# # Copyright (c) 1998 The Regenstrief Institute. All rights reserved. # # This program is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation; either version 2 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program; if not, write to the Free Software # Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. # # Author: Gunther Schadow. # # $Id: comprehensive.units,v 1.8 1998/08/13 02:49:19 schadow Exp schadow $ # ####################################################################### # # Gunther Schadow's Comprehensive Table of Units # # Includes customary, SI, ISO 1000, and other units. # # Note: None of the currently available standards is useable in its # entirety. They are all incomplete, they are all inconsistent and # contain conflicts. This definition borrows from ISO 2955 and ANSI # X3.50 while trying to be more complete and consistent. # # All customary units are enclosed in square brackets. This helps # overcome conflicts and ``stigmatizes'' them such as to encurage use # of metric alternatives. Note that this table provides more customary # units to be used than ANSI X3.50 or HL7! # # ASCII character set, no Omega, degree or mu # case sensitive # # PREFICES # prefix Y 1E24 # yotta prefix Z 1E21 # zetta prefix E 1E18 # exa prefix P 1E15 # peta prefix T 1E12 # tera prefix G 1E9 # giga prefix M 1E6 # mega prefix k 1E3 # kilo prefix h 1E2 # hecto prefix da 1E1 # deka prefix d 1E-1 # deci prefix c 1E-2 # centi prefix m 1E-3 # milli prefix u 1E-6 # micro prefix n 1E-9 # nano prefix p 1E-12 # pico prefix f 1E-15 # fempto prefix a 1E-18 # atto prefix z 1E-21 # zepto prefix y 1E-24 # yocto # # BASE UNITS # # We use a non-SI base here as described in the article. Essentially # we drop the mole but admit the radian. # dimensions 7 base m # length meter base rad # plane angle radian base s # time second base g # mass gram base K # temperature Kelvin base C # electric charge Coulomb base cd # luminous intensity candela # UNITS WHOSE DIMENSION IS 1 10* = 10 1 nonmetric # ten, for arbitrary powers of 10 % = 1 10*-2 nonmetric # percent, i.e. one hundredth [pi] = 3.1415926535897932384626433832795028841971693993751058209749445923 1 nonmetric # # SI UNITS WITH THEIR OWN NAME (FROM ISO 1000) # sr = 1 rad2 metric # solid angle streadian Hz = 1 s-1 metric # frequency Herz N = 1 kg.m/s2 metric # force Newton Pa = 1 N/m2 metric # pressure, stress Pascal J = 1 N.m metric # energy, work, Joule # quantity of heat W = 1 J/s metric # power Watt A = 1 C/s metric # electric charge Coulomb # quantity of electricity V = 1 J/C metric # electric charge Volt # potential difference # tension, electromotive force F = 1 C/V metric # electric capacitance Farad Ohm = 1 V/A metric # electric resistance Ohm S = 1 Ohm-1 metric # electric conductance Siemens Wb = 1 V.s metric # flux of magnetic induction Weber # magnetic flux Cel = cel(1 K) nonmetric # Celsius temperature degree Celsius T = 1 Wb/m2 metric # magnetic flux density Tesla # magnetic induction H = 1 Wb/A metric # inductance Henry lm = 1 cd.sr metric # luminous flux lumen lx = 1 lm/m2 metric # illuminance lux Bq = 1 s-1 metric # activity (of a radionuclide) Becquerel Gy = 1 J/kg metric # absorbed dose, specific Gray # energy imparted, kerma, # absorbed dose index Sv = 1 J/kg metric # dose equivalent Sievert # # OTHER UNITS FROM ISO 1000, ISO 2955, AND ANSI X3.50 # deg = 2 [pi].rad/360 nonmetric# plane angle degree ' = 1 deg/60 nonmetric # plane angle minute '' = 1 '/60 nonmetric # plane angle second gon = .9 deg nonmetric # plane angle grade) l = 1 dm3 metric # volume litre(liter) L = 1 l metric [ar] = 100 m2 nonmetric # area are [har] = 100 [ar] nonmetric # area are min = 60 s nonmetric # time minute h = 60 min nonmetric # time hour d = 24 h nonmetric # time day a_s = 365.2422 d nonmetric # time year (solar) a_c = 365.25 d nonmetric # time year (mean calendar) # alias for year (even the astronomic light year is defined on the calendar year!) a = 1 a_c wk = 7 d nonmetric # mass week mo = 1 a/12 nonmetric # mass month(2) t = 1e3 kg metric # mass tonne bar = 10e5 Pa metric # pressure of fluid bar e = 1.60217733e-19 C metric # electrical charge elementary charge eV = 1 e.V metric # energy electronvolt u = 1.6605655e-24 g metric # mass of an atom atomic mass [AU] = 149597.870 Mm nonmetric # length astronomic unit [pc] = 3.085678E16 m nonmetric # length parsec # # 1) Assuming a mean solar year not a mean calendar year, which would # be 365.25 days. # #10) Assuming a mean calendar month, not a lunar month which would be # 29 days, 12 hours and 44 minutes. # # ``Natural units'', i.e. physical constants # [c] = 299792458 m/s metric # velocity of light [h] = 6.6260755E-34 J.s metric # Planck constant [g] = 9.80665 m/s2 metric # acceleration of free fall (standard) # Light year [ly] = 1 [c].a nonmetric # lenth light-year # # CUSTOMARY UNITS # # Conversions are as exact as possible by using only few references to # the metric system. Factors are taken from WWWebster. We root in the # inch as it is equal to the old German ``Zoll'' that is known to be # 2.54 cm. I found no more ``exact'' conversion factor of inch to cm. # However, in case of the nautic mile we have to use the second # external reference as it was officially adopted to be 1852 m and not, # as it origianlly was, 6080 ft (= 1853.2 m). Thus, we can't hook the # customary system at the nautic mile. # # http://www.m-w.com/mw/table/weight.htm # # We use suffices in order to distinguish between different nonmetric # systems. # # SFX MEANING # ----- -------------------------------- # _us U.S. survey (until 1959) # _br British imperial (until 1963) # _av Avoirdupois (standard in the US) # _tr Troy # _ap Apothecaries' # # International Customary Units for length and area don't have a suffix # [in] = 2.54 cm nonmetric # length inch [hd] = 4 [in] nonmetric # height of horses hand [ft] = 12 [in] nonmetric # length foot [yd] = 3 [ft] nonmetric # length yard [mi] = 5280 [ft] nonmetric # length statute mile [mil] = 1e-3 [in] nonmetric # length mil # ``Nautical'' units [fth] = 6 [ft] nonmetric # depth of water fathom [nmi] = 1852 m nonmetric # length nautic mile [kn] = 1 [nmi]/h nonmetric # velocity knot # redundant square- and cubic- units [sin] = 1 [in]2 nonmetric # area square inch [sft] = 1 [ft]2 nonmetric # area square foot [syd] = 1 [yd]2 nonmetric # area square yard [cin] = 1 [in]3 nonmetric # volume cubic inch [cft] = 1 [ft]3 nonmetric # volume cubic foot [cyd] = 1 [yd]3 nonmetric # volume cubic yard # the circular mil as a curiosity [cmi] = 1 [pi]/4.[mil]2 nonmetric # area circular mil # # U.S. survey units (1893--1959, and today for specific uses) # [ft_us] = 1200 m/3937 nonmetric # length foot [yd_us] = 3 [ft_us] nonmetric # length yard [in_us] = 1 [ft_us]/12 nonmetric # length inch [rd_us] = 16.5 [ft_us] nonmetric # length rod, pole, or perch [ch_us] = 4 [rd_us] nonmetric # length chain (Gunter's or Surveyor's chain) [lk_us] = 1 [ch_us]/100 nonmetric # length link (for Gunter's chain) [rch_us]= 100 [ft_us] nonmetric # length chain (Ramden's or Engineer's chain) [rlk_us]= 1 [rch_us]/100 nonmetric # length link (for Ramden's chain) [fth_us]= 6 [ft_us] nonmetric # length fathom [fur_us]= 40 [rd_us] nonmetric # length furlong [mi_us] = 8 [fur_us] nonmetric # length mile (U.S. survey) [acr_us]= 160 [rd_us]2 nonmetric # area acre (this is THE acre) [srd_us]= 1 [rd_us]2 nonmetric # area square rod [smi_us]= 1 [mi_us]2 nonmetric # area square mile [mil_us]= 1e-3 [in_us] nonmetric # length mil [sct] = 1 [mi_us]2 nonmetric # area section [twp] = 36 [sct] nonmetric # area township # # British Imperial (based on the Imperial Standard Yard of 1845) # [in_br] = 2.539998 cm nonmetric # length inch [ft_br] = 12 [in_br] nonmetric # length foot [rd_br] = 16.5 [ft_br] nonmetric # length foot [ch_br] = 4 [rd_br] nonmetric # length chain (also Gunter's chain) [lk_br] = 1 [ch_br]/100 nonmetric # length link (for Gunter's chain) [fth_br]= 6 [ft_br] nonmetric # length fathom [pc_br] = 2.5 [ft_br] nonmetric # length pace [yd_br] = 3 [ft_br] nonmetric # length yard [mi_br] = 5280 [ft_br] nonmetric # length british mile [nmi_br]= 6080 [ft_br] nonmetric # length british nautic mile [kn_br] = 1 [nmi_br]/h nonmetric # velocity knot [acr_br]= 4840 [yd_br]2 nonmetric # area acre # # VOLUME (including so called ``capacity'' measures, i.e. fluid volume) # # U.S. liquid measures (based on the international inch) # [gal_us]= 231 [in]3 nonmetric # volume gallon (Queen Anne's wine gallon) [bbl_us]= 42 [gal_us] nonmetric # volume barrel [qt_us] = 1 [gal_us]/4 nonmetric # volume quart [pt_us] = 1 [qt_us]/2 nonmetric # volume pint [gil_us]= 1 [pt_us]/4 nonmetric # volume gill [foz_us]= 1 [gil_us]/4 nonmetric # volume fluid ounce [fdr_us]= 1 [foz_us]/8 nonmetric # volume fluid dram [min_us]= 1 [fdr_us]/60 nonmetric # volume minim [crd_us]= 128 [ft]3 nonmetric # volume cord # # U.S. dry measures (based on the international inch) # [bu_us] = 2150.42 [in]3 nonmetric # volume bushel (cylinder: d=18.5in, h=8in) [pk_us] = 1 [bu_us]/4 nonmetric # volume peck [dqt_us]= 1 [pk_us]/8 nonmetric # volume dry quart [dpt_us]= 1 [dqt_us]/2 nonmetric # volume dry pint [gal_wi]= 1 [bu_us]/8 nonmetric # volume winchester gallon (historical) # # British, liquid and dry (based on the international inch) # was also used in Canada. # # was based on the gallon to be 277.274 [in_??]3 and later corrected to # 277.421 [in_??]3. However, NIST gives a metric equivalent said to be exact. # [gal_br]= 4.54609 l nonmetric # volume gallon [pk_br] = 2 [gal_br] nonmetric # volume bushel [bu_br] = 4 [pk_br] nonmetric # volume peck [qt_br] = 1 [gal_br]/4 nonmetric # volume quart [pt_br] = 1 [qt_br]/2 nonmetric # volume pint [gil_br]= 1 [pt_br]/4 nonmetric # volume gill [foz_br]= 1 [gil_br]/5 nonmetric # volume fluid ounce [fdr_br]= 1 [foz_br]/8 nonmetric # volume fluid dram [min_br]= 1 [fdr_br]/60 nonmetric # volume minim # # Apothecaries' volumes (based on the U.S. fluid ounce) # [tbs_ap]= 1 [foz_us]/2 nonmetric # volume tablespoon [tsp_ap]= 1 [tbs_ap]/3 nonmetric # volume teaspoon [cup_ap]= 16 [tbs_ap] nonmetric # volume cup # # MASS (essentially the same 3 systems used for U.S. and Brititsh) # # The grain seems to be the same for Avoirdupois, Troy and Apothecaries' # [gr] = 64.798918 mg nonmetric # mass grain # # Avoirdupois(6) # [gr_av] = 1 [gr] nonmetric # mass grain [lb_av] = 7000 [gr_av] nonmetric # mass pound [oz_av] = 1 [lb_av]/16 nonmetric # mass ounce [dr_av] = 1 [oz_av]/16 nonmetric # mass dram [scwt_av]= 100 [lb_av] nonmetric # mass short hundredweight (U.S.) [lcwt_av]= 112 [lb_av] nonmetric # mass long hunderdweight (Brit.) [ston_av]= 20 [scwt_av] nonmetric # mass short ton (U.S.) [lton_av]= 20 [lcwt_av] nonmetric # mass long ton (British) [stone] = 14 [lb_av] nonmetric # mass stone (British) [lbf_av]= 1 [lb_av].[g] nonmetric # force pound force # # Troy # [gr_tr] = 1 [gr] nonmetric # mass grain [pwt_tr]= 24 [gr_tr] nonmetric # mass pennyweight [oz_tr] = 20 [pwt_tr] nonmetric # mass ounce [lb_tr] = 12 [oz_tr] nonmetric # mass pound # # Apothecaries' # [gr_ap] = 1 [gr] nonmetric # mass grain [sc_ap] = 20 [gr_ap] nonmetric # mass scruple [dr_ap] = 3 [sc_ap] nonmetric # mass dram [oz_ap] = 8 [dr_ap] nonmetric # mass ounce [lb_ap] = 12 [oz_ap] nonmetric # mass pound # # MISCELLANEA # # Beautiful angular units # circ = 2 [pi].rad nonmetric # plane angle circle sph = 4 [pi].sr nonmetric # sphere spere # # Fahrenheit degrees are not even defined by ANSI X3.50 # [degF] = degf(5 K/9) nonmetric # temperature degree Fahrenheit # # the different Sv factors # Sv_a = 0.04 Gy metric # Sievert (alpha rays) Sv_b = 1 Gy metric # Sievert (beta rays) Sv_g = 1 Gy metric # Sievert (gamma rays) Sv_x = 1 Gy metric # Sievert (X-rays) Sv_n = 0.2 Gy metric # Sievert (neutrons) Sv_p = 0.1 Gy metric # Sievert (protons) # # CGS-Units # Gal = 1 cm/s2 metric # acceleration Gal dyn = 1 g.cm/s2 metric # force dyne erg = 1 dyn.cm metric # energy erg P = 1 dyn.s/cm2 metric # dynamic viscosity Poise St = 1 cm2/s metric # kinematic viscosity Stokes Mx = 1e-8 Wb metric # flux of magnetic induction Weber Gs = 1e-4 T metric # magnetic flux density Gauss Oe = 250 /[pi].A/m metric # magnetic field intensity Oersted Gb = 1 Oe.cm metric # magnetic tension Gilbert sb = 1 cd/cm2 metric # lum. intensity density stilb Lmb = 1 cd/cm2/[pi] metric # brightness Lambert ph = 1e-4 lx metric # illuminance phot Ci = 3.7e10 Bq metric # radioactivity Curie R = 2.58E-4 C/kg metric # ion dosis Roentgen Bi = 1 A metric # ion dosis rate Biot RAD = 100 erg/g metric # energy dose radiation absorbed dose REM = 1 RAD metric # dose equivalent radiation equivalent man REM_a = 0.04 RAD metric # dose equivalent of alpha rays REM_b = 1 RAD metric # dose equivalent of beta rays REM_g = 1 RAD metric # dose equivalent of gamma rays REM_x = 1 RAD metric # dose equivalent of X-rays REM_n = 0.2 RAD metric # dose equivalent of neutrons REM_p = 0.1 RAD metric # dose equivalent of protons # # Bel and decibel measures # B = ln(1 1) nonmetric # bel dB = 10lg(1 1) nonmetric # decibel dB[SPL] = 20lg(2 10*-5.Pa) nonmetric # decibel sound pressure dB[V] = 20lg(1 V) nonmetric # decibel volts dB[mV] = 20lg(1 mV) nonmetric # decibel milivolts dB[uV] = 20lg(1 uV) nonmetric # decibel microvolts dB[W] = 10lg(1 W) nonmetric # decibel watts dB[kW] = 10lg(1 kW) nonmetric # decibel kilowatts # # Finally here goes the mole et. al # mol = 6.0221367 10*23 metric # amount of substance mole -- Avogadro's number eq = 1 mol metric # equivalents [pH] = pH(1 mol/l) nonmetric # strength of acidity pH kat = 1 mol/s metric # enzymatic activity katal U = 1 umol/min metric # enzymatic activity Unit osm = 1 mol metric # osmole (dissolved particles) g% = 1 g/dl metric # gram percent (concentration in water) # # other units for volume # [drp] = 1 ml/12 nonmetric # volume drop # # diopter: 1 [diop] = 1/(1.m), 2 [diop] = 1/(2.m), x [diop] = 1/(x.m) # [diop] = inv(1 /m) nonmetric # refraction of a lens diopter # # Typsetter's lengths # #[point] = 1/72 [in] #[pica] = 12 [point] #[didot] = ?? #[cicero]= 12 [didot] # light year! # # Old, deprecated or difficult stuff # # this falls into the following categories: # # 1. real units that are quite outdated but resist any fading out # 2. units for which reasonable alternatives are not available # 3. units of biological function # 4. dumb units, i.e. things that are not units of measure and # are not necessary at all # 1. real units that are quite outdated but resist any fading out st = 1 m3 metric # volume stere Ao = 0.1 nm nonmetric # length Ångström b = 100 fm2 nonmetric # area (action) barn atm = 101.325 kPa nonmetric # pressure atmosphere [S] = 1 10*-13.s nonmetric # sedimentat. coeff. Svedberg unit m[H2O] = 9.80665 kPa metric # pressure meter of water column m[Hg] = 133.3220 kPa metric # pressure meter of mercury column [in_H2O]= 1 m[H2O].[in]/m nonmetric # pressure inch of water column [in_Hg] = 1 m[Hg].[in]/m nonmetric # pressure inch of mercury column [Btu_IT]= 1055.05585262 J nonmetric # energy British thermal unit (intl. table) [Btu_th]= 1054.350 J nonmetric # energy British thermal unit (thermochemical) [Btu] = 1055.87 J nonmetric # energy British thermal unit (mean) cal = 4.1868 J metric # energy (gram) calorie [Cal] = 1 kcal nonmetric # energy (kilogram) calorie [car] = 0.2 g nonmetric # mass carat (metric) # note that there are other Btu's at 39, 59, and 60 degree Fahrenheit # 2. Units for which reasonable alternatives are not available # # FIXME: High and low power field should translate to an Area [HPF] = 1 1 nonmetric # high power field (view area in microscope) [LPF] = 1 1 nonmetric # low power field (view area in microscope) [hnsf_U]= 1 1 nonmetric # Hounsfield unit x-ray attenuation in CT scann #[PRU] = 1 1 nonmetric # peripheral vascular resistance unit # 3. units of biological function [iU] = 1 1 metric # international unit (kilo and mega are common) [arb_U] = 1 1 nonmetric # arbitary unit [USP_U] = 1 1 nonmetric # United States Pharmacopeia unit [GPL_U] = 1 1 nonmetric # anticardiolipin IgG [MPL_U] = 1 1 nonmetric # anticardiolipin IgM [APL_U] = 1 1 nonmetric # anticardiolipin IgA [beth_U]= 1 1 nonmetric # Bethesda unit for factor VIII inhibitors [todd_U]= 1 1 nonmetric # Todd unit for antistreptolysin O [dye_U] = 1 1 nonmetric # Dye unit for amylase [smgy_U]= 1 1 nonmetric # Somogyi unit for amylase [bdsk_U]= 1 1 nonmetric # Bodansky unit for phosphatase [ka_U] = 1 1 nonmetric # King-Armstrong unit for phosphatase [mclg_U = 1 1 nonmetric # Mac Lagan units for ?? [tb_U] = 1 1 nonmetric # tuberculin unit # 4. dumb units [ppb] = 1e-9 1 nonmetric # parts per billion [ppm] = 1e-6 1 nonmetric # parts per million [ppth] = 1e-3 1 nonmetric # parts per thousand [ppt] = 1e-12 1 nonmetric # parts per trillion # # SUMMARY OF CONFLICTS # # conflict: Gb vs. G-b Type IVa (metric-nonmetric) # conflict: Pa vs. P-a Type IVa (metric-nonmetric) # conflict: ph vs. p-h Type IVa (metric-nonmetric) # conflict: dB vs. d-B Type III (nonmetric-nonmetric) # conflict: cd vs. c-d Type IVa (metric-nonmetric)