# Default Pint units definition file # Based on the International System of Units # Language: english # :copyright: 2013,2019 by Pint Authors, see AUTHORS for more details. # Syntax # ====== # Units # ----- # = [= ] [= ] [ = ] [...] # # The canonical name and aliases should be expressed in singular form. # Pint automatically deals with plurals built by adding 's' to the singular form; plural # forms that don't follow this rule should be instead explicitly listed as aliases. # # If a unit has no symbol and one wants to define aliases, then the symbol should be # conventionally set to _. # # Example: # millennium = 1e3 * year = _ = millennia # # # Prefixes # -------- # - = [= ] [= ] [ = ] [...] # # Example: # deca- = 1e+1 = da- = deka- # # # Derived dimensions # ------------------ # [dimension name] = # # Example: # [density] = [mass] / [volume] # # Note that primary dimensions don't need to be declared; they can be # defined for the first time in a unit definition. # E.g. see below `meter = [length]` # # # Additional aliases # ------------------ # @alias = [ = ] [...] # # Used to add aliases to already existing unit definitions. # Particularly useful when one wants to enrich definitions # from defaults_en.txt with custom aliases. # # Example: # @alias meter = my_meter # See also: https://pint.readthedocs.io/en/latest/defining.html @defaults group = international system = mks @end #### PREFIXES #### # decimal prefixes quecto- = 1e-30 = q- ronto- = 1e-27 = r- yocto- = 1e-24 = y- zepto- = 1e-21 = z- atto- = 1e-18 = a- femto- = 1e-15 = f- pico- = 1e-12 = p- nano- = 1e-9 = n- # The micro (U+00B5) and Greek mu (U+03BC) are both valid prefixes, # and they often use the same glyph. micro- = 1e-6 = µ- = μ- = u- milli- = 1e-3 = m- centi- = 1e-2 = c- deci- = 1e-1 = d- deca- = 1e+1 = da- = deka- 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- ronna- = 1e27 = R- quetta- = 1e30 = Q- # 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- # extra_prefixes semi- = 0.5 = _ = demi- sesqui- = 1.5 #### BASE UNITS #### meter = [length] = m = metre second = [time] = s = sec ampere = [current] = A = amp candela = [luminosity] = cd = candle gram = [mass] = g mole = [substance] = mol kelvin = [temperature]; offset: 0 = K = degK = °K = degree_Kelvin = degreeK # older names supported for compatibility radian = [] = rad bit = [] count = [] #### CONSTANTS #### @import constants_en.txt #### UNITS #### # Common and less common, grouped by quantity. # Conversion factors are exact (except when noted), # although floating-point conversion may introduce inaccuracies # Angle turn = 2 * π * radian = _ = revolution = cycle = circle degree = π / 180 * radian = deg = arcdeg = arcdegree = angular_degree arcminute = degree / 60 = arcmin = arc_minute = angular_minute arcsecond = arcminute / 60 = arcsec = arc_second = angular_second milliarcsecond = 1e-3 * arcsecond = mas grade = π / 200 * radian = grad = gon mil = π / 32000 * radian # Solid angle steradian = radian ** 2 = sr square_degree = (π / 180) ** 2 * sr = sq_deg = sqdeg # Information baud = bit / second = Bd = bps byte = 8 * bit = B = octet # byte = 8 * bit = _ = octet ## NOTE: B (byte) symbol can conflict with Bell # Ratios percent = 0.01 = % ppm = 1e-6 # Length angstrom = 1e-10 * meter = Å = ångström = Å micron = micrometer = µ = μ fermi = femtometer = fm light_year = speed_of_light * julian_year = ly = lightyear astronomical_unit = 149597870700 * meter = au # since Aug 2012 parsec = 1 / tansec * astronomical_unit = pc nautical_mile = 1852 * meter = nmi bohr = hbar / (alpha * m_e * c) = a_0 = a0 = bohr_radius = atomic_unit_of_length = a_u_length x_unit_Cu = K_alpha_Cu_d_220 * d_220 / 1537.4 = Xu_Cu x_unit_Mo = K_alpha_Mo_d_220 * d_220 / 707.831 = Xu_Mo angstrom_star = K_alpha_W_d_220 * d_220 / 0.2090100 = Å_star planck_length = (hbar * gravitational_constant / c ** 3) ** 0.5 # Mass metric_ton = 1e3 * kilogram = t = tonne unified_atomic_mass_unit = atomic_mass_constant = u = amu dalton = atomic_mass_constant = Da grain = 64.79891 * milligram = gr gamma_mass = microgram carat = 200 * milligram = ct = karat planck_mass = (hbar * c / gravitational_constant) ** 0.5 # Time minute = 60 * second = min hour = 60 * minute = h = hr day = 24 * hour = d week = 7 * day fortnight = 2 * week year = 365.25 * day = a = yr = julian_year month = year / 12 # decade = 10 * year ## NOTE: decade [time] can conflict with decade [dimensionless] century = 100 * year = _ = centuries millennium = 1e3 * year = _ = millennia eon = 1e9 * year shake = 1e-8 * second svedberg = 1e-13 * second atomic_unit_of_time = hbar / E_h = a_u_time gregorian_year = 365.2425 * day sidereal_year = 365.256363004 * day # approximate, as of J2000 epoch tropical_year = 365.242190402 * day # approximate, as of J2000 epoch common_year = 365 * day leap_year = 366 * day sidereal_day = day / 1.00273790935079524 # approximate sidereal_month = 27.32166155 * day # approximate tropical_month = 27.321582 * day # approximate synodic_month = 29.530589 * day = _ = lunar_month # approximate planck_time = (hbar * gravitational_constant / c ** 5) ** 0.5 # Temperature degree_Celsius = kelvin; offset: 273.15 = °C = celsius = degC = degreeC degree_Rankine = 5 / 9 * kelvin; offset: 0 = °R = rankine = degR = degreeR degree_Fahrenheit = 5 / 9 * kelvin; offset: 233.15 + 200 / 9 = °F = fahrenheit = degF = degreeF degree_Reaumur = 4 / 5 * kelvin; offset: 273.15 = °Re = reaumur = degRe = degreeRe = degree_Réaumur = réaumur atomic_unit_of_temperature = E_h / k = a_u_temp planck_temperature = (hbar * c ** 5 / gravitational_constant / k ** 2) ** 0.5 # Area [area] = [length] ** 2 are = 100 * meter ** 2 barn = 1e-28 * meter ** 2 = b darcy = centipoise * centimeter ** 2 / (second * atmosphere) hectare = 100 * are = ha # Volume [volume] = [length] ** 3 liter = decimeter ** 3 = l = L = litre cubic_centimeter = centimeter ** 3 = cc lambda = microliter = λ stere = meter ** 3 # Frequency [frequency] = 1 / [time] hertz = 1 / second = Hz revolutions_per_minute = revolution / minute = rpm revolutions_per_second = revolution / second = rps counts_per_second = count / second = cps # Wavenumber [wavenumber] = 1 / [length] reciprocal_centimeter = 1 / cm = cm_1 = kayser # Velocity [velocity] = [length] / [time] [speed] = [velocity] knot = nautical_mile / hour = kt = knot_international = international_knot mile_per_hour = mile / hour = mph = MPH kilometer_per_hour = kilometer / hour = kph = KPH kilometer_per_second = kilometer / second = kps meter_per_second = meter / second = mps foot_per_second = foot / second = fps # Volumetric Flow Rate [volumetric_flow_rate] = [volume] / [time] sverdrup = 1e6 * meter ** 3 / second = sv # Acceleration [acceleration] = [velocity] / [time] galileo = centimeter / second ** 2 = Gal # Force [force] = [mass] * [acceleration] 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_metric_ton = g_0 * metric_ton = tf = metric_ton_force = force_t = t_force atomic_unit_of_force = E_h / a_0 = a_u_force # Energy [energy] = [force] * [length] joule = newton * meter = J erg = dyne * centimeter watt_hour = watt * hour = Wh = watthour electron_volt = e * volt = eV rydberg = ℎ * c * R_inf = Ry hartree = 2 * rydberg = E_h = Eh = hartree_energy = atomic_unit_of_energy = a_u_energy calorie = 4.184 * joule = cal = thermochemical_calorie = cal_th international_calorie = 4.1868 * joule = cal_it = international_steam_table_calorie fifteen_degree_calorie = 4.1855 * joule = cal_15 british_thermal_unit = 1055.056 * joule = Btu = BTU = Btu_iso international_british_thermal_unit = 1e3 * pound / kilogram * degR / kelvin * international_calorie = Btu_it thermochemical_british_thermal_unit = 1e3 * pound / kilogram * degR / kelvin * calorie = Btu_th quadrillion_Btu = 1e15 * Btu = quad therm = 1e5 * Btu = thm = EC_therm US_therm = 1.054804e8 * joule # approximate, no exact definition ton_TNT = 1e9 * calorie = tTNT tonne_of_oil_equivalent = 1e10 * international_calorie = toe atmosphere_liter = atmosphere * liter = atm_l # Power [power] = [energy] / [time] watt = joule / second = W volt_ampere = volt * ampere = VA horsepower = 550 * foot * force_pound / second = hp = UK_horsepower = hydraulic_horsepower boiler_horsepower = 33475 * Btu / hour # unclear which Btu metric_horsepower = 75 * force_kilogram * meter / second electrical_horsepower = 746 * watt refrigeration_ton = 12e3 * Btu / hour = _ = ton_of_refrigeration # approximate, no exact definition cooling_tower_ton = 1.25 * refrigeration_ton # approximate, no exact definition standard_liter_per_minute = atmosphere * liter / minute = slpm = slm conventional_watt_90 = K_J90 ** 2 * R_K90 / (K_J ** 2 * R_K) * watt = W_90 # Momentum [momentum] = [length] * [mass] / [time] # Density (as auxiliary for pressure) [density] = [mass] / [volume] mercury = 13.5951 * kilogram / liter = Hg = Hg_0C = Hg_32F = conventional_mercury water = 1.0 * kilogram / liter = H2O = conventional_water mercury_60F = 13.5568 * kilogram / liter = Hg_60F # approximate water_39F = 0.999972 * kilogram / liter = water_4C # approximate water_60F = 0.999001 * kilogram / liter # approximate # Pressure [pressure] = [force] / [area] pascal = newton / meter ** 2 = Pa barye = dyne / centimeter ** 2 = Ba = barie = barad = barrie = baryd bar = 1e5 * pascal technical_atmosphere = kilogram * g_0 / centimeter ** 2 = at torr = atm / 760 pound_force_per_square_inch = force_pound / inch ** 2 = psi kip_per_square_inch = kip / inch ** 2 = ksi millimeter_Hg = millimeter * Hg * g_0 = mmHg = mm_Hg = millimeter_Hg_0C centimeter_Hg = centimeter * Hg * g_0 = cmHg = cm_Hg = centimeter_Hg_0C inch_Hg = inch * Hg * g_0 = inHg = in_Hg = inch_Hg_32F inch_Hg_60F = inch * Hg_60F * g_0 inch_H2O_39F = inch * water_39F * g_0 inch_H2O_60F = inch * water_60F * g_0 foot_H2O = foot * water * g_0 = ftH2O = feet_H2O centimeter_H2O = centimeter * water * g_0 = cmH2O = cm_H2O sound_pressure_level = 20e-6 * pascal = SPL # Torque [torque] = [force] * [length] foot_pound = foot * force_pound = ft_lb = footpound # Viscosity [viscosity] = [pressure] * [time] poise = 0.1 * Pa * second = P reyn = psi * second # Kinematic viscosity [kinematic_viscosity] = [area] / [time] stokes = centimeter ** 2 / second = St # Fluidity [fluidity] = 1 / [viscosity] rhe = 1 / poise # Amount of substance particle = 1 / N_A = _ = molec = molecule # Concentration [concentration] = [substance] / [volume] molar = mole / liter = M # Catalytic activity [activity] = [substance] / [time] katal = mole / second = kat enzyme_unit = micromole / minute = U = enzymeunit # Entropy [entropy] = [energy] / [temperature] clausius = calorie / kelvin = Cl # Molar entropy [molar_entropy] = [entropy] / [substance] entropy_unit = calorie / kelvin / mole = eu # Radiation becquerel = counts_per_second = Bq curie = 3.7e10 * becquerel = Ci rutherford = 1e6 * becquerel = Rd gray = joule / kilogram = Gy sievert = joule / kilogram = Sv rads = 0.01 * gray rem = 0.01 * sievert roentgen = 2.58e-4 * coulomb / kilogram = _ = röntgen # approximate, depends on medium # Heat transimission [heat_transmission] = [energy] / [area] peak_sun_hour = 1e3 * watt_hour / meter ** 2 = PSH langley = thermochemical_calorie / centimeter ** 2 = Ly # Luminance [luminance] = [luminosity] / [area] nit = candela / meter ** 2 stilb = candela / centimeter ** 2 lambert = 1 / π * candela / centimeter ** 2 # Luminous flux [luminous_flux] = [luminosity] lumen = candela * steradian = lm # Illuminance [illuminance] = [luminous_flux] / [area] lux = lumen / meter ** 2 = lx # Intensity [intensity] = [power] / [area] atomic_unit_of_intensity = 0.5 * ε_0 * c * atomic_unit_of_electric_field ** 2 = a_u_intensity # Current biot = 10 * ampere = Bi abampere = biot = abA atomic_unit_of_current = e / atomic_unit_of_time = a_u_current mean_international_ampere = mean_international_volt / mean_international_ohm = A_it US_international_ampere = US_international_volt / US_international_ohm = A_US conventional_ampere_90 = K_J90 * R_K90 / (K_J * R_K) * ampere = A_90 planck_current = (c ** 6 / gravitational_constant / k_C) ** 0.5 # Charge [charge] = [current] * [time] coulomb = ampere * second = C abcoulomb = 10 * C = abC faraday = e * N_A * mole conventional_coulomb_90 = K_J90 * R_K90 / (K_J * R_K) * coulomb = C_90 ampere_hour = ampere * hour = Ah # Electric potential [electric_potential] = [energy] / [charge] volt = joule / coulomb = V abvolt = 1e-8 * volt = abV mean_international_volt = 1.00034 * volt = V_it # approximate US_international_volt = 1.00033 * volt = V_US # approximate conventional_volt_90 = K_J90 / K_J * volt = V_90 # Electric field [electric_field] = [electric_potential] / [length] atomic_unit_of_electric_field = e * k_C / a_0 ** 2 = a_u_electric_field # Electric displacement field [electric_displacement_field] = [charge] / [area] # Reduced electric field [reduced_electric_field] = [electric_field] * [area] townsend = 1e-21 * V * m^2 = Td # Resistance [resistance] = [electric_potential] / [current] ohm = volt / ampere = Ω abohm = 1e-9 * ohm = abΩ mean_international_ohm = 1.00049 * ohm = Ω_it = ohm_it # approximate US_international_ohm = 1.000495 * ohm = Ω_US = ohm_US # approximate conventional_ohm_90 = R_K / R_K90 * ohm = Ω_90 = ohm_90 # Resistivity [resistivity] = [resistance] * [length] # Conductance [conductance] = [current] / [electric_potential] siemens = ampere / volt = S = mho absiemens = 1e9 * siemens = abS = abmho # Capacitance [capacitance] = [charge] / [electric_potential] farad = coulomb / volt = F abfarad = 1e9 * farad = abF conventional_farad_90 = R_K90 / R_K * farad = F_90 # Magnetic flux [magnetic_flux] = [electric_potential] * [time] weber = volt * second = Wb unit_pole = µ_0 * biot * centimeter # Inductance [inductance] = [magnetic_flux] / [current] henry = weber / ampere = H abhenry = 1e-9 * henry = abH conventional_henry_90 = R_K / R_K90 * henry = H_90 # Magnetic field [magnetic_field] = [magnetic_flux] / [area] tesla = weber / meter ** 2 = T gamma = 1e-9 * tesla = γ # Magnetomotive force [magnetomotive_force] = [current] ampere_turn = ampere = At biot_turn = biot gilbert = 1 / (4 * π) * biot_turn = Gb # Magnetic field strength [magnetic_field_strength] = [current] / [length] # Electric dipole moment [electric_dipole] = [charge] * [length] debye = 1e-9 / ζ * coulomb * angstrom = D # formally 1 D = 1e-10 Fr*Å, but we generally want to use it outside the Gaussian context # Electric quadrupole moment [electric_quadrupole] = [charge] * [area] buckingham = debye * angstrom # Magnetic dipole moment [magnetic_dipole] = [current] * [area] bohr_magneton = e * hbar / (2 * m_e) = µ_B = mu_B nuclear_magneton = e * hbar / (2 * m_p) = µ_N = mu_N # Logaritmic Unit Definition # Unit = scale; logbase; logfactor # x_dB = [logfactor] * log( x_lin / [scale] ) / log( [logbase] ) # Logaritmic Units of dimensionless quantity: [ https://en.wikipedia.org/wiki/Level_(logarithmic_quantity) ] decibelmilliwatt = 1e-3 watt; logbase: 10; logfactor: 10 = dBm decibelmicrowatt = 1e-6 watt; logbase: 10; logfactor: 10 = dBu decibel = 1 ; logbase: 10; logfactor: 10 = dB # bell = 1 ; logbase: 10; logfactor: = B ## NOTE: B (Bell) symbol conflicts with byte decade = 1 ; logbase: 10; logfactor: 1 ## NOTE: decade [time] can conflict with decade [dimensionless] octave = 1 ; logbase: 2; logfactor: 1 = oct neper = 1 ; logbase: 2.71828182845904523536028747135266249775724709369995; logfactor: 0.5 = Np # neper = 1 ; logbase: eulers_number; logfactor: 0.5 = Np #### UNIT GROUPS #### # Mostly for length, area, volume, mass, force # (customary or specialized units) @group USCSLengthInternational thou = 1e-3 * inch = th = mil_length inch = yard / 36 = in = international_inch = inches = international_inches hand = 4 * inch foot = yard / 3 = ft = international_foot = feet = international_feet yard = 0.9144 * meter = yd = international_yard # since Jul 1959 mile = 1760 * yard = mi = international_mile circular_mil = π / 4 * mil_length ** 2 = cmil square_inch = inch ** 2 = sq_in = square_inches square_foot = foot ** 2 = sq_ft = square_feet square_yard = yard ** 2 = sq_yd square_mile = mile ** 2 = sq_mi cubic_inch = in ** 3 = cu_in cubic_foot = ft ** 3 = cu_ft = cubic_feet cubic_yard = yd ** 3 = cu_yd @end @group USCSLengthSurvey link = 1e-2 * chain = li = survey_link survey_foot = 1200 / 3937 * meter = sft fathom = 6 * survey_foot rod = 16.5 * survey_foot = rd = pole = perch chain = 4 * rod furlong = 40 * rod = fur cables_length = 120 * fathom survey_mile = 5280 * survey_foot = smi = us_statute_mile league = 3 * survey_mile square_rod = rod ** 2 = sq_rod = sq_pole = sq_perch acre = 10 * chain ** 2 square_survey_mile = survey_mile ** 2 = _ = section square_league = league ** 2 acre_foot = acre * survey_foot = _ = acre_feet @end @group USCSDryVolume dry_pint = bushel / 64 = dpi = US_dry_pint dry_quart = bushel / 32 = dqt = US_dry_quart dry_gallon = bushel / 8 = dgal = US_dry_gallon peck = bushel / 4 = pk bushel = 2150.42 cubic_inch = bu dry_barrel = 7056 cubic_inch = _ = US_dry_barrel board_foot = ft * ft * in = FBM = board_feet = BF = BDFT = super_foot = superficial_foot = super_feet = superficial_feet @end @group USCSLiquidVolume minim = pint / 7680 fluid_dram = pint / 128 = fldr = fluidram = US_fluid_dram = US_liquid_dram fluid_ounce = pint / 16 = floz = US_fluid_ounce = US_liquid_ounce gill = pint / 4 = gi = liquid_gill = US_liquid_gill pint = quart / 2 = pt = liquid_pint = US_pint fifth = gallon / 5 = _ = US_liquid_fifth quart = gallon / 4 = qt = liquid_quart = US_liquid_quart gallon = 231 * cubic_inch = gal = liquid_gallon = US_liquid_gallon @end @group USCSVolumeOther teaspoon = fluid_ounce / 6 = tsp tablespoon = fluid_ounce / 2 = tbsp shot = 3 * tablespoon = jig = US_shot cup = pint / 2 = cp = liquid_cup = US_liquid_cup barrel = 31.5 * gallon = bbl oil_barrel = 42 * gallon = oil_bbl beer_barrel = 31 * gallon = beer_bbl hogshead = 63 * gallon @end @group Avoirdupois dram = pound / 256 = dr = avoirdupois_dram = avdp_dram = drachm ounce = pound / 16 = oz = avoirdupois_ounce = avdp_ounce pound = 7e3 * grain = lb = avoirdupois_pound = avdp_pound stone = 14 * pound quarter = 28 * stone bag = 94 * pound hundredweight = 100 * pound = cwt = short_hundredweight long_hundredweight = 112 * pound ton = 2e3 * pound = _ = short_ton long_ton = 2240 * pound slug = g_0 * pound * second ** 2 / foot slinch = g_0 * pound * second ** 2 / inch = blob = slugette force_ounce = g_0 * ounce = ozf = ounce_force force_pound = g_0 * pound = lbf = pound_force force_ton = g_0 * ton = _ = ton_force = force_short_ton = short_ton_force force_long_ton = g_0 * long_ton = _ = long_ton_force kip = 1e3 * force_pound poundal = pound * foot / second ** 2 = pdl @end @group AvoirdupoisUK using Avoirdupois UK_hundredweight = long_hundredweight = UK_cwt UK_ton = long_ton UK_force_ton = force_long_ton = _ = UK_ton_force @end @group AvoirdupoisUS using Avoirdupois US_hundredweight = hundredweight = US_cwt US_ton = ton US_force_ton = force_ton = _ = US_ton_force @end @group Troy pennyweight = 24 * grain = dwt troy_ounce = 480 * grain = toz = ozt troy_pound = 12 * troy_ounce = tlb = lbt @end @group Apothecary scruple = 20 * grain apothecary_dram = 3 * scruple = ap_dr apothecary_ounce = 8 * apothecary_dram = ap_oz apothecary_pound = 12 * apothecary_ounce = ap_lb @end @group ImperialVolume imperial_minim = imperial_fluid_ounce / 480 imperial_fluid_scruple = imperial_fluid_ounce / 24 imperial_fluid_drachm = imperial_fluid_ounce / 8 = imperial_fldr = imperial_fluid_dram imperial_fluid_ounce = imperial_pint / 20 = imperial_floz = UK_fluid_ounce imperial_gill = imperial_pint / 4 = imperial_gi = UK_gill imperial_cup = imperial_pint / 2 = imperial_cp = UK_cup imperial_pint = imperial_gallon / 8 = imperial_pt = UK_pint imperial_quart = imperial_gallon / 4 = imperial_qt = UK_quart imperial_gallon = 4.54609 * liter = imperial_gal = UK_gallon imperial_peck = 2 * imperial_gallon = imperial_pk = UK_pk imperial_bushel = 8 * imperial_gallon = imperial_bu = UK_bushel imperial_barrel = 36 * imperial_gallon = imperial_bbl = UK_bbl @end @group Printer pica = inch / 6 = _ = printers_pica point = pica / 12 = pp = printers_point = big_point = bp didot = 1 / 2660 * m cicero = 12 * didot tex_point = inch / 72.27 tex_pica = 12 * tex_point tex_didot = 1238 / 1157 * tex_point tex_cicero = 12 * tex_didot scaled_point = tex_point / 65536 css_pixel = inch / 96 = px pixel = [printing_unit] = _ = dot = pel = picture_element pixels_per_centimeter = pixel / cm = PPCM pixels_per_inch = pixel / inch = dots_per_inch = PPI = ppi = DPI = printers_dpi bits_per_pixel = bit / pixel = bpp @end @group Textile tex = gram / kilometer = Tt dtex = decitex denier = gram / (9 * kilometer) = den jute = pound / (14400 * yard) = Tj aberdeen = jute = Ta RKM = gf / tex number_english = 840 * yard / pound = Ne = NeC = ECC number_meter = kilometer / kilogram = Nm @end #### CGS ELECTROMAGNETIC UNITS #### # === Gaussian system of units === @group Gaussian franklin = erg ** 0.5 * centimeter ** 0.5 = Fr = statcoulomb = statC = esu statvolt = erg / franklin = statV statampere = franklin / second = statA gauss = dyne / franklin = G maxwell = gauss * centimeter ** 2 = Mx oersted = dyne / maxwell = Oe = ørsted statohm = statvolt / statampere = statΩ statfarad = franklin / statvolt = statF statmho = statampere / statvolt @end # Note this system is not commensurate with SI, as ε_0 and µ_0 disappear; # some quantities with different dimensions in SI have the same # dimensions in the Gaussian system (e.g. [Mx] = [Fr], but [Wb] != [C]), # and therefore the conversion factors depend on the context (not in pint sense) [gaussian_charge] = [length] ** 1.5 * [mass] ** 0.5 / [time] [gaussian_current] = [gaussian_charge] / [time] [gaussian_electric_potential] = [gaussian_charge] / [length] [gaussian_electric_field] = [gaussian_electric_potential] / [length] [gaussian_electric_displacement_field] = [gaussian_charge] / [area] [gaussian_electric_flux] = [gaussian_charge] [gaussian_electric_dipole] = [gaussian_charge] * [length] [gaussian_electric_quadrupole] = [gaussian_charge] * [area] [gaussian_magnetic_field] = [force] / [gaussian_charge] [gaussian_magnetic_field_strength] = [gaussian_magnetic_field] [gaussian_magnetic_flux] = [gaussian_magnetic_field] * [area] [gaussian_magnetic_dipole] = [energy] / [gaussian_magnetic_field] [gaussian_resistance] = [gaussian_electric_potential] / [gaussian_current] [gaussian_resistivity] = [gaussian_resistance] * [length] [gaussian_capacitance] = [gaussian_charge] / [gaussian_electric_potential] [gaussian_inductance] = [gaussian_electric_potential] * [time] / [gaussian_current] [gaussian_conductance] = [gaussian_current] / [gaussian_electric_potential] @context Gaussian = Gau [gaussian_charge] -> [charge]: value / k_C ** 0.5 [charge] -> [gaussian_charge]: value * k_C ** 0.5 [gaussian_current] -> [current]: value / k_C ** 0.5 [current] -> [gaussian_current]: value * k_C ** 0.5 [gaussian_electric_potential] -> [electric_potential]: value * k_C ** 0.5 [electric_potential] -> [gaussian_electric_potential]: value / k_C ** 0.5 [gaussian_electric_field] -> [electric_field]: value * k_C ** 0.5 [electric_field] -> [gaussian_electric_field]: value / k_C ** 0.5 [gaussian_electric_displacement_field] -> [electric_displacement_field]: value / (4 * π / ε_0) ** 0.5 [electric_displacement_field] -> [gaussian_electric_displacement_field]: value * (4 * π / ε_0) ** 0.5 [gaussian_electric_dipole] -> [electric_dipole]: value / k_C ** 0.5 [electric_dipole] -> [gaussian_electric_dipole]: value * k_C ** 0.5 [gaussian_electric_quadrupole] -> [electric_quadrupole]: value / k_C ** 0.5 [electric_quadrupole] -> [gaussian_electric_quadrupole]: value * k_C ** 0.5 [gaussian_magnetic_field] -> [magnetic_field]: value / (4 * π / µ_0) ** 0.5 [magnetic_field] -> [gaussian_magnetic_field]: value * (4 * π / µ_0) ** 0.5 [gaussian_magnetic_flux] -> [magnetic_flux]: value / (4 * π / µ_0) ** 0.5 [magnetic_flux] -> [gaussian_magnetic_flux]: value * (4 * π / µ_0) ** 0.5 [gaussian_magnetic_field_strength] -> [magnetic_field_strength]: value / (4 * π * µ_0) ** 0.5 [magnetic_field_strength] -> [gaussian_magnetic_field_strength]: value * (4 * π * µ_0) ** 0.5 [gaussian_magnetic_dipole] -> [magnetic_dipole]: value * (4 * π / µ_0) ** 0.5 [magnetic_dipole] -> [gaussian_magnetic_dipole]: value / (4 * π / µ_0) ** 0.5 [gaussian_resistance] -> [resistance]: value * k_C [resistance] -> [gaussian_resistance]: value / k_C [gaussian_resistivity] -> [resistivity]: value * k_C [resistivity] -> [gaussian_resistivity]: value / k_C [gaussian_capacitance] -> [capacitance]: value / k_C [capacitance] -> [gaussian_capacitance]: value * k_C [gaussian_inductance] -> [inductance]: value * k_C [inductance] -> [gaussian_inductance]: value / k_C [gaussian_conductance] -> [conductance]: value / k_C [conductance] -> [gaussian_conductance]: value * k_C @end # === ESU system of units === # (where different from Gaussian) # See note for Gaussian system too @group ESU using Gaussian statweber = statvolt * second = statWb stattesla = statweber / centimeter ** 2 = statT stathenry = statweber / statampere = statH @end [esu_charge] = [length] ** 1.5 * [mass] ** 0.5 / [time] [esu_current] = [esu_charge] / [time] [esu_electric_potential] = [esu_charge] / [length] [esu_magnetic_flux] = [esu_electric_potential] * [time] [esu_magnetic_field] = [esu_magnetic_flux] / [area] [esu_magnetic_field_strength] = [esu_current] / [length] [esu_magnetic_dipole] = [esu_current] * [area] @context ESU = esu [esu_magnetic_field] -> [magnetic_field]: value * k_C ** 0.5 [magnetic_field] -> [esu_magnetic_field]: value / k_C ** 0.5 [esu_magnetic_flux] -> [magnetic_flux]: value * k_C ** 0.5 [magnetic_flux] -> [esu_magnetic_flux]: value / k_C ** 0.5 [esu_magnetic_field_strength] -> [magnetic_field_strength]: value / (4 * π / ε_0) ** 0.5 [magnetic_field_strength] -> [esu_magnetic_field_strength]: value * (4 * π / ε_0) ** 0.5 [esu_magnetic_dipole] -> [magnetic_dipole]: value / k_C ** 0.5 [magnetic_dipole] -> [esu_magnetic_dipole]: value * k_C ** 0.5 @end #### CONVERSION CONTEXTS #### @context(n=1) spectroscopy = sp # n index of refraction of the medium. [length] <-> [frequency]: speed_of_light / n / value [frequency] -> [energy]: planck_constant * value [energy] -> [frequency]: value / planck_constant # allow wavenumber / kayser [wavenumber] <-> [length]: 1 / value @end @context boltzmann [temperature] -> [energy]: boltzmann_constant * value [energy] -> [temperature]: value / boltzmann_constant @end @context energy [energy] -> [energy] / [substance]: value * N_A [energy] / [substance] -> [energy]: value / N_A [energy] -> [mass]: value / c ** 2 [mass] -> [energy]: value * c ** 2 @end @context(mw=0,volume=0,solvent_mass=0) chemistry = chem # mw is the molecular weight of the species # volume is the volume of the solution # solvent_mass is the mass of solvent in the solution # moles -> mass require the molecular weight [substance] -> [mass]: value * mw [mass] -> [substance]: value / mw # moles/volume -> mass/volume and moles/mass -> mass/mass # require the molecular weight [substance] / [volume] -> [mass] / [volume]: value * mw [mass] / [volume] -> [substance] / [volume]: value / mw [substance] / [mass] -> [mass] / [mass]: value * mw [mass] / [mass] -> [substance] / [mass]: value / mw # moles/volume -> moles requires the solution volume [substance] / [volume] -> [substance]: value * volume [substance] -> [substance] / [volume]: value / volume # moles/mass -> moles requires the solvent (usually water) mass [substance] / [mass] -> [substance]: value * solvent_mass [substance] -> [substance] / [mass]: value / solvent_mass # moles/mass -> moles/volume require the solvent mass and the volume [substance] / [mass] -> [substance]/[volume]: value * solvent_mass / volume [substance] / [volume] -> [substance] / [mass]: value / solvent_mass * volume @end @context textile # Allow switching between Direct count system (i.e. tex) and # Indirect count system (i.e. Ne, Nm) [mass] / [length] <-> [length] / [mass]: 1 / value @end #### SYSTEMS OF UNITS #### @system SI second meter kilogram ampere kelvin mole candela @end @system mks using international meter kilogram second @end @system cgs using international, Gaussian, ESU centimeter gram second @end @system atomic using international # based on unit m_e, e, hbar, k_C, k bohr: meter electron_mass: gram atomic_unit_of_time: second atomic_unit_of_current: ampere atomic_unit_of_temperature: kelvin @end @system Planck using international # based on unit c, gravitational_constant, hbar, k_C, k planck_length: meter planck_mass: gram planck_time: second planck_current: ampere planck_temperature: kelvin @end @system imperial using ImperialVolume, USCSLengthInternational, AvoirdupoisUK yard pound @end @system US using USCSLiquidVolume, USCSDryVolume, USCSVolumeOther, USCSLengthInternational, USCSLengthSurvey, AvoirdupoisUS yard pound @end