British system was revised in England.

The chain was proposed by Edmund Gunter in England of the 17th century. It is possible that Gunter's chain and Ramden's chain are related to other European traditional units such as the English “rope” (measuring 20 feet) or the old German “Landseil” (measuring 52 ells or 104 feet) named after ropes or chains that could be spanned in order to measure land. The difference in the definitions of those units is no surprise as there is nothing that restricts a chain or rope to a particular length. However, these units are still similar in magnitude.

The U.S. fluid volumes have been defined based on Queen Anne's wine gallon which was in turn defined exactly as 231 cubic inch. Although we used international inch, we are not sure what inch definition is actually used for defining the exact size of a U.S. gallon. However, the differences between the various inches are minimal, even when raised to the 3rd power (i.e., the difference between the U.S. inch and the British Imperial inch remains in the sixth decimal digit.)

Dry measures are based on the bushel (corn bushel), originally defined in 1701 as “any round measure with a plain and even bottom, being 18.5 inches wide throughout and 8 inches deep.” This definition, being (18.5/2)2 π × 8 = 2150.42017138221... cubic inch was later truncated to 2150.42 cubic inch exactly. At times the bushel was closely related with the Winchester gallon (corn gallon), which has been mentioned as an historical curiosity.

ANSI X3.50 defines symbols for the units cup, tablespoon and teaspoon which are predominantly used in cooking recipes but also in practical medicine. Similar units can often be found in European cook books, but are usually translated into metric units outside the U.S. For practical medicine these are still very handy units to give instructions to patients.

The British Weights and Measures Act of 1824 removed the medieval distinction between wine and grain measures and defined one unified system of volumes based on a new Gallon that was defined similarly as the metric unit liter: “10 imperial pounds weight of distilled water weighed in air against brass weights with the water and the air at a temperature of 62 degrees of Fahrenheit's thermometer and with the barometer at 30 inches.”

With the current definition of the gallon as 277.421 cubic inches (approximately) and a density of water of 0.99878 kg/l according to NIST data, the inch must have been approximately 2.5371 cm at that time. Because of this difficulty with the original definition of the British gallon we based the British Imperial volumes on the gallon for which there is an exact metric equivalence, according to NIST, which provides usually well researched data.

Note that the subdivisions of the British Imperial system of volumes differs from the U.S. system of fluid volumes between gill and fluid ounce: in the British system 1 oz fl equals 1/5 gill where in the U.S. system 1 oz fl equals 1/4 gill. Thus, although the British system starts out with a 20% larger gallon, the British fluid ounce, fluid dram and minim are 4% smaller than the U.S. units with the same name.

The avoirdupois system is used in the U.S. as well as in countries that use the British Imperial system. Avoirdupois is the default system of mass units used for all goods that “have weight” (fr. avoir du poids). Interestingly all three systems of weight are based on the same grain of barley, standardized to 64.79891 mg exactly [NIST].

The troy system originates in Troyes, a City in the Champagne (France) that hosted a major European fair. The troy system was later used for measuring precious metals. The World Monetary Fund valued all currencies against the troy ounce of gold at least until the 1960s (advice appreciated). The troy ounce is still used in worldwide trade with gold, even in countries that otherwise use metric units (de. “feinunze”). The troy system retains the original Roman subdivision of the pound in 12 ounces. The Roman uncia was “one twelfth” of a libra (hence the symbol “lb” for the pound), just as the inch (also originating from la. “libra” is one twelfth of a foot. The subdivision of 12 ounces/inches per pound/foot and 2 foot per ell (la. “cubit” apparently originated in the ancient Egypt and was carried on by the Greeks and Romans into the medieval Europe. However, there was always an ambiguity such that the subdivision of 1/12 could become 1/16 and vice versa, hence the avoirdupois ounce of 1/16 pound.

Note also that the troy pound was abolished in England on January 6, 1879 [Jacques J. Proot, Anglo-Saxon weights & measures, URL: http://members.aol.com/JackProot/met/spvolas.html].

Note that some U.S. pharmacies still use this system of apothecaries' weights when measuring the amount of drugs. This system is very different from the avoirdupois system though based on the same grain. The apothecaries' dram is more than twice as much as the avoirdupois dram, the ounce is still 10% greater than the avoirdupois ounce while the pound is 20% less than the avoirdupois pound. The apothecaries' system, just as the troy system, keeps the original Roman subdivision of an ounce (la. “uncia” to be 1/12 pound (la. “libra”). Hence is the apothecaries' pound about 22% smaller than the avoirdupois pound, while its subdivisions are greater than the respective avoirdupois subdivisions (ounce 10%, dram 119%). This difference in the weight systems is the most important reason why ANSI X3.50 should not be applied in medicine, where both systems are being used and therefore misinterpretations are inevitable.

There are three systems of typesetter's lengths in use today: Françcois-Ambroise Didot (1730-1804), a publisher in Paris, invented this system based on the traditional subdivisions of the customary units: 1 line was 1/12 inch and 1/6 line was one point. Henceforth the size of letters were measured in point. However, the Didot system is based on the pouce, i.e. the french inch, which, just as the English inch, is 1/12 pied (foot). But the French foot was about 6.5% greater than the British Imperial foot. In the Anglo-American realm the typesetter's point was based on the British Imperial inch, with the same subdivisions. However, in the type foundries' industry the original definition of a point drifted apart, and in the late 19th century U.S. type foundries reestablished a slightly (0.375%) greater standard point. This point made its way back to the British. However, recently, the computer typesetting industry readjusted the point to its original size of 1/72 inch. All three systems, however, are still being used today.

The degree Fahrenheit was missing in ANSI X3.50. HL7's “ISO+/ANS+” code defined the degree Fahrenheit under the symbol “DEGF” which is reflected here. This is the reason why The Unified Code for Units of Measure does not define a new symbol “Fah” similar to “Cel” of ISO 2955 for the degree Celsius.

Defining precise semantics for legacy units for “quantity of heat” is difficult. The many variants of these units are frequently confused because there is not just a calorie and not just a British thermal unit. The different calories usually being used vary by 1% but the confusion can result in an error as high as 100000%! Thus, if exactness and non-ambiguity is important one should use the joule to report amounts of heat, just like for any other energy and work kind-of-quantities.

The gram-calorie, sometimes called “small calorie” is defined as the amount of heat required to raise the temperature of 1 gram of Water from 14.5 °C to 15.5 °C. According to Encyclopedia Britannica, this is the calorie most often used in engineering. There is also a less frequently used gram-calorie at 19.5 °C to 20.5 °C and a mean calorie that is 1/100 of the amount of heat required to raise the temperature from 0 °C to 100 °C. The International Table calorie is defined by the International Conference on the Properties of Steam (1956) and is used in steam engineering. In chemistry a “thermochemical” calorie is used for reaction enthalpies.

To complete the confusion, there is also a kilogram-calorie (“large calorie” , that has a similar definition based on a kilogram instead of a gram of water. This kilocalorie has also been called “calorie” in the sloppy speech of everyday life about food. U.S. “Nutrition Facts” that label almost every American food say “Calories: xxx” The International Union of Nutritional Sciences recommends using either the joule or a kilocalorie based on the thermochemical calorie. Because of a perceived popular demand The Unified Code for Units of Measure defines the nutrition Calorie as “Cal” with the conventional capital first letter. For the case insensitive variant of The Unified Code for Units of Measure, the symbol is enclosed in square brackets (“[CAL]”).

Only the International Table calorie and the thermochemical calorie have exact definitions. To give some guidance in the confusing plenty of different calories, The Unified Code for Units of Measure defines a default symbol “cal” as an alias for the thermochemical calorie, because the calorie is mostly used today in medicine and biochemistry. On the other hand, we consider engineers smart enough to select the precise calorie they mean.

Similar to the calories, various “British Thermal Unit” (Btu) are defined and the confusion continues. One Btu is defined as the amount of heat necessary to raise the temperature of one avoirdupois pound of water by one degree Fahrenheit beginning from various temperatures (39 °F, 59 °F, or 60 °F). There is also the International Table Btu and the thermochemical Btu. Just as with the calorie we define a default symbol “Btu” as an alias for the thermochemical Btu.

Clinical medicine all over the world still uses  mm Hg to measure arterial blood pressure, and often the instruments used are real mercury columns. Likewise, the central venous blood pressure is often measured using simple water columns which is very practical for the routine. The units  m H2O and  m Hg are metric units even though they are “not accepted” for use with the SI for quite a while. Although more and more hospitals in Europe switch to using the pascal to measure partial pressures in blood gas analysis, the older units will not vanish any time soon.

In the U.S. the inch is sometimes used instead of the millimeter, and because the inch is non-metric the inch of mercury or water columns is non-metric as well.

The peripheral vascular resistance unit is the vascular resistance on which a perfusion pressure of 1 mm Hg causes a flow of 1 ml/s.

The “mesh” occurs in the NIST Guide to the SI. It seems like it is the customary counterpart of the diopter.

The unit “charrière” originates from a French manufacturer of medical instruments by that name. One charrière is the gauge of a catheter with a circumference of approximately 1 mm such that it is by convention exactly one third of a millimeter. In the U.S. the charrière is simply called “french”

A drop is a variable amount of fluid and depends on the device and technique used to produce the drop and on the physical properties of the fluid. This is similar to units like cup, tablespoon, and teaspoon that depend on the spoon or cup and are not exact either. However, in clinical medicine medication is dispensed by drops and unlike a “tablet” a drop refers to a real physical kind of quantity, volume, though not very exact.

The Hounsfield unit is a unit of X-ray attenuation used in evaluating CT scans. It is defined on an interval scale where air is -1000 HF, water is 0 HF and bone is +1000 HF. Any advice as to how this unit can be related to metric units of radiant intensity decremence is appreciated.

We have always pointed out that the homeopathic teaching takes potency not as equivalent to dilution and the C and X series would not equate to each other in the strictly numerical manner. Homeopathic potency includes the “agitation” (a vigorous shaking) that needs to occur in every step of the dilluting process. Therefore as of April 2010, the homeopathic units are declared "arbitrary units", that is, they are no longer convertible. Therefore, also, we discontinue defining them using the dilution functions. The dilution functions sometimes cause truly astronomical values, leading to overflow conditions, e.g. in such potencies as 30 C or 100 X or 10 M, which do actually occur in homeopathics that are on the market. The previous units continue to exist as "retired", but their symbols now have a prime (apostrophe) in them.

The amount of electrolytes (including acids and bases) is often reported as equivalents instead of amount of substance. This habit originates in the measuring technique of titration. The Unified Code for Units of Measure does not endorse using equivalents. We rather recommend to calculate the proper amount of substance after titration, so that 1 eq of Na+ ions is 1 mol, but 1 eq of Ca++ ions is 0.5 mol. The problem with equivalents is that the measurement results are difficult to compare because their magnitude depends on the degree of ionization of the substance. That is to say, the meaning of equivalents depend not only on the substance, but also on the state that the substance is in. For example, in iron we have to distinguish Fe2+ from Fe3+, so that no one can be sure how much 1 eq of iron really is.

Degrees of acidity are normally measured as “the pH value” that is the negative decadic logarithmus of the concentration of free protons (or hydronium ions) expressed in 1 mol/l. Usually the pH value is considered a dimensionless quantity. With the semantics of special units (§§21ff). The Unified Code for Units of Measure can link the pH value tighter to the system of proper units. Thus “[pH]” is defined as a unit symbol with the corresponding unit 1 mol/l. This allows conversions between pH and concentrations, and---because The Unified Code for Units of Measure identifies the mole with the Avogadro number---can be converted to an absolute number of protons: for example, pH 7.4 converts instantly to 0.04 μmol/l and approximately 23975 protons per picoliter.

The unit osmol as the amount of dissolved particles is to be used with caution because it interferes with “osmolar” which is the amount of dissolved particles per liter.

The gram-percent (g%) is a metric unit that has the same origin as %vol. Originally it was a dimensionless quantity expressing a ratio of two masses and thus equal to 1/100 g/g. Because water is the most important solvent in biochemistry and 1 g of a solution in water has a volume of approximately 1 ml, the meaning of the unit 1 g% drifted towards 1/100 g/ml and farther off to 1 g/dl. That way, the unit 1 g% regained a proper dimension (mass concentration, M/L3). Most often it is used as 1 mg% = 1 mg/dl but all other SI prefixes are possible.

The Svedberg unit S is used to classify macromolecules (e.g., ribosomes) in different phases of a centrifugate.

The units “high power field” (HPF) and “low power field” (LPF) are used in microscopic analysis mostly of urine sediments. These units are used in semi-quantitative estimations of the abundance of things like crystals, bacteria or red and white blood cells. The number of the objects of interest is counted in one view field in the microscope with a 10 times (low) or 100 times (high) magnifying objective lens and then reported as the number per LPF or per HPF respectively. Obviously the number of objects seen depends on the way the slide is prepared: the amount of emulgate dropped, its initial dilution, and the way the drop is smeared. These preparations of the slides are usually carried out with great routine but little exactness, hence LPF and HPF can hardly relate to any exact and meaningful volume.

The best we could do is to define LPF and HPF as areas of the viewed field. However, the area of the field varies with the kind of eyepiece used in the microscope. The so called “field number” of the eyepiece, i.e., the diameter of the view area is typically between 18 mm and 25 mm which is divided by the magnification of the objective lense to yield the actual field diameter d. Because the area A = π d2, the LPF can be anywhere between 2.5 mm^2 and 5 mm^2 and the HPF between 0.025 mm^2 and 0.05 mm^2. Because of this inexactness, we define LPF and HPF as dimensionless quantities with magnitudes that reflect the ratio of the view areas, i.e. 100:1. This allows at least to convert between numbers per LPF and per HPF and vice versa.

The unit “U” of enzymatic activity was defined in 1964 by the International Union of Biochemistry as the catalytic activity that catalyzes the transformation of 1 μmol of the substrate per minute. This unit is defined so that normal biological enzyme activities are in the range of 1 U-100 U. This unit could not be adopted by the CGPM because it violates the style rules of the SI, i.e. “unit” is a very indistinctive word, “U” is a capital letter, and the definition is not coherent with the SI.

An SI-coherent unit katal 1 kat = 1 mol/s, had been proposed for adoption into the SI over 30 years ago and was finally adopted by the CGPM in 1999. However, perhaps because the unit katal is 7 orders of magnitudes greater than normal catalytic activities, in practice the katal has not gained much in popularity over the unit “U”.

In its 1999 decision to add the katal to the SI, the CGPM explicitly “recommends that when the katal is used, the measurand be specified by reference to the measurement procedure; the measurement procedure must identify the indicator reaction.” The general problem with catalytic activities is that these heavily depend not only on the substance but on many side-conditions, such as temperature, acidity of the solution, presence or absence of cofactors, inhibitors or activators, and the amount of substrate. Particularly a catalytic activity measured in vitro says little about the activity in vivo. Hence the use of katal alone without specifying exactly the measurement method, is not sufficient to improve comparability of the measurement of catalytic substances.

Because of the influence of the measurement method, results of biologic activity measurement cannot usually be converted. This is a particular problem with the many named arbitrary units that are still used. The Unified Code for Units of Measure initially defined all arbitrary units as dimensionless. But since this leads to the false conclusion that all arbitrary units are the same, the Unified Code for Units of Measure now accounts for arbitrary units using a special flag. When a unit is marked as arbitrary, it is isolated from all other units, and no result can be converted from and to that unit (See §24).

The unit “TCID50” expresses the result of quantifying an infectious agent in tissue culture. It is a titer, expressing the highest dilution of the specimen which produces a cytopathic effect in 50% of the cell cultures or wells inoculated. [Sources: Clinical Microbiology Reviews, July 1998, Vol. 11(3), p. 533-554]

The unit “CCID50” expresses the result of quantifying an infectious agent in a cell culture. It is a titer, expressing the highest dilution of the specimen which produces a cytopathic effect in 50% of the cell cultures or wells inoculated. [Sources: Schmidt NJ. Cell culture procedures for diagnostic virology, p. 78-79. In Schmidt NJ, Emmons RW (ed.), Diagnostic procedures for viral, rickettsial and chlamydial infections, 5th ed. American Public Health Association, Inc., Washington, D.C.]

The unit “PFU” measures viral infectivity in a sensitive assay in cell culture where the titer is determined by counting the number of visible plaques developed following viral infection of a sensitive cell culture and results recorded as PFU/ml.

The unit “FFU” measures viral infectivity in a sensitive assay in cell culture, for example, using immunofocus or vital dyes technology. For example, the titer is determined by visualizing infected areas of a cell monolayer by probing with virus-specific antibodies and results are recorded as FFU/ml. [Sources: WHO expert committee on biological standardization (55th Edition). WHO Technical Report #932;]

The unit “BAU” measures amount of an allergen based on an in-vivo calibrated test using the Intradermal Dilution for 50mm sum of Erythema Diameters (ID50EAL) Method. [Source: Turkeltaub PC. Biological Standardization based on Quantitative Skin Testing - The 1D50 EAL Method. Arbeiten aus dem Paul-Ehrlich-Institut, dem Georg-Speyer-Haus und dem Ferdinand-Blum-Institut, Band 80 Gustav Fischer Verlag' Stuttgart, New York. 1987]

EDITORIAL NOTE: This method needs to be further investigated to determine a quantitative model which relates that would relate 1 BAU with a standardized amount of substance of the standardized allergenic protein. The situation is not unlike the titer and is not worse than for many of the arbitrary units listed already. In a future revision a stronger formalized metrologic model will be added to this specification.

The unit “AU” (for allergen unit) is for the amount of an allergen based some procedure defined and allergen specific reference standard. Note, do not confuse with astronomical unit, distinguish [AU] from AU

The unit “IR” has been defined to measure the allergenicity of an allergen extract. The allergen extract contains 100 IR/ml when, on a skin prick-test using a Stallerpoint®, it induces a wheal diameter of 7 mm in 30 patients sensitized to this allergen, (geometric mean). The cutaneous reactivity of these patients is simultaneously demonstrated by a positive skin prick-test to either 9 % codeine phosphate or 10 mg/ml histamine. The IR unit of Stallergenes is not comparable to the units used by other allergen manufacturers.

EDITORIAL NOTE: Should more manufacturer specific units come up in the future, we will include a manufacturer abbreviation in the unit symbol.

The unit “Amb a 1 U” is an arbitrary unit for the amount of Amb a 1, a 38 kD glycoprotein that is the major allergen in short ragweed (Ambrosia artemisiifolia) pollen allergen extracts. The amount of Amb a 1 units are determined by an in-vitro comparison of a test short ragweed extract to a FDA CBER Amb a 1 reference standard. Amb a 1 is the up-to-date term for the short ragweed pollen allergen that was originally described as Antigen E. They are synonyms. Although Antigen E is no longer used in the scientific literature, its meaning is unambiguous. The manufacturers are still licensed to use Antigen E as the designation. Therefore, Amb a 1 U = AgE U. There is an empiric relationship between Amb a 1 U and BAU (350 Amb a 1 U/mL = 100,000 BAU/mL). It was based on studies done decades ago on 15 study subjects. FDA's CBER considered mandating a conversion to BAU/mL in the labeling of short ragweed pollen products, based on AgE content, but this was never implemented. CBER provides two US standard reagents to manufacturers for their determination of Amb a 1 content, a reference standard and a reference serum. The assay used is a radial immunodiffusion assay (RID). Solid references discussing the relationship between Antigen E U/mL/Amb a 1 U/mL and micrograms of Antigen E U/mL/Amb a 1/mL are being researched.

EDITORIAL NOTE: The University of Texas' Structural Database of Allergenic Proteins (SDAP) contains close to 1000 allergens, isoallergens. Comparing the prospect of thousands of such special units for every allergen, one begins to appreciate even the metrologically complex BAU unit.

The unit “PNU” is defined as follows: 1 PNU/ml is equivalent to 1 x 10-5 mg of nitrogen determined to be in the material precipitated from 1 ml of allergenic extract by phosphotungstic acid (micro-Kjeldahl method). Typically, 1 mg of protein nitrogen equals 100,000 PNU. The unit “PNU” is an old protein unit unrelated to SI units. Several hundred products, from several manufacturers, are labeled in PNUs, and a switch to SI units for protein content is impractical.

The unit “Lf” is called the “Limit of Flocculation” or “limes flocculationis”. It is based on an antigen-antibody precipitation reaction and used for the quantification of the antigenic content of tetanus and diphteria toxin and toxoid. The limes flocculationis is the smallest amount of antigen that when mixed with one unit (Ramon) of antitoxin (antibody), produces the most rapid floccules in the flocculation test. For a purified crystalline tetanus or diphteria toxin 1 Lf is equivalent to ~ 2 μg of protein. For tetanus and diphtheria toxoids, antigenic purity is defined and controlled by Lf units per mg of protein nitrogen.

Many sources describe the unit of antitoxin as "international unit" (IU), however, this is no longer correct. It was correct for the first international standard for antitoxin, established in 1920s. It had an arbitrary unit defined as IU for in vivo antitoxic activity and that unit was also used for establishing Lf units of toxins and toxoids, that is why this standard had a ratio of 1 between flocculating activity (Lf) and antitoxic activity (IU). When WHO replaced that standard in 1970s, the second international standard related to Lf by a factor of 1.4 instead of 1. Ultimately, WHO decided to move to the toxoid standards and calibrated tetanus toxoid for flocculation using Lf unit (not IU). With the implementation of WHO standards for flocculation as tetanus and diphtheria toxoids, antitoxin standards were discontinued by the WHO. [Source: Lyng J. Quantitative Estimation of Diphtheria and Tetanus Toxoids - 4 - Toxoids as International Reference Materials Defining Lf-units for Diphtheria and Tetanus Toxoids. Biologicals (1990) 18, 11-17. Also on the definition of the IU for antitoxin: Spaun J, Lyng J. Replacement of the International Standard for Tetanus Antitoxin and the Use of the Standard in the Flocculation Test. Bull. Wid Hith Org. 1970, 42, 523-534.http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2427455 and personal communication with FDA CBER representatives.]

These units are “pseudo-units” because of their standardized definition as being logarithms of a ratio of two measurements with the same kind-of-quantity: first, the units cancel out, and second, the logarithm does not produce a new unit. These units were defined as “metric” because they are used as such, although a multiplication operation is not defined on these quantities. Multiplication of the measurement value with a scalar r is equivalent to raising the original ratio to the r-th power.

According to NIST, the neper is used as the ratio level of field quantities and the bel is used for the level of power quantities. The factor 2 comes into play when field quantities (like electric potential) are expressed in decibel. The specialized bel-units B(V), B(mV), B(W), etc. are defined as the level of the measured quantity with reference quantities 1 V, 1 mV, and 1 W respectively. [NIST Sp. Pub. 811, 1995 Edition]

Given the sound pressure level expressed in dB(SPL) it is feasible to define dB(A) for the A scale of loudness. Similar units such as phon and sone could be defined as well if a good approximation for the respective characteristic functions are available. Any advice is welcome.

Although called “metric carat,” the carat really is a customary unit, still used for precious gems. The word carat comes from Greek κερατίκον (small horn) that originally was the horn-shaped grain of a locust-tree species in the pea family, hence the carat grain is about three barley grain that the other English systems of weights are based on. The arab carat was 1/24 of an ounce, the Imperial carat (1877) was 205.3 mg or 3.168 grain. In other European cities, the carat was 205.8 mg (Hamburg, Lisboa) but there were great variations from 188.5 mg (Bologna) to 213.5 mg (Torino). Due to these variations no customary carat has gained importance today aside from the “metric carat” defined as 200 mg exactly. [All About Carats URL: http://www.channel1.com/users/scales/carat-def.htm]

The “Mark” was a mass unit for precious metals (Köln 234 g, Paris 245 g, Wien 277 g). A mark of gold was subdivided into 24 “karat,” a mark of silver into 16 “lot.” This led to the other use of the unit “carat” to mean 1/24 in measuring the finesse of pure gold in an alloy. For example, an 8 carat gold alloy contains 8 parts of gold on 16 parts of silver = 8/24 = 1/3, or 333 per mille. This carat is spelled “karat” in the U.S. while other countries do not use different spellings.

The unit “[m/s2/Hz^(1/2)]” is defined as a special unit to represent the odd fractional exponent of the second obtaining for the unit of the amplitude spectral density (ASD). It is defined based on the unit for the power spectral density (PSD), that is 1 (m/s2)2/Hz or 1 m2 · s-3. Since the two measurements are directly comparable, PSD = ASD2.

This table is not complete. There are other units such as shannon (Sh), erlang (E), or hartley (Hart), for which we had no quantitative definitions. Any advice is appreciated.

The bit is defined twice. One definition with a subscript letter ‘s‘ is defined as the logarithmus dualis of the number of distinct signals. However this unit can not practically be used to express more than 1000 bits. Especially when the bit is used to express transmission rate or memory capacities, floating point registers would quickly overflow. Therefore we define a second symbol for bit, without the suffix, to be the dimensionless unit 1.

The baud (Bd) is the number of distinct signals transmitted per second, it is not the same as bits per second since one distinct signal usually carries more than one bit of information.

This table reflects proposed prefixes which are not yet standardized. [Bruce Barrow, A Lesson in Megabytes. IEEE Standards Bearer, January 1997]