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The Guide to Life, The Universe and Everything.

3. Everything / Maths, Science & Technology / Mathematics
3. Everything / Maths, Science & Technology / Physics

Created: 22nd March 2001
Units of Measurement
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Kitchen scales
The 'root cause' of the loss of the spacecraft was the failed translation of English units into metric units in a segment of ground-based, navigation-related mission software.
– Arthur Stephenson, NASA chairman of the Mars Climate Orbiter Mission Failure Investigation Board, 1999

Units are of vital importance in every civilisation as they are an essential means of communication. Extensive use of them is made in trade and science and they also play a significant role in everyday life. However, they are in no way an attainment of modern times. Whether a caveman wanted to pose with the size of the fish he had caught or a physicist wants to determine the relaxation time of an electron gas, units are needed everywhere on all levels of technological and cultural development.

Please note that some browsers can't display all the characters used below. Some browsers are better than others, so if a character doesn't appear below in your browser, it might work in others.

In order to have fun with them, however, a system of units must fulfil some basic requirements:

  • All people have to use the same units.
  • The set of units must be minimal.
  • The units must be defined as exactly as possible.
  • The units should be connected with each other in such a way that formulae using them become as simple as possible.

The Earth has followed a rocky road to such a system.

A Short History of Units

For the very first units, sizes of body parts were used: Ulna1(cubit), foot, thumb (inch). However people don't share the same body sizes and it was unbearable to have measured data depending on the measurer.

To overcome this, cultures began to keep standards of their units (standard lengths or bars, standard weights and so on) in temples or, later, in government buildings. The oldest known unit is the Babylonian foot from 2100 BC, which is of a length of 264.5mm. Political leaders often took such definitions very personally. For example, for several years the distance between the tip of the nose of King Henry I and his thumb was the defined British yard.

Under the rule of Charlemagne in the 9th Century AD, Europe had a uniform unit scheme, introduced in 789 AD. The subsequent disunity of Europe during the Middle Ages led to a wild assortment of completely unstandardised units, differing even from town to town. It is reported that in Baden, in southwestern Germany, in 1810 there were 112 different yards, 92 units of square measure, 65 units of volume, 183 units for cereals and 80 different pounds! This may have been fun if you wanted to cheat the farmer of your neighbouring village, however it made extra-territorial trade very difficult, and was useless for science.

But a solution had already been found, in Paris.

The SI

In 1791 Delambre and Méchain completed the measurement of the distance between Dunkerque (France) and Barcelona (Spain) which was used by a pan-European group of scientists to estimate the length of one Earth quadrant – one quarter of the circumference of the earth. Its 107th part was called one metre. Furthermore 1/1000 cubic metre was one litre and one litre of water had a mass of one kilogram. These new units were introduced in France in 1795 and in Germany in 1868. Seven years later, in 1875, 17 countries joined the metric union, called the CGPM (Conférence Général des Poids et Mesures).

In 1960 the CGPM decided to build a unit system, consisting of six (later seven) base units and their derivatives and called it Système International d'Unités: the SI. Since then, only the definitions of the base units have been improved, besides which tinkering the SI is state-of-the-art. It dominates the metric countries and international science. Its home is near Paris at the Bureau International des Poids et Mesures (BIPM).

So much for history.

Base Units of the SI

The SI developed from the metric system but today both terms can be used synonymously. It is worth mentioning that all metric countries have a different set of legal units, including some non-metric ones. The SI, in most cases, represents the core of the metric system, though.

The science that deals with measuring quantities and definition of units is metrology. Many countries run metrological institutes and partly they work as standardising authorities in their respective domains.

In regular international meetings these institutes decide about (re-)definitions of SI units. Since 1983 the seven base units have been defined as follows:

SI Base Units

QuantityNameDefinitionDimension
lengthmetre (m)length of path travelled by light in vacuum during 1/299,792,458 of a secondL
timesecond (s)duration of 9,192,631,770 periods of radiation of the transition between the two hyperfine levels of the ground state of 133CsT
masskilogram (kg)equal to the mass of the international platinum-iridium kilogram prototype kept under three glass bells in a safe (with three keys given to three different people) in the cellar of the Pavillion de Breteuil in Paris.M
electric currentampère (A)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 of 2·10−7 N (newton) per metre of lengthI
thermodynamic temperaturekelvin (K)1/273.16 of the thermodynamic temperature of the triple point of waterK
amount of substancemole (mol)amount of substance which contains as many particles as there are atoms in 12 g (gram) of 12CN
luminous intensitycandela (cd)luminous intensity, in a given direction, of a source that emits monochromatic radiation of 540·1012 Hz (hertz) that has a radiant intensity in that direction of 1/683 W/sr (watt per steradian)P

Derived Units of the SI

Another great convenience of the SI is that all units are either base units or simple products of them according to their dimension – no coefficients, no zero point shifts. This is called a coherent system. Therefore, it's superfluous to list any conversion factors: there aren't any.

SI Derived Units

QuantityDimensionName
frequency T−1 hertz (Hz)
force LMT−2newton (N)
pressureL−1MT-2pascal (Pa)
energyL2MT−2joule (J)
powerL2MT−3watt (W)
Photometric Units
luminous fluxPlumen (lm)
illuminanceL−2Plux (lx)
Radioactivity
activityT−1becquerel (Bq)
dose equivalentL2T−2sievert (Sv)
absorbed doseL2T−2gray (Gy)
Electrical Units
chargeTIcoulomb (C)
potential differenceL2MT−3I−1volt (V)
resistanceL2MT−3I−2ohm
conductanceL−2M−1T3I2siemens (S)
capacitanceL−2M−1T4I2farad (F)
magnetic fluxL2MT−2I−1weber (Wb)
magnetic flux densityMT−2I−1tesla (T)
inductanceL2MT−2I−2henry (H)
Others
catalytic activityT−1Nkatal (kat)
refractive powerL−1diopter (dpt)

The disadvantage of a coherent system is that some units are tiny; the pascal for example, while others are huge like the tesla. Therefore there are a few units in use that are very closely related to SI units – namely by powers of ten. These are:

SI Related Units

NameValueUse
barn (b)10−28 m2cross section in atomic and nuclear physics
gauss (G)10−4 Tmagnetic flux density
bar105 Papressure
litre (l)10−3 m3volume (mostly of liquids)
tonne (t)1000 kgweight
ångström (Å)10−10 mdimensions in crystallography
micron (µ)10−6 mmicroscopic lengths
fermi (fm)10−15 mlengths on sub-atomic scale

Metric Prefixes

A much more general solution for titchy or gigantic units are prefixes. Placing them directly before units will change their values by powers of ten. For example, 1 nF (one nano farad) is equal to 10−9 F = 0.000 000 001 F.

Although there are no further rules for using prefixes, there is a sort of conventional etiquette:

  • Yotta, zetta, zepto and yocto are not regarded as part of the SI.
  • Use deci only with metre.
  • Use centi only with litre and metre.
  • Use hecto only with litre and pascal.
  • Don't use deka.

Metric Prefixes

FactorNameSymbolFactorNameSymbol
(1024yottaY)10−1decid
(1021zettaZ)10−2centic
1018exaE10−3millim
1015petaP10−6mikroµ
1012teraT10−9nanon
109gigaG10−12picop
106megaM10−15femtof
103kilok10−18attoa
102hectoh(10−21zeptoz)
101dekada(10−24yoctoy)

In information theory the same prefixes are applied to its fundamental unit, the byte (B). However, in a majority of cases of use, 1 MB actually represents 1024·1024 B = 1,048,576 bytes, rather than a strictly accurate 1,000,000 B. Therefore some metric purists called for clear distinction. The result was published in 1998. Now 1024 B are one kibibyte (1 KiB), 10242 B are one mebibyte (1 MiB) and 10243 B are one gibibyte (1 GiB). This well-meant, albeit slightly academic approach, while approved by many standardisation authorities, hasn't yet made it into everyday practice.

Minutes and Hours

Minutes and hours as measures of time are not part of the core of the SI but they are very closely linked with it, particularly in everyday use of the SI system. 60 seconds are one minute (min) and 60 minutes are one hour (h).

Most people think that 24 hours are one day, which is – again, strictly speaking – only an approximation. The length of the day is adjusted to the course of the sun, which is a little bit irregular. The same is true for the week and even more for months and years. The realm of actual standard units of measurement ends at the hour.

Non-SI Units in Use

Maybe life would be too boring if all people used SI units. Sometimes non-SI units are used because they make a certain specific calculations easier, however in most cases people are simply not bold enough to break with tradition, or are reluctant to 'learn' the SI unit.

For a typical example of this type of usage, a car with 150 hp has a good deal of power – but a car with 112 kW? Well, as you might guess, they are exactly the same.

Even scientists frequently prefer non-SI units. Tradition plays a role here, too, but sometimes they have a real excuse: natural units. These are useless in practice but have the convenient effect that natural constants become equal to one, which keeps formulae and calculations simple. For example, Einstein's famous equation E=mc2 is reduced to a very elegant E=m.

In the following tables numbers in bold face are exact per definitionem.

Scientific and International Non-SI Units

NameValueDimensionUse
astronomical unit (AU, ua)1.49597870·1011 mLastronomy, distances within the solar system
lightyear (ly)0.9460530·1016 mLdistance in astronomy
parsec (pc)3.0857·1016 mLdistance in astronomy
(typographic) point (pt)0.3514598 mmLdimensions in typography
big point (bp)0.3527778 mmLdimensions in typography
international nautical mile (INM, NM)1.852 kmLocean navigation
knot (kn)1 INM/h = 0.5144 m/sLT−1speed of ships
register ton (reg to, RT)2.831685 m3L3water displacement of ships
are (a)100 m2L2area of farmland
hectare (ha)10000 m2L2area of farmland
electronvolt (eV)1.6021892·10−19 JML2T−2energy in solid state and particle physics
calorie (cal)4.1868 JML2T−2energy, calorific value of food2
tons equivalent hard coal (TET)2.93076·1010 JML2T−27 Gcal; energy
tons equivalent petroleum (TEP)4.1868·1010 JML2T−210 Gcal; energy
tons equivalent TNT4.184·109 JML2T−21 Mcal; energy release of bombs
atomic mass unit (u)1.6605655·10−27 kgMmass of atoms and elementary particles
carat0.2 gMmass of gems
denier (den)1.111·10−7 kg/mML−11/9 g/km; specific weight of threads
millimetre of mercury (mmHg)133.322 PaML−1T−2eg blood pressure
torr (Torr)133.3224 PaML−1T−2gas pressure
atmosphere (atm)1.01325·105 PaML−1T−2gas pressure
pounds per square inch (psi)6895.0 PaML−1T−2gas pressure
gal (Gal)10−2 m/s2LT−2fall acceleration in geophysics
ørsted (Oe)79.5775 A/mIL−1103/4π A/m; magnetic field strength
curie (Ci)3.7·1010 BqT−1radioactive activity
rad (rd)0.01 GyL2T−2(radioactive) energy dose
röntgen equivalent man (rem)0.01 SvML−1T−2(radioactive) equivalent dose
röntgen (R)2.58·10−4 C/kgIM−1T(radioactive) ion dose
baud1 bit/sT−1data transmission speed (pronounce 'bohd')

United Kingdom

To facilitate being part of the European Union, the UK was urged to abandon all imperial units. The pint as a measure of beer or milk is still legal, as is buying pizza by the inch, but you can hire the other units for a decent fine of 5000.

Practically, however, the imperial units are still widely used. A big supermarket chain tested metric units for six months, then switched back to pounds and ounces because the customers had felt 'puzzled and bemused'.

Imperial Units

NameValueRemarks
Length
nautical mile (n mile)1.853184 kmocean navigation
mile1.609344 km80 ch = 1760 yd
yard (yd)91.44 cm36 in
foot (ft)30.48 cm12 in
inch (in, '')2.54 cm
milliinch (mil, ''')25.4 µm1/1000 in
hand10.16 cm4 in; height of horses
furlong (fur)201.168 m220 yd; horse racing
chain (ch)20.1168 m22 yd
fathom1.8288 m2 yd; depth of sea
Area
acre4046.86 m24840 yd2 = 10 ch2
Volume
gallon (UKgal)4.54609 l
pint (pt)0.568261 l1/8 UKgal
fluid ounce (fl oz)28.41304 ml1/160 UKgal
barrel163.659 l36 UKgal; for beer
Mass (avoirdupois system)
pound (lb)0.45359237 kg
ton1.016047 t2240 lb
stone6.3502932 kg14 lb; weight of people
ounce (oz)28.34952 g1/16 lb
dram (dr)1.771845 g1/16 oz
Mass of gems and precious metals
troy ounce (oz tr)31.1034768 g
pennyweight (dwt)1.55517384 g1/20 oz tr
Others
poundal (pdl)0.138255 N1 lb·ft/s2; force
horsepower (hp)745.700 Wpower
British thermal unit (Btu)1.05506 kJenergy
therm105.506 MJ105 Btu; energy

USA

The USA are bottom of the metric league. Metric units have been legal national standard in the US since 1866, though nobody cares. Curiously enough, metric units are used in most US science fiction series. Hopefully they are not complete fiction. The National Institute for Standards and Technology (NIST) tries hard to enforce the use of the SI in the USA but has hitherto had little success.

Partly the following table refers to obsolete UK units.

US Units

NameValueRemarks
Length
mile (mi), yard, foot, inch, milliinch, hand, furlong, chain, rod perch, pole and fathom (fath) as in the UK
link (li)20.1168 cm0.01 ch
line0.635 mm1/40 in
gauge (gg, g)25.4 µm1 mil
survey foot30.48006 cm1200/3937 m
Area
rood, acre and circular inch as in the UK
Volume of liquids
hogshead as in the UK
gallon (gal)3.7854118 l
liquid quart (liq qt)0.9463529 l1/4 gal
liquid pint (liq pt)0.4731765 l1/8 gal
gill118.2941 ml1/32 gal
liquid ounce (liq oz)29.57353 ml1/128 gal
minim (minim)0.0616115 ml
fluid dram (fl dr)3.69669 ml60 minim
tablespoon14.78676 ml1/2 liq oz
teaspoon9.8578432 ml1/3 liq oz
cup236.58824 ml16 tablespoon
barrel, barrel petroleum158.9873 l42 gal, only petroleum
Volume of dry goods
dry barrel (bbl)115.6271 l7056 in3
bushel (bu)35.2391 l
peck (peck)8.80977 l1/4 bu
dry quart (dry qt)1.101221 l1/8 peck
dry pint (dry pt)0.550610 l1/2 quart
Mass
pound, short ton, ounce, dram, grain (grain) and slug as in the UK
long ton1.016047 t2240 lb
long hundredweight (cwt)50.8024 kg112 lb
short hundredweight (sh cwt)45.3592 kg100 lb
Mass of gems and precious metals
troy ounce and pennyweight as in the UK
troy pound (lb tr)0.37324172 kg12 oz tr
Mass of drugs
apothecaries' pound (lb ap)0.37324172 kg1 lb tr
apothecaries' dram (dr ap)3.8879346 g1 drachm
apothecaries' scruple (s ap)1.2959782 g1 scruple (UK)
Others
poundal and horsepower as in the UK

Germany

Since the old days in Baden the measurement situation has been greatly improved. As in most continental countries, the use of non-SI units has become very rare here. Responsible is the PTB in Braunschweig, which calls itself the 'Guardian of Units'.

German Units

NameValueUseImperial Counterpart3
Pfund0.5 kgesp. eatablespound
Zentner50 kgweight of goods and fat peoplehundredweight
Pferdestärke (PS)735.49875 Wpower of engineshorse power

Peculiar Units in Use

Temperature

Temperature is basically a rather simple concept. There is a point of absolute zero temperature (0 K – ie, no heat at all) and from there you can measure temperature just like length or mass. Unfortunately this leads to very odd values for everyday temperatures – around 300 K. Therefore people use other scales with other zero points eg, °C, °F. This makes it necessary to give formulae rather than mere factors to convert between temperature units.

Let's assume you wanted to know how much Fahrenheit 20 °C is. The table says (5th column, 4th row) °F = 1.8 · C + 32'. This yields 68 °F. Voilà.

Rankine and reaumur are obsolete temperature units. The Rankine was intended to be for Fahrenheit what kelvin is for Celsius – a thermodynamic temperature scale. Celsius made the race all over the world, however, which meant the end of the rankine.

Temperature Conversion Formulae

K =°R =°C =°F =°Re =
kelvin
(K)
1.8 · KK − 273.151.8 · K − 459.670.8 · K − 218.52
rankine
(°R)
5/9 · R5/9 · R − 273.15R − 459.674/9 · R − 218.52
Celsius
(°C)
C + 273.151.8 · C + 491.671.8 · C + 320.8 · C
Fahrenheit
(°F)
5/9 · (F − 32) + 273.15F + 459.675/9 · (F − 32)4/9 · (F − 32)
reaumur
(°Re)
1.25 · Re + 273.152.25 · Re + 491.671.25 · Re2.25 · Re + 32

Historical remark: Probably you have noticed all the degree signs in the temperature units. These have nothing to do with angles of course, but with a problem of the early days of temperature measurement: What does zero temperature mean, really?

  • Fahrenheit (1714) said 'temperature of a mixture of water, ice and ammoniac'.
  • Reaumur (1730) said 'temperature of a mixture of water and ice'.
  • Celsius (1742) said 'temperature of boiling water'. Later people found this potty and changed it to Reaumur's definition.

Because all of this was arbitrary, these units were disfigured with degree signs. The real zero point remained a mystery until W Thompson, or Lord Kelvin, determined it in 1848. Hence the kelvin has no '°' and is allowed to wear metric prefixes like mK or µK.

Pureness of Precious Metals

It is not only that outside the SI there are many units for the same quantity, sometimes even within the SI one unit can indicate multiple quantities. The carat, for example, is a unit of mass, but it can also be used to indicate how much gold, silver etc is contained in a given alloy. 25/6 · carat gives the percentage of pureness. Thus a say 22-carat gold chain contains 92% gold. Pure gold has 24 carats, so higher values would be a metallurgical miracle (or simply a lie).

Logarithmic Units

A simplified conception of the Weber-Fechner law says that our perception of external stimulation is proportional to the logarithm of that stimulation. This is only a very rough approximation, but it explains the need for logarithmic units, especially if our senses are involved.

Mathematical note: Unfortunately the logarithm can't stand units. In order to get rid of them one has to divide the quantity by another quantity of the same unit. This second quantity is part of the definition and is usually very small to avoid negative values.

decibel (dB): Actually the decibel is a far more general measurement, but mostly it is used to indicate the loudness of sound. Let p be the sound pressure, then 10·log(p/20µPa) is the loudness in decibels. 40 dB is normal small talk, 140 dB is a jet engine and 180 dB is lethal. However our ears are not equally sensitive for all frequencies; the maximum is at approx. 1000 Hz. The phon scale takes this into account (at 1000 Hz, phon and dB are identical).

magnitudines (m): Astronomers specify the brightness of stars in magnitudines (or magnitudes) which is based on an ancient Greek system. In this the brightest stars had 1m and the faintest 6m. Today's exact definition is m=−2.5·log(s/s0). Here s indicates the illuminance of the star seen from earth and s0 is adjusted in such a way that the Pole Star has exactly 2.12m. Later it was found that the brightness of the Pole Star is in fact slightly variable, but astronomers are very patient people.

Richter scale: It's a measure for the intensity of earthquakes. Let A be the maximal amplitude of the ground oscillation 100 km away from the epicentre of an earthquake, then log(A/1µm) is its value on the Richter scale. Earthquakes beyond 6 are regarded as really big ones, for them A can be several metres.

pH scale: A measure of acidity. Let n be the molar concentration of H+-ions in a solution, then −log(n/(1mol/l)) is its pH value. In water, values from 0 (strong acid) up to 14 (strong alkali) are possible. Pure water has a pH of 7 (neutral), yet drinking water is a little bit lower.

bit: The bit can be seen as a logarithmic measure of information. If a certain data container can represent N different possible contents (eg numbers) it has (3.322·log N) bit. For example, a variable that can have values from 0 up to 255 is a 3.322·log 256 = 8 bit variable. 8 bit form one byte. There are even larger units like word, double word and paragraph, however their sizes are not clearly standardised. See also the discussion of binary metric prefixes above4.

Angular Units

The only mathematically legitimate unit of plane angle is the radian (rad). It's the length of the corresponding arc in the unit circle. For all non-mathematicians: 2π rad is the full angle, π/2 rad5 is a right angle.

For solid angle the steradian (sr) is used. It's the area of the corresponding sphere segment of the unit sphere. The full sphere has 4π sr.

There aren't actually any other sensible – or equally intuitive – possibilities to measure angles, but mankind is not very sensible and highly imaginative. One degree (°) is (π/180) rad (so 360° are the full angle). Every degree is divided into 60 arc minutes (') end every arc minute into 60 arc seconds ('').

One gon is (π/200) rad. Gon is also called grade or new degree (g). Every new degree is divided into 100 new minutes (c)6 and every new minute into 100 new seconds (cc). Remarkably enough the gon is a legal unit, however almost nobody uses it.

There are other angular units which are even more bizarre. All the units in the following table, for example – legal or not – must also be regarded as obsolete units, excluding degree and its derivatives.

Angular Units

NameValueFull AngleRemarks
Plane angle
degree (°)1.745329·10−2 rad360°π/180 rad
(arc) minute (')2.908882·10−4 rad21600'(1/60)°
(arc) second ('')4.848137·10−6 rad1,296,000''(1/3600)°
(arc) gon (gon), grade (grade), new degree (g)1.570796·10−2 rad400 gon(1/200) rad
new minute (c), cgon1.570796·10−4 rad40000c(1/100) gon
new second (cc)1.570796·10−6 rad4,000,000cc(1/10000) gon
revolution (r)6.283185 rad1 r2π rad
mil (mil), (artilleristic) point (¯)9.817477·10−4 rad6400 milπ/3200 rad
(nautical) point ('')0.1963495 rad32 pointπ/16 rad; ocean navigation
Solid angle
square degree ((°)2)3.046174·10−4 sr41252.97(°)2(π/180)2 sr

Obsolete Units

The following passages contain units not used anymore. However you may still come across them sometimes.

It is virtually impossible to list all units, there being almost as many potential units as there are human beings. If you encounter an unknown unit and want to look for its value, a rather good starting point is one of the national genealogy institutes, especially if it is a historical unit. Otherwise the metrological authorities are worth a try.

Obsolete Scientific and International Units

NameValueDimensionUse
x-unit (KX)1.00202·10−10 mLspectroscopy
didot point (dd)0.376 mmLcontinental typography
cicero (cc)4.531 mmLcontinental typography
pica4.218 mmLtypography
geographical mile7.421591 kmL
eötvös (E)10−9 s−2T−2acceleration in geophysics
franklin (Fr)3.33564·10−10 CTIelectric charge
debye (D)3.33564·10−30 CmLTIelectric dipole momentum
clausius (Cl)4.1868 J/KML2T−2K−11 cal/K; entropy
rutherford (Rd)106 BqT−1radioactive activity
jansky (Jy)10−26 J/m2MT−2irradiation
biot (Bi)10 AIelectric current
maxwell (M, Mx)10−8 WbL2MT−2I−1magnetic flux
gilbert (Gb)0.795775 AI10/4π A; magnetic tension
new candle (NK)1 cdPluminous intensity
international candle (IK)1.019 cdPluminous intensity
nit (nt)1 cd/m2PL−2luminous density
stilb (sb)104 cd/m2PL−2luminous density
apostilb (asb)0.318310 cd/m2PL−2(1/π) cd/m2; luminous density
lambert (La)3183.10 cd/m2PL−2(1/π) cd/cm2; luminous density
phot (ph)104 lxPL−2illuminance
litre atmosphere (l atm)101.325 JML2T−2energy
gamma (γ)10−9 kgMmass
pond (p)9.80665·10−2 NMLT−2force
dyne (dyn)10−5 NMLT−2force
poise (P)0.1 Pa sML−1T−1dynamic viscosity
stokes (St)10−4 m2/sL2T−1kinematic viscosity
erg10−7 JML2T−2energy
enzyme unit (U)1.6667·10−8 katNT−11 µmol/minute

United Kingdom

Obsolete Imperial Units

NameValueRemarks
Length
rod, perch, pole (rod)5.0292 m5.5 yd
Area
rood1011.71 m240 rod2 = 1/4 acre
circular inch5.06707 cm2(π/4) in2
Volume
peck9.09218 l2 UKgal
bushel36.3687 l8 UKgal
quarter290.9498 l64 UKgal
chaldron1.309273 m34 quarter
quart (qt)1.136523 l1/4 UKgal
gill142.0652 ml1/32 UKgal
minim (min)0.0591939 ml1/180 fl oz
fluid drachm (fl dr)3.55163 ml60 min
fluid scruple1.183877 ml20 min
hogshead (hhg)238.4809 lonly for liquids
Mass
short ton0.907185 t2000 lb
hundredweight (cwt)50.8024 kg8 stone = 112 lb
cenral (sh cwt)45.3592 kg100 lb
quarter12.7005864 kg1/4 cwt
grain (gr)64.7989 mg1/7000 lb
slug14.59390 kg
Mass of drugs
apothecaries' ounce (oz ap)31.1034768 g480 gr
drachm3.8879346 g60 gr
scruple1.2959782 g20 gr

Germany

The following units are all Prussian apart from one. Prussia was the north-eastern part of Germany, and the industrial and scientific heartland of the country. The exception is the Deutsche Meile, a general, historical German unit.

Obsolete German Units

NameQuantityValue
Deutsche Meile (mile)length7.5 km
Linie (line)length0.218 cm
Zoll (inch)length12 Linien = 2.615 cm
Fuß (foot)length12 Zoll = 31.39 cm
Elle (cubit)length25.5 Zoll = 66.69 cm
Klafterlength6 Fu  = 1.883 m
Rute (rod)length2 Klafter = 3.766 m
Meile (mile)length2000 Ruten = 7.532 km
Schritt (yard)length1/10000 Meile = 75.32 cm

Russia

Today Russia uses the metric system in almost all measurements – even in their airplanes, which is potentially dangerous since western control towers normally use imperial units. Note that the Russian dujm and fut are exactly equal to the inch and foot. The names are mere transcriptions from Cyrillic.

Obsolete Russian Units

Name7QuantityValue
dujm (inch)length2.540 cm
fut (foot)length12 dujm = 0.3048 m
arschin (cubit)length7/3 fut = 71.12 cm
milja (mile)length10500 arschin = 7.468 km
funt (pound)mass409.512 g
tonna (ton)mass4800 funt = 1965.658 kg

Status and Future of the SI

Today, 94.5% of the world's population uses the metric system. On the whole only three countries haven't included it into their industrial standards: The USA, Myanmar and Liberia.

Most other systems have been connected to the SI. Since 1959, the inch is defined using the metre, and the avoirdupois, troy and apothecaries' systems via the kilogram.

The Convention of the Metre of 1875 is still the basis of all international agreement on units of measurement. There are now 48 member countries in the BIPM, including all major industrialised nations. However, practical enforcement of usage varies heavily from country to country.

The US National Institute of Standards and Technology (NIST) has launched a 'Metric Program' under the banner 'Toward a Metric America'. Hopefully they will succeed in converting the US to usage of metric units. However, doing this comprehensively and quickly would probably cost hundreds of billions of dollars.

Fortunately the German Physikalisch-Technische Bundesanstalt (PTB) needn't do this. They focus on more accurate definitions of units. For example the kilogram is defined in a rather anachronistic way by a prototype that is likely to change over the centuries. Their project 'Avogadro' ia an attempt at an overhaul.


1 The thin long bone in the human forearm.
2 For food mostly kcal = 1000 cal are used. People often refer to it as plain calories.
3 Note that 'counterpart' does not imply equal value.
4 By the way 3.322 is an approximation for 1/log 2.
5 You can omit the 'rad', although it is considerably less confusing for non-mathematicians to include it.
6 You may also call this a centigon.
7 Note that other sources may differ in spelling.


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ENTRY DATA
Written and Researched by:

Cefpret

Edited by:

Hypoman

Referenced Entries:

Natural Units
Parsecs
Astronomical Units
Absolute Zero
Super-cooling and a Brief History of Temperature
Lord Kelvin - the Physicist
A Chronology of Time
Stellar Magnitudes

Referenced Sites:

Bureau International des ...
National Institute of Sta...
National Physical Laborat...

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