Handling of units and dimensions

The Hydra server implements checks that make sure that the units of a dataset assigned to an attribute are consistent with the physical dimension asked for by the attribute. This requires some conventions about how physical dimensions are denoted in the respective fields of the database. Also, a standard way of describing physical units needs to be defined. This document describes these conventions and provides a controlled vocabulary for both, dimensions and units.

Definitions

Dimension

In this document a dimension is the physical dimension of a physical quantity. A dimension is independent of the units used to describe a physical quantity.

Unit

A unit defines the magnitude of a physical quantity. A unit is defined by convention and refers to a system of measurement, such as SI.

Dimensions

Basic concepts

There are two basic ways of defining physical dimensions.

1. Define a dimension as mathematical expression based on the seven fundamental quantities:

   Base quantity	Symbol
   Length	L
   Mass	M
   Time	T
   Electric current	I
   Temperature	\Theta
   Amount of substance	N
   Luminous intensity	J

   All derived quantities can be expressed based on these fundamental quantities. For example Energy would be written as M L^{2} T^{-2}.

2. Define a dimension using a keyword. This will allow to set fundamental and derived quantities using a name defined by a controlled vocabulary.

In Hydra the second definition is implemented since expressing all the derived quantities based on the fundamental ones is rather complicated, even for quantities that are used frequently (such as energy, power, etc.).

List of dimension keywords

Length
Mass
Time
Temperature
Area
Volume
Angle
Speed
Energy
Force
Power
Pressure
Volumetric flow rate
Monetary value
Unit price (volume)
Unit price (mass)
Energy price
Dimensionless

Units

Unit	Abbr.	Linear factor	Constant fac.	Description
Dimensionless
No unit	-	1.0	0.0	Dimensionless parameter without units
Percent	%	0.01	0.0
Energy price
US Dollars per joule	USD J^-1	1.0	0.0	Cost in US Dollars per Joule
US Dollars per kilojoule	USD kJ^-1	0.001	0.0
US Dollars per kilowatt-hour	USD kWh^-1	2.77777777e-07	0.0
Mass flow rate
kilograms per second	kg s^-1	1.0	0.0
kilograms per minute	kg min^-1	0.0166666667	0.0
kilograms per hour	kg h^-1	0.000277777778	0.0
kilograms per day	kg day^-1	1.15740741e-05	0.0
kilograms per month	kg mon^-1	3.80265176e-07	0.0
kilograms per year	kg yr^-1	3.16887646e-08	0.0
grams per second	g s^-1	0.001	0.0
tonnes per second	kg s^-1	1000.0	0.0
tonnes per minute	kg min^-1	16.66666666667	0.0
tonnes per hour	kg h^-1	0.277777777778	0.0
tonnes per day	kg day^-1	1.15740741e-02	0.0
tonnes per month	kg mon^-1	3.80265176e-04	0.0
tonnes per year	kg yr^-1	3.16887646e-05	0.0
Volumetric flow rate
cubic metres per second	m^3 s^-1	1.0	0.0	SI unit for volumetric flow rate.
cubic metres per minute	m^3 min^-1	0.0166666667	0.0
cubic metres per hour	m^3 h^-1	0.000277777778	0.0
cubic metres per day	m^3 day^-1	1.15740741e-05	0.0
cubic metres per month	m^3 mon^-1	3.80265176e-07	0.0
cubic hectometres per second	hm^3 s^-1	1000000.0	0.0	SI unit for volumetric flow rate.
cubic hectometres per minute	hm^3 min^-1	16666.6667	0.0
cubic hectometres per hour	hm^3 h^-1	277.777778	0.0
cubic hectometres per day	hm^3 day^-1	11.5740741	0.0
cubic hectometres per month	hm^3 mon^-1	0.380265176	0.0
cubic foot per second	ft^3 s^-1	0.0283168466	0.0
cubic foot per minute	ft^3 min^-1	0.000471947443	0.0
cubic foot per hour	ft^3 h^-1	7.86579072e-06	0.0
cubic foot per day	ft^3 day^-1	3.2774128e-07	0.0
cubic foot per month	ft^3 mon^-1	1.07679106e-08	0.0
gallons per second	gal s^-1	0.00378541178	0.0
gallons per minute	gal min^-1	6.30901964e-05	0.0
gallons per hour	gal h^-1	1.05150327e-06	0.0
gallons per day	gal day^-1	4.38126364e-08	0.0
gallons per month	gal mon^-1	1.43946028e-09	0.0
acre-foot per second	ac-ft s^-1	1233.48184	0.0
acre-foot per minute	ac-ft min^-1	20.5580306	0.0
acre-foot per hour	ac-ft h^-1	0.342633844	0.0
acre-foot per day	ac-ft day^-1	0.0142764102	0.0
acre-foot per month	ac-ft mon^-1	0.000469050188	0.0
acre-inch per second	ac-in s^-1	102.790153	0.0
acre-inch per minute	ac-in min^-1	1.71316922	0.0
acre-inch per hour	ac-in h^-1	0.0285528203	0.0
acre-inch per day	ac-in day^-1	0.00118970085	0.0
acre-inch per month	ac-in mon^-1	3.90875157e-05	0.0
litre per second	l s^-1	0.001	0.0
litre per minute	l min^-1	1.66666667e-05	0.0
litre per hour	l h^-1	2.77777778e-07	0.0
litre per day	l day^-1	1.15740741e-08	0.0
litre per month	l mon^-1	3.80265176e-10	0.0
megalitre per second	Ml s^-1	1000	0.0
megalitre per minute	Ml min^-1	1.66666667	0.0
megalitre per hour	Ml h^-1	2.77777778e-01	0.0
megalitre per day	Ml day^-1	1.15740741e-02	0.0
megalitre per month	Ml mon^-1	3.80265176e-04	0.0
Angle
degree	°	1.0	0.0	Is a measurement of plane angle, representing 1/360 of a full rotation
grad or gon	grd	0.9	0.0	One grad equals 9/10 of a degree or π/200 of a radian
radian	rad	57.29577951	0.0	1 rad=180/π
minutes	'	0.0166666666	0.0	1°=1/60
seconds	''	0.00027777777778	0.0	1°=1/3600
Temperature
Celsius	°C	1.0	273.15	The Celsius scale sets 0.01 °C to be at the triple point of water and a degree Celsius to be 1/273.16 of the difference in temperature between the triple point of water and absolute zero. Until 1954 the scale was defined with the freezing point of water at 0 °C and the boiling point at 100 °C at standard atmospheric pressure.
Delisle	°De	-0.666666666667	373.15	The Delisle scale is a temperature scale invented in 1732 by the French astronomer Joseph-Nicolas Delisle (16881768). It is similar to that of Reaumur
Electronvolt	eV	11605.0	0.0	In some fields, plasma physics in particular, the electronvolt (eV) is used as a unit of ‘temperature’
Fahrenheit	°F	0.555555555556	255.372222222	In this scale, the freezing point of water is 32 degrees Fahrenheit (written as 32 °F), and the boiling point is 212 degrees, placing the boiling and melting points of water 180 degrees apart. Thus the unit of this scale, a degree Fahrenheit, is 5/9ths of a kelvin (which is a degree Celsius), and negative 40 degrees Fahrenheit is equal to negative 40 degrees Celsius
Kelvin	K	1.0	0.0	The kelvin, unit of thermodynamic temperature is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. [13th CGPM (1967), Resolution 4]
Rankine	°Ra	0.555555555556	0.0	Like Kelvin, Rankine zero is absolute zero, but Fahrenheit degrees are used. As a result, a difference of 1°R is equal to a difference of 1°F, but 0°R is 459.67°F
Réaumur	°Ré	1.25	273.15	The freezing point of water is 0 degrees Réaumur, the boiling point 80 degrees Réaumur. Hence a degree Reaumur is 1.25 degrees Celsius or kelvins. The Réaumur temperature scale is also known as the octogesimal division (division octogesimale)
Rømer	°Rø	1.90476190476	258.864285714	Rømer is a disused temperature scale named after the Danish astronomer Ole Christensen Rømer, who proposed it in 1701
Power
BTU/hour	BTU h^-1	0.29301067	0.0
BTU/minutes	BTU min^-1	17.56863	0.0
BTU/seconds	BTU s^-1	1055.056	0.0
calorie/seconds	cal s^-1	4.183076	0.0
gigawatt	GW	1000000000.0	0.0
horsepower	hp	745.699871582	0.0	The mechanical horsepower is originally proposed by James Watt in 1782.
watt	W	1.0	0.0	One watt is one joule of energy per second
kilowatt	kW	1000.0	0.0
megawatt	MW	1000000.0	0.0
gigawatt	GW	1000000000.0	0.0
volt-ampere	VA	1.0	0.0	A volt-ampere in electrical terms, means the amount of apparent power in an alternating current circuit equal to a current of one ampere at an emf of one volt. It is dimensionally equivalent to watts
Area
square metre	m^2	1.0	0.0
square kilometre	km^2	1000000.0	0.0
are	a	100.0	0.0
acre	ac	4046.8564224	0.0	International acre.
acre(US)	ac (US)	4046.87261	0.0	United States survey acre.
hectare	ha	10000.0	0.0	Commonly used for measuring land area.
square yard	yd^2	0.83612736	0.0
square foot	ft^2	0.09290304	0.0
square inch	in^2	0.00064516	0.0
square mile	mi^2	2589988.11034	0.0
Energy
BTU(IT)	BTU	1055.056	0.0	The British thermal unit (BTU or Btu) is a unit of energy used in the United States. In most other areas, it has been replaced by the SI unit of energy, the joule (J). A Btu is defined as the amount of heat required to raise the temperature of one pound avoirdupois of water by one degree Fahrenheit. 143 Btu is required to melt a pound of ice. As is the case with the calorie, several different definitions of the Btu exist, here ISO BTU is used 1 ISO BTU = 1055.056 J
calorie(IT)	cal	4.1868	0.0	The small calorie or gram calorie approximates the energy needed to increase the temperature of 1 g of water by 1C. Here the definition adopted by the Fifth International Conference on Properties of Steam (London, July 1956) is used. 1 cal = 4.1868 J exactly.
Electronvolt	eV	11605.0	0.0	In some fields, plasma physics in particular, the electronvolt (eV) is used as a unit of ‘temperature’
erg	erg	1e-07	0.0	An erg is the unit of energy and mechanical work in the centimetre-gram-second (CGS) system of units. Its name is derived from the Greek word meaning ‘work’. The erg is a quite small unit, equal to a force of one dyne exerted for a distance of one centimetre
gigajoule	GJ	1000000000.0	0.0
horsepower-hours	hph	2684520.0	0.0
joule	J	1.0	0.0	The joule is a derived unit defined as the work done or energy required, to exert a force of one newton for a distance of one metre, so the same quantity may be referred to as a newton metre or newton-metre with the symbol N·m. However, the newton metre is usually used as a measure of torque, not energy
kilojoule	kJ	1000.0	0.0
kilocalorie	kcal	4184.0	0.0
watt-hour	Wh	3600.0	0.0	One watt-hour is equivalent to one watt of power used for one hour. This is equivalent to 3,600 joules. For example, a sixty watt light bulb uses 60 watt-hours of energy every hour
kilowatt-hour	kWh	3600000.0	0.0
Megawatt-hour	MWh	3600000000.0	0.0
Gigawatt-hour	GWh	3.6e+12	0.0
megajoule	MJ	1000000.0	0.0
Volume
barrel(oil)	bbl	0.158987295	0.0	The standard oil barrel is used in the United States for crude oil or other petroleum products. 1 Oil barrel = 42 US gallons
centilitre	cl	1e-05	0.0
cubic centimetre	cm^3	1e-06	0.0
cubic decimetre	dm^3	0.001	0.0
cubic hectometre	hm^3	1000000.0	0.0
cubic foot	ft^3	0.028316846592	0.0
cubic inch	in^3	1.6387064e-05	0.0
cubic metre	m^3	1.0	0.0
cubic millimetre	mm^3	1e-09	0.0
cubic yard	yd^3	0.764554857984	0.0
decilitre	dl	0.0001	0.0
fluid ounce(US)	fl oz	2.9574e-05	0.0
gallon, liquid(US)	gal	0.003785411784	0.0	US liquid gallon is 231 in^3 or 128 fl oz or 3.785411784 L.
litre	L	0.001	0.0	A litre is defined as a special name for a cubic decimetre (1 L = 1 dm^3).
decilitre	dl	0.0001	0.0
millilitre	ml	1e-06	0.0
megalitre	Ml	1000	0.0	A megalitre is a unit used in water management (1 Ml = 10^3 m^3)
pint, liquid(US)	pt	0.000473176475	0.0
acre-foot	ac-ft	1.23348184	0.0	An acre foot is the volume of water that covers one acre in one foot. This unit is popular among irrigation people in the US.
acre-inch	ac-in	0.102790153	0.0	See acre-foot.
Pressure
atmosphere	atm	101325.0	0.0	an atmosphere (symbol: atm) or standard atmosphere is a unit of pressure roughly equal to the average atmospheric pressure at sea level on Earth. It is defined as 101.325 kPa and equal to the pressure under 760 mm of mercury
pascal	Pa	1.0	0.0	The pascal is equivalent to one newton per square metre, and was used in SI under that name before the name pascal was adopted by the 14th CGPM in 1971. The same unit is also used for stress, Young’s modulus, and tensile strength
bar	bar	100000.0	0.0
hectopascal	hPa	100.0	0.0
iches of water	inH2O	249.08891	0.0
inches of mercury	inHg	3386.388	0.0	Inches of mercury is a non-SI unit for pressure. It is defined as the pressure exerted by a column of mercury of 1 inch in height at 0 °C at the standard acceleration of gravity. 1 inHg = 3386.389 pascals at 0 °C.
kilopascal	kPa	1000.0	0.0
metre of water	mH2O	9806.65	0.0
microbar	µbar	0.1	0.0
milibar	mbar	100.0	0.0
millimetre of mercury	mmHg	133.322	0.0
millimetre of water	mmH2O	9.80665	0.0
lbf/in^2	psi	6894.76	0.0	The pound-force per square inch (symbol: lbf/in^2) is a non-SI unit of pressure based on avoirdupois units. In casual English language use it is rendered as ‘pounds per square inch’, abbreviated to psi with little distinction between ‘mass’ and ‘force’
technical atmosphere	at	98066.5	0.0	A technical atmosphere is a non-SI unit of pressure equal to 1 kilogram-force per square centimetre, i.e. 98.066 5 kilopascals (kPa) or about 0.96784 standard atmospheres
torr	torr	133.322	0.0	The torr (symbol: Torr) or millimetre of mercury (mmHg) is a non-SI unit of pressure. It is the atmospheric pressure that supports a column of mercury 1 millimetre high
Length
angström	Å	1e-10	0.0	Angstrom sometimes used expressing the size of atoms, and lengths of chemical bonds and visible-light spectra.
astronomical unit	AU	1.4959855e+11	0.0	Is a unit of length approximately equal to the distance from the Earth to the Sun.
centimetre	cm	0.01	0.0
decimetre	dm	0.1	0.0
femtometre	fm	1e-15	0.0
foot	ft	0.3048	0.0	International foot. Foot is a unit of length, in a number of different systems, including English units, Imperial units, and United States customary units. Its size can vary from system to system, but in each is around a quarter to a third of a metre. The most commonly used foot today is the international foot.
hectometre	hm	100.0	0.0
inch	in	0.0254	0.0	The international inch is defined to be precisely 25.4 mm
kilometre	km	1000.0	0.0
light-year	ly	9.460528405e+15	0.0	A light-year is the distance that light travels in a vacuum in one year. While there is no authoritative decision on which year is used, the International Astronomical Union (IAU) recommends the Julian year.
metre	m	1.0	0.0	Is the fundamental unit of length in the International System of Units (SI). The metre is defined as the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 second.
micrometre	µm	1e-06	0.0
mile	mi	1609.344	0.0	The international mile is defined to be precisely 1760 international yards (by definition, 0.9144 m each) and is therefore exactly 1609.344 metres.
mile(nautical)	nmi	1852.0	0.0	Corresponds approximately to one minute of latitude along any meridian. It is a non-SI unit used by special interest groups such as navigators in the shipping and aviation industries. It is commonly used in international law and treaties, especially regarding the limits of territorial waters. It developed from the geographical mile.
millimetre	mm	0.001	0.0
nanometre	nm	1e-09	0.0
parsec	pc	3.0856776e+16	0.0	The name parsec stands for ‘’parallax of one second of arc’‘, and one parsec is defined to be the distance from the Earth to a star that has a parallax of 1 arcsecond.
picometre	pm	1e-12	0.0
yard	yd	0.9144	0.0	The international yard is defined as 3 feet, 36 inches, or 1/1760 of a mile, which is exactly 0.9144 metres.
Mass
carat	carat	0.0002	0.0	The carat is a unit of mass used for gems, and equals 200 milligrams. The word derives from the Greek keration (fruit of the carob), via Arabic and Italian. Carob seeds were used as weights on precision scales because of their uniform weight. In the distant past, different countries each had their own carat, roughly equivalent to a carob seed
gram	g	0.001	0.0
kilogram	kg	1.0	0.0	The kilogram is the unit of mass equal to the mass of the international prototype of kilogram. [1st CGPM (1889), 3rd CGPM (1901)]. It is the only SI unit that is still defined in relation to an artifact rather than to a fundamental physical property that can be reproduced in different laboratories.
microgram	µg	1e-09	0.0
milligram	mg	1e-06	0.0
ounce	oz	0.02835	0.0	International avoirdupois ounce (most common). The abbreviation ‘’oz’’ comes from the old Italian word ‘’onza’’ (now spelled oncia), meaning ounce.
pound	lbm	0.45359237	0.0	The pound is the name of a number of units of mass, all in the range of 300 to 600 grams. Most commonly, it refers to the avoirdupois pound (454 g), divided into 16 avoirdupois ounces.
tonne	t	1000.0	0.0
Time
day	day	86400.0	0.0
hour	h	3600.0	0.0
minute	min	60.0	0.0
month	mon	2629743.8328	0.0	Here: 1 month = 1/12 year. January = 31 days February, 28 days, 29 in leap years, or 30 on certain occasions in related calendars March, 31 days April, 30 days May, 31 days June, 30 days July, 31 days August, 31 days September, 30 days October, 31 days November, 30 days December, 31 days
second	s	1.0	0.0	The second is the SI base unit of time and is defined as 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. This definition refers to a caesium atom at rest at a temperature of 0 K
millisecond	ms	0.001	0.0
microsecond	μs	1e-06	0.0
nanosecond	ns	1e-09	0.0
picosecond	ps	1e-12	0.0
year	yr	31556925.9936	0.0	Here: 1 year = 365.242199 days.
Force
dyne	dyn	1e-05	0.0	The dyne is a unit of force specified in the centimetre-gram-second (cgs) system of units. One dyne is equal to exactly 10-5 newtons. The dyne can be defined as ‘the force required to accelerate a mass of one gram at a rate of one centimetre per second squared’
gram-force	gf	0.00980665	0.0
joule/metre	J m^-1	1.0	0.0
kg·m/s^2	kg m s^-2	1.0	0.0	Same as 1 newton
kilogram-force	kgf	9.80665	0.0
kilopond	kp	9.80665	0.0	The deprecated unit kilogram-force (kgf) or kilopond (kp) is defined as the force exerted by one kilogram of mass in standard Earth gravity. Although the gravitational pull of the Earth varies as a function of position on earth, it is here defined as exactly 9.80665 m/s^2. So one kilogram-force is by definition equal to 9.80665 newtons
kilopound-force	kipf	4448.22161525	0.0
lb·ft/s^2	lb ft s^-2	0.138254954376	0.0	Same as 1 poundal
newton	N	1.0	0.0	A newton is the amount of force required to accelerate a mass of one kilogram at a rate of one metre per second squared. In addition, 1N is the force of gravity on a small apple on Earth
ounce-force	ozf	0.278013850953	0.0
pond	p	0.00980665	0.0
pound-force	lbf	4.448222	0.0	The pound-force is a non-SI unit of force or weight. The pound-force is equal to a mass of one avoirdupois pound (which is currently defined as exactly 0.45359237 kilogram) multiplied by the standard acceleration due to gravity on Earth. (The pound-force is thus roughly the force exerted due to gravity by a mass of one pound at the surface of the Earth)
poundal	pdl	0.138254954376	0.0	The poundal is a non-SI unit of force. It is a part of the absolute foot-pound-second system of units, a coherent subsystem of English units introduced in 1879, and one of several specialized subsystems of mechanical units used as aids in calculations. It is defined as 1 lb·ft/s^2
tonne-force(metric)	tf	9806.65	0.0
Speed
metre/second	m s^-1	1.0	0.0
foot/hour	fph	8.4666666666e-05	0.0
inch/minute	ipm	0.00042333333333	0.0
foot/minute	fpm	0.00508	0.0
inch/second	ips	0.0254	0.0
kilometre/hour	km h^-1	0.277777777778	0.0
foot/second	fps	0.3048	0.0
mile/hour	mph	0.44704	0.0
knot(admiralty)	kn	0.514773	0.0
mile/minute	mpm	26.8224	0.0
mile/second	mps	1609.344	0.0
speed of light in vacuum	c	299792458.0	0.0	The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning ‘swiftness’. It is the speed of all electromagnetic radiation, including visible light, in a vacuum. More generally, it is the speed of anything having zero rest mass.
Monetary value
US Dollar	$	1.0	0.0
Unit price (volume)
US Dollar per square metre	$ m^-3	1.0	0.0
Unit price (mass)
US Dollar per kilogram	$ kg^-1	1.0	0.0
Energy price
USDollars per kilowatt-hour	$ kWh^-1	2.77777777e-07	0.0	Cost in US Dollars per energy unit (kilowatt-hour).
USDollars per kilojoule	$ kJ^-1	0.001	0.0	Cost in US Dollars per energy unit (kilojoule).
USDollars per joule	$ J^-1	1.0	0.0	Cost in US Dollars per energy unit (joule).
Specific cost (time)
US Dollar per second	$ s^-1	1.0	0.0
US Dollar per minute	$ min^-1	0.0166666667	0.0
US Dollar per hour	$ h^-1	0.000277777778	0.0
US Dollar per day	$ day^-1	1.15740741e-05	0.0
US Dollar per month	$ mon^-1	3.80265176e-07	0.0
US Dollar per year	$ yr^-1	3.16887646e-08	0.0

Basic concepts

List of unit keywords