Semantics of units

Units are divided into base units (meter, second, mole etc.) and non-base units (dimensionless, minute, hour etc.). 

A notable distinction from the International System of Units (SI) is that base units never have prefixes; so the base unit of mass is gram, not kilogram.

Let u1, u2, ... be the set of base units. Then the meaning of any unit is the expression C * u1**p1 * u2**p2 * ..., where C is real, p1, p2 ... are integers, and u1, u2 ... are the base units treated as abstract variables for the purpose of algebraic manipulations. Such an expression is called a dimensional quantity.

The interpretation of dimensional quantity (denoted as [[unit]]) is then straightforward:

• [[dimensionless]] = 1.
• [[named_unit]] is just named_unit for base units; for derived units the interpretation follows those units' definitions, e.g. [[minute]] = 60 * second.
• [[prefix, "*", named_unit]] = C * [[named_unit]], where C is the numerical factor corresponding to that prefix. E.g. [[kilo named_unit]] = 1000 * [[named_unit]].
• [[unit1, "*", unit2]] = [[unit1]] * [[unit2]].

Examples

• to define a molar mass, a unit that can be used is unit = g / mmol
• a volume velocity can be expressed with unit = mol * m**(-3) * s**(-1)

Exhaustive list of units

Below is a list of all the units and prefixes that can be used in the platform.

Base units

• meter = [length] = m = metre
• second = [time] = s = sec
• gram = [mass] = g
• mole = [substance] = mol
• degK = [temperature] = K = kelvin
• ampere = [current] = A = amp
• candela = [luminosity] = cd = candle
• radian = [] = rad
• bit = []
• count = []
• dimensionless = []

Length units

• angstrom = 1e-10 * meter
• inch = 2.54 * centimeter = international_inch = inches = international_inches = in
• foot = 12 * inch = international_foot = ft = feet = international_foot = international_feet
• mile = 5280 * foot = mi = international_mile
• yard = 3 * feet = yd = international_yard
• mil = inch / 1000 = thou
• parsec = 3.08568025e16 * meter = pc
• light_year = speed_of_light * julian_year = ly = lightyear
• astronomical_unit = 149597870691 * meter = au
• nautical_mile = 1.852e3 * meter = nmi
• printers_point = 127 * millimeter / 360 = point
• printers_pica = 12 * printers_point = pica
• US_survey_foot = 1200 * meter / 3937
• US_survey_yard = 3 * US_survey_foot
• US_survey_mile = 5280 * US_survey_foot = US_statute_mile
• rod = 16.5 * US_survey_foot = pole = perch
• furlong = 660 * US_survey_foot
• fathom = 6 * US_survey_foot
• chain = 66 * US_survey_foot
• barleycorn = inch / 3
• arpentlin = 191.835 * feet
• kayser = 1 / centimeter = wavenumber

Area units

• are = 100 * m**2
• barn = 1e-28 * m ** 2 = b
• cmil = 5.067075e-10 * m ** 2 = circular_mils
• darcy = 9.869233e-13 * m ** 2
• acre = 4046.8564224 * m ** 2 = international_acre
• US_survey_acre = 160 * rod ** 2

Volume units

• liter = 1e-3 * m ** 3 = l = L = litre
• cc = centimeter ** 3 = cubic_centimeter
• stere = meter ** 3
• gross_register_ton = 100 * foot ** 3 = register_ton = GRT
• acre_foot = acre * foot = acre_feet
• board_foot = foot ** 2 * inch = FBM
• bushel = 2150.42 * inch ** 3 = bu = US_bushel
• dry_gallon = bushel / 8 = US_dry_gallon
• dry_quart = dry_gallon / 4 = US_dry_quart
• dry_pint = dry_quart / 2 = US_dry_pint
• gallon = 231 * inch ** 3 = liquid_gallon = US_liquid_gallon
• quart = gallon / 4 = liquid_quart = US_liquid_quart
• pint = quart / 2 = pt = liquid_pint = US_liquid_pint
• cup = pint / 2 = liquid_cup = US_liquid_cup
• gill = cup / 2 = liquid_gill = US_liquid_gill
• floz = gill / 4 = fluid_ounce = US_fluid_ounce = US_liquid_ounce
• imperial_bushel = 36.36872 * liter = UK_bushel
• imperial_gallon = imperial_bushel / 8 = UK_gallon
• imperial_quart = imperial_gallon / 4 = UK_quart
• imperial_pint = imperial_quart / 2 = UK_pint
• imperial_cup = imperial_pint / 2 = UK_cup
• imperial_gill = imperial_cup / 2 = UK_gill
• imperial_floz = imperial_gill / 5 = UK_fluid_ounce = imperial_fluid_ounce
• barrel = 42 * gallon = bbl
• tablespoon = floz / 2 = tbsp = Tbsp = Tblsp = tblsp = tbs = Tbl
• teaspoon = tablespoon / 3 = tsp
• peck = bushel / 4 = pk
• fluid_dram = floz / 8 = fldr = fluidram
• firkin = barrel / 4

Time Units

• minute = 60 * second = min
• hour = 60 * minute = h = hr
• day = 24 * hour
• week = 7 * day
• fortnight = 2 * week
• year = 31556925.9747 * second
• month = year/12
• shake = 1e-8 * second
• sidereal_day = day / 1.00273790935079524
• sidereal_hour = sidereal_day/24
• sidereal_minute = sidereal_hour/60
• sidereal_second =sidereal_minute/60
• sidereal_year = 366.25636042 * sidereal_day
• sidereal_month = 27.321661 * sidereal_day
• tropical_month = 27.321661 * day
• synodic_month = 29.530589 * day = lunar_month
• common_year = 365 * day
• leap_year = 366 * day
• julian_year = 365.25 * day
• gregorian_year = 365.2425 * day
• millenium = 1000 * year = millenia = milenia = milenium
• eon = 1e9 * year
• work_year = 2056 * hour
• work_month = work_year/12

Frequency units

• hertz = 1 / second = Hz = rps
• revolutions_per_minute = revolution / minute = rpm
• counts_per_second = count / second = cps

Velocity units

• knot = nautical_mile / hour = kt = knot_international = international_knot = nautical_miles_per_hour
• mph = mile / hour = MPH
• kph = kilometer / hour = KPH

Mass units

• ounce = 28.349523125 * gram = oz = avoirdupois_ounce
• dram = oz / 16 = dr = avoirdupois_dram
• pound = 0.45359237 * kilogram = lb = avoirdupois_pound
• stone = 14 * lb = st
• carat = 200 * milligram
• grain = 64.79891 * milligram = gr
• long_hundredweight = 112 * lb
• short_hundredweight = 100 * lb
• metric_ton = 1000 * kilogram = t = tonne
• pennyweight = 24 * gram = dwt
• slug = 14.59390 * kilogram
• troy_ounce = 480 * gram = toz = apounce = apothecary_ounce
• troy_pound = 12 * toz = tlb = appound = apothecary_pound
• drachm = 60 * gram = apdram = apothecary_dram
• atomic_mass_unit = 1.660538782e-27 * kilogram = u = amu = dalton = Da
• scruple = 20 * gram
• bag = 94 * lb
• ton = 2000 * lb = short_ton

Force units

• newton = kilogram * meter / second ** 2 = N
• dyne = gram * centimeter / second ** 2 = dyn
• force_kilogram = g_0 * kilogram = kgf = kilogram_force = pond
• force_gram = g_0 * gram = gf = gram_force
• force_ounce = g_0 * ounce = ozf = ounce_force
• force_pound = g_0 * lb = lbf = pound_force
• force_ton = 2000 * force_pound = ton_force
• poundal = lb * feet / second ** 2 = pdl
• kip = 1000*lbf

Energy units

• joule = newton * meter = J
• erg = dyne * centimeter
• btu = 1.05505585262e3 * joule = Btu = BTU = british_thermal_unit
• eV = 1.60217653e-19 * J = electron_volt
• thm = 100000 * BTU = therm = EC_therm
• cal = 4.184 * joule = calorie = thermochemical_calorie
• international_steam_table_calorie = 4.1868 * joule
• ton_TNT = 4.184e9 * joule = tTNT
• US_therm = 1.054804e8 * joule
• E_h = 4.35974394e-18 * joule = hartree = hartree_energy
• watt_hour = watt * hour = Wh = watthour

Pressure units

• Hg = gravity * 13.59510 * gram / centimeter ** 3 = mercury = conventional_mercury
• mercury_60F = gravity * 13.5568 * gram / centimeter ** 3
• H2O = gravity * 1000 * kilogram / meter ** 3 = h2o = water = conventional_water
• water_4C = gravity * 999.972 * kilogram / meter ** 3 = water_39F
• water_60F = gravity * 999.001 * kilogram / m ** 3
• pascal = newton / meter ** 2 = Pa
• bar = 100000 * pascal
• atmosphere = 101325 * pascal = atm = standard_atmosphere
• technical_atmosphere = kilogram * gravity / centimeter ** 2 = at
• torr = atm / 760
• psi = pound * gravity / inch ** 2 = pound_force_per_square_inch
• ksi = kip / inch ** 2 = kip_per_square_inch
• barye = 0.1 * newton / meter ** 2 = barie = barad = barrie = baryd = Ba
• mmHg = millimeter * Hg = mm_Hg = millimeter_Hg = millimeter_Hg_0C
• cmHg = centimeter * Hg = cm_Hg = centimeter_Hg
• inHg = inch * Hg = in_Hg = inch_Hg = inch_Hg_32F
• inch_Hg_60F = inch * mercury_60F
• inch_H2O_39F = inch * water_39F
• inch_H2O_60F = inch * water_60F
• footH2O = ft * water
• cmH2O = centimeter * water
• foot_H2O = ft * water = ftH2O
• standard_liter_per_minute = 1.68875 * Pa * m ** 3 / s = slpm = slm
• Velocity units

Viscosity units

• poise = 1e-1 * Pa * second = P
• stokes = 1e-4 * meter ** 2 / second = St
• rhe = 10 / (Pa * s)

Power units

• watt = joule / second = W = volt_ampere = VA
• horsepower = 33000 * ft * lbf / min = hp = UK_horsepower = British_horsepower
• boiler_horsepower = 33475 * btu / hour
• metric_horsepower = 75 * force_kilogram * meter / second
• electric_horsepower = 746 * watt
• hydraulic_horsepower = 550 * feet * lbf / second
• refrigeration_ton = 12000 * btu / hour = ton_of_refrigeration

Substance units

• avogadro = 6.02214076e23
• substance_count = 1 / avogadro * mole = substcount = scount
• katal = mole / second = kat

Electromagnetic units

• esu = 1 * erg**0.5 * centimeter**0.5 = statcoulombs = statC = franklin = Fr
• esu_per_second = 1 * esu / second = statampere
• ampere_turn = 1 * A
• gilbert = 10 / (4 * pi ) * ampere_turn = G
• coulomb = ampere * second = C
• volt = joule / coulomb = V
• farad = coulomb / volt = F
• ohm = volt / ampere
• siemens = ampere / volt = S = mho
• weber = volt * second = Wb
• tesla = weber / meter ** 2 = T
• henry = weber / ampere = H
• elementary_charge = 1.602176487e-19 * coulomb = e
• chemical_faraday = 9.64957e4 * coulomb
• physical_faraday = 9.65219e4 * coulomb
• faraday = 96485.3399 * coulomb = C12_faraday
• gamma = 1e-9 * tesla
• gauss = 1e-4 * tesla
• maxwell = 1e-8 * weber = mx
• oersted = 1000 / (4 * pi) * A / m = Oe
• statfarad = 1.112650e-12 * farad = statF = stF
• stathenry = 8.987554e11 * henry = statH = stH
• statmho = 1.112650e-12 * siemens = statS = stS
• statohm = 8.987554e11 * ohm
• statvolt = 2.997925e2 * volt = statV = stV
• unit_pole = 1.256637e-7 * weber

Luminosity units

• lumen = candela * steradian = lm
• lux = lumen / meter **2 = lx

Angle Units

• turn = 2 * pi * radian = revolution = cycle = circle
• degree = pi / 180 * radian = deg = arcdeg = arcdegree = angular_degree
• arcminute = arcdeg / 60 = arcmin = arc_minute = angular_minute
• arcsecond = arcmin / 60 = arcsec = arc_second = angular_second
• steradian = radian ** 2 = sr

Information units

• byte = 8 * bit = Bo = octet
• baud = bit / second = Bd = bps

Textile units

• denier = gram / (9000 * meter)
• tex = gram/ (1000 * meter)
• dtex = decitex

Nuclear units

• Bq = Hz = becquerel
• curie = 3.7e10 * Bq = Ci
• rutherford = 1e6*Bq = rd = Rd
• Gy = joule / kilogram = gray = Sv = sievert
• rem = 1e-2 * sievert
• rads = 1e-2 * gray
• roentgen = 2.58e-4 * coulomb / kilogram = R

Constants

• pi = 3.141592653589793
• gstandard_gravity = 9.806650 * meter / second ** 2 = g_0 = g_n = gravity
• speed_of_light = 299792458 * meter / second = c

Decimal prefixes

• yocto- = 1e-24 = y-
• zepto- = 1e-21 = z-
• atto- = 1e-18 = a-
• femto- = 1e-15 = f-
• pico- = 1e-12 = p-
• nano- = 1e-9 = n-
• micro- = 1e-6 = u-
• milli- = 1e-3 = m-
• centi- = 1e-2 = c-
• deci- = 1e-1 = d-
• deca- = 1e+1 = da-
• hecto- = 1e2 = h-
• kilo- = 1e3 = k-
• mega- = 1e6 = M-
• giga- = 1e9 = G-
• tera- = 1e12 = T-
• peta- = 1e15 = P-
• exa- = 1e18 = E-
• zetta- = 1e21 = Z-
• yotta- = 1e24 = Y-

Binary prefixes

• kibi- = 2**10 = Ki-
• mebi- = 2**20 = Mi-
• gibi- = 2**30 = Gi-
• tebi- = 2**40 = Ti-
• pebi- = 2**50 = Pi-
• exbi- = 2**60 = Ei-
• zebi- = 2**70 = Zi-
• yobi- = 2**80 = Yi-