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.
Table of Contents
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.
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}.
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 kilowatthour 
USD kWh^1 
2.77777777e07 
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 
1.15740741e05 
0.0 

kilograms per month 
kg mon^1 
3.80265176e07 
0.0 

kilograms per year 
kg yr^1 
3.16887646e08 
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 
1.15740741e02 
0.0 

tonnes per month 
kg mon^1 
3.80265176e04 
0.0 

tonnes per year 
kg yr^1 
3.16887646e05 
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 
1.15740741e05 
0.0 

cubic metres per month 
m^3 mon^1 
3.80265176e07 
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 
7.86579072e06 
0.0 

cubic foot per day 
ft^3 day^1 
3.2774128e07 
0.0 

cubic foot per month 
ft^3 mon^1 
1.07679106e08 
0.0 

gallons per second 
gal s^1 
0.00378541178 
0.0 

gallons per minute 
gal min^1 
6.30901964e05 
0.0 

gallons per hour 
gal h^1 
1.05150327e06 
0.0 

gallons per day 
gal day^1 
4.38126364e08 
0.0 

gallons per month 
gal mon^1 
1.43946028e09 
0.0 

acrefoot per second 
acft s^1 
1233.48184 
0.0 

acrefoot per minute 
acft min^1 
20.5580306 
0.0 

acrefoot per hour 
acft h^1 
0.342633844 
0.0 

acrefoot per day 
acft day^1 
0.0142764102 
0.0 

acrefoot per month 
acft mon^1 
0.000469050188 
0.0 

acreinch per second 
acin s^1 
102.790153 
0.0 

acreinch per minute 
acin min^1 
1.71316922 
0.0 

acreinch per hour 
acin h^1 
0.0285528203 
0.0 

acreinch per day 
acin day^1 
0.00118970085 
0.0 

acreinch per month 
acin mon^1 
3.90875157e05 
0.0 

litre per second 
l s^1 
0.001 
0.0 

litre per minute 
l min^1 
1.66666667e05 
0.0 

litre per hour 
l h^1 
2.77777778e07 
0.0 

litre per day 
l day^1 
1.15740741e08 
0.0 

litre per month 
l mon^1 
3.80265176e10 
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 
2.77777778e01 
0.0 

megalitre per day 
Ml day^1 
1.15740741e02 
0.0 

megalitre per month 
Ml mon^1 
3.80265176e04 
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 JosephNicolas 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 

voltampere 
VA 
1.0 
0.0 
A voltampere 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 
1e07 
0.0 
An erg is the unit of energy and mechanical work in the centimetregramsecond (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 

horsepowerhours 
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 newtonmetre 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 

watthour 
Wh 
3600.0 
0.0 
One watthour 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 watthours of energy every hour 
kilowatthour 
kWh 
3600000.0 
0.0 

Megawatthour 
MWh 
3600000000.0 
0.0 

Gigawatthour 
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 
1e05 
0.0 

cubic centimetre 
cm^3 
1e06 
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 
1.6387064e05 
0.0 

cubic metre 
m^3 
1.0 
0.0 

cubic millimetre 
mm^3 
1e09 
0.0 

cubic yard 
yd^3 
0.764554857984 
0.0 

decilitre 
dl 
0.0001 
0.0 

fluid ounce(US) 
fl oz 
2.9574e05 
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 
1e06 
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 

acrefoot 
acft 
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. 
acreinch 
acin 
0.102790153 
0.0 
See acrefoot. 
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 nonSI 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 poundforce per square inch (symbol: lbf/in^2) is a nonSI 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 nonSI unit of pressure equal to 1 kilogramforce 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 nonSI unit of pressure. It is the atmospheric pressure that supports a column of mercury 1 millimetre high 
Length 

angström 
Å 
1e10 
0.0 
Angstrom sometimes used expressing the size of atoms, and lengths of chemical bonds and visiblelight 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 
1e15 
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 

lightyear 
ly 
9.460528405e+15 
0.0 
A lightyear 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 
1e06 
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 nonSI 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 
1e09 
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 
1e12 
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 
1e09 
0.0 

milligram 
mg 
1e06 
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 caesium133 atom. This definition refers to a caesium atom at rest at a temperature of 0 K 
millisecond 
ms 
0.001 
0.0 

microsecond 
μs 
1e06 
0.0 

nanosecond 
ns 
1e09 
0.0 

picosecond 
ps 
1e12 
0.0 

year 
yr 
31556925.9936 
0.0 
Here: 1 year = 365.242199 days. 
Force 

dyne 
dyn 
1e05 
0.0 
The dyne is a unit of force specified in the centimetregramsecond (cgs) system of units. One dyne is equal to exactly 105 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’ 
gramforce 
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 
kilogramforce 
kgf 
9.80665 
0.0 

kilopond 
kp 
9.80665 
0.0 
The deprecated unit kilogramforce (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 kilogramforce is by definition equal to 9.80665 newtons 
kilopoundforce 
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 
ounceforce 
ozf 
0.278013850953 
0.0 

pond 
p 
0.00980665 
0.0 

poundforce 
lbf 
4.448222 
0.0 
The poundforce is a nonSI unit of force or weight. The poundforce 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 poundforce 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 nonSI unit of force. It is a part of the absolute footpoundsecond 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 
tonneforce(metric) 
tf 
9806.65 
0.0 

Speed 

metre/second 
m s^1 
1.0 
0.0 

foot/hour 
fph 
8.4666666666e05 
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 kilowatthour 
$ kWh^1 
2.77777777e07 
0.0 
Cost in US Dollars per energy unit (kilowatthour). 
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 
1.15740741e05 
0.0 

US Dollar per month 
$ mon^1 
3.80265176e07 
0.0 

US Dollar per year 
$ yr^1 
3.16887646e08 
0.0 