Council Directive 80/181/EEC of 20 December 1979 on the approximation of the laws of the Member States relating to units of measurement and on the repeal of Directive 71/354/EEC

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ANNEX CHAPTER I LEGAL UNITS OF MEASUREMENT REFERRED TO IN ARTICLE 1 (a) 1.   SI UNITS AND THEIR DECIMAL MULTIPLES AND SUBMULTIPLES 1.1.   SI base units Quantity Unit Name Symbol Time second s Length metre m Mass kilogram kg Electric current ampere A Thermodynamic temperature kelvin K Amount of substance mole mol Luminous intensity candela cd Definitions of SI base units: Unit of time The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency Δν Cs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9 192 631 770 when expressed in the unit Hz, which is equal to s–1. Unit of length The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299 792 458 when expressed in the unit m/s, where the second is defined in terms of Δν Cs. Unit of mass The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6,626 070 15 × 10–34 when expressed in the unit J s, which is equal to kg m2 s–1, where the metre and the second are defined in terms of c and Δν Cs. Unit of electric current The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge e to be 1,602 176 634 × 10–19 when expressed in the unit C, which is equal to A s, where the second is defined in terms of Δν Cs. Unit of thermodynamic temperature The kelvin, symbol K, is the SI unit of thermodynamic temperature. It is defined by taking the fixed numerical value of the Boltzmann constant k to be 1,380 649 × 10–23 when expressed in the unit J K–1, which is equal to kg m2 s–2 K–1, where the kilogram, metre and second are defined in terms of h, c and Δν Cs. Unit of amount of substance The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6,022 140 76 × 1023 elementary entities. This number is the fixed numerical value of the Avogadro constant, N A, when expressed in the unit mol–1 and is called the Avogadro number. The amount of substance, symbol n, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles. Unit of luminous intensity The candela, symbol cd, is the SI unit of luminous intensity in a given direction. It is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz, K cd, to be 683 when expressed in the unit lm W–1, which is equal to cd sr W–1, or cd sr kg–1 m–2 s3, where the kilogram, metre and second are defined in terms of h, c and Δν Cs. 1.1.1. Special name and symbol of the SI derived unit of temperature for expressing Celsius temperature Quantity Unit Name Symbol Celsius temperature degree Celsius °C Celsius temperature t is defined as the difference t = T – T0 between the two thermodynamic temperatures T and T 0 where T 0 = 273,15 K. An interval or difference of temperature may be expressed either in kelvins or in degrees Celsius. The unit ‘degree Celsius’ is equal to the unit ‘kelvin’. 1.2.   SI derived units ————— 1.2.2.   General rule for SI derived units Units derived coherently from SI base units are given as algebraic expressions in the form of products of powers of the SI base units with a numerical factor equal to 1. 1.2.3.   SI derived units with special names and symbols Quantity Unit Expression Name Symbol In terms of other SI units In terms of SI base units Plane angle radian rad m · m–1 Solid angle steradian sr m2 · m–2 Frequency hertz Hz s–1 Force newton N m · kg · s–2 Pressure, stress pascal Pa N · m–2 m–1 · kg · s–2 Energy, work; quantity of heat joule J N · m m2 · kg · s–2 Power (1), radiant flux watt W J · s–1 m2 · kg · s–3 Quantity of electricity, electric charge coulomb C s · A Electric potential, potential difference, electromotive force volt V W · A–1 m2 · kg · s–3 · A–1 Electric resistance ohm Ω V · A–1 m2 · kg · s–3 · A–2 Conductance siemens S A · V–1 m–2 · kg–1 · s3 · A2 Capacitance farad F C · V–1 m–2 · kg–1 · s4 · A2 Magnetic flux weber Wb V · s m2 · kg · s–2 · A–1 Magnetic flux density tesla T Wb · m–2 kg · s–2 · A–1 Inductance henry H Wb · A–1 m2 · kg · s–2 · A–2 Luminous flux lumen lm cd · sr cd Illuminance lux lx lm · m–2 m–2 · cd Activity (of a radionuclide) becquerel Bq s–1 Absorbed dose, specific energy imparted, kerma, absorbed dose index gray Gy J · kg–1 m2 · s–2 Dose equivalent sievert Sv J · kg–1 m2 · s–2 Catalytic activity katal kat mol · s–1 (1) Special names for the unit of power: the name volt–ampere (symbol ‘VA’) when it is used to express the apparent power of alternating electric current, and var (symbol ‘var’) when it is used to express reactive electric power. The ‘var’ is not included in GCPM resolutions. Units derived from SI base units may be expressed in terms of the units listed in Chapter I. In particular, derived SI units may be expressed by the special names and symbols given in the above table; for example, the SI unit of dynamic viscosity may be expressed as m–1 · kg · s–1 or N · s · m–2 or Pa · s. 1.3.   Prefixes and their symbols used to designate certain decimal multiples and submultiples Factor Prefix Symbol 1024 yotta Y 1021 zetta Z 1018 exa E 1015 peta P 1012 tera T 109 giga G 106 mega M 103 kilo k 102 hecto h 101 deca da 10-1 deci d 10-2 centi c 10-3 milli m 10-6 micro μ 10-9 nano n 10-12 pico p 10-15 femto f 10-18 atto a 10-21 zepto z 10-24 yocto y The names and symbols of the decimal multiples and submultiples of the unit of mass are formed by attaching prefixes to the word ‘gram’ and their symbols to the symbol ‘g’. Where a derived unit is expressed as a fraction, its decimal multiples and submultiples may be designated by attaching a prefix to units in the numerator or the denominator, or in both these parts. Compound prefixes, that is to say prefixes formed by the juxtaposition of several of the above prefixes, may not be used. 1.4.   Special authorized names and symbols of decimal multiples and submultiples of SI units Quantity Unit Name Symbol Value Volume litre 1 or L (1) 1 l = 1 dm3 = 10-3 m3 Mass tonne t 1 t = 1 Mg = 103 kg Pressure, stress bar bar (2) 1 bar = 105 Pa (1) The two symbols ‘I’and ‘L’ may be used for the litre unit. (Sixteenth CGPM (1979), resolution 6). (2) Unit listed in the International Bureau of Weights and Measures booklet as among the units to be permitted temporarily. Note: The prefixes and their symbols listed in 1.3 may be used in conjunction with the units and symbols contained in Table 1.4. 2.   UNITS WHICH ARE DEFINED ON THE BASIS OF SI UNITS BUT ARE NOT DECIMAL MULTIPLES OR SUBMULTIPLES THEREOF Quantity Unit Name Symbol Value Plane angle revolution* (1) () 1 revolution = 2 π rad grade* or gon* gon* degree ° minute of angle ′ second of angle ″ Time minute min 1 min = 60 s hour h 1 h = 3 600  s day d 1 d = 86 400  s (1) The character (*) after a unit name or symbol indicates that it does not appear in the lists drawn up by the CGPM, CIPM o BIPM. This applies to the whole of this Annex. (2) No international symbol exists. Note: The prefixes listed in 1.3 may only be used in conjunction with the names ‘grade’ or ‘gon’ and the symbol ‘gon’. 3.   UNITS USED WITH THE SI, WHOSE VALUES IN SI ARE OBTAINED EXPERIMENTALLY Quantity Unit Name Symbol Definition Energy Electronvolt eV The electron volt is the kinetic energy acquired by an electron in passing through a potential difference of 1 volt in vaccum Mass Unified atomic mass unit u The unified atomic mass units is equal to 1/12 of the mass of an atom of the nuclide 12C. Note: The prefixes and their symbols listed in 1.3 may be used in conjunction with these two units and with their symbols. 4.   UNITS AND NAMES OF UNITS PERMITTED IN SPECIALIZED FIELDS ONLY Quantity Unit Name Symbol Value Vergency of optical systems dioptre* 1 dioptre = 1 m-1 Mass of precious stones metric carat 1 metric carat = 2 × 10-4 kg Area of farmland and building land are a 1 a = 102 m2 Mass per unit length of textile yarns and threads tex* tex* 1 tex = 10-6 kg · m-1 Blood pressure and pressure of other body fluids Millimetre of mercury mm Hg(*) 1 mm Hg = 133,322 Pa Effective cross-sectional area Barn b 1 b = 10-28 m2 Note: The prefixes and their symbols listed in 1.3 may be used in conjunction with the above units and symbols, with the exception of the millimetre of mercury and its symbol. The multiple of 102a is, however, called a ‘hectare’. 5.   COMPOUND UNITS Combinations of the units listed in Chapter I form compound units. CHAPTER II LEGAL UNITS OF MEASUREMENT REFERRED TO IN ARTICLE 1 (b), PERMITTED FOR SPECIFIC USES ONLY Field of application Unit Name Approximate value Symbol Road traffic signs, distance and speed measurement mile 1 mile = 1 609  m mile yard 1 yd = 0,9144 m yd foot 1 ft = 0,3048 m ft inch 1 in = 2,54 × 10-2 m in Dispense of draught beer and cider; milk in returnable containers pint 1 pt = 0,5683 × 10-3 m3 pt ————— Transaction in precious metals troy ounce 1 oz tr = 31,10 × 10-3 kg oz tr The units listed in this Chapter may be combined with each other or with those in Chapter I to form compound units. CHAPTER III LEGAL UNITS OF MEASUREMENT REFERRED TO IN ARTICLE 1 (c) QUANTITIES, NAMES OF UNITS, SYMBOLS AND APPROXIMATE VALUES ————— Length inch 1 in = 2·54 × 10-2 m foot 1 ft = 0·3048 m ————— mile 1 mile = 1 609  m yard 1 yard = 0·9144 m Area square foot 1 sq ft = 0·929 × 10-1 m2 acre 1 ac = 4 047  m2 square yard 1 sq yd = 0·8361 m2 Volume fluid ounce 1 fl oz = 28·41 × 10-6 m3 gill 1 gill = 0·1421 × 10-3 m3 pint 1 pt = 0·5683 × 10-3 m3 quart 1 qt = 1·137 × 10-3 m3 gallon 1 gal = 4·546 × 10-3 m3 Mass ounce (avoirdupois) 1 oz = 28·35 × 10-3 kg troy ounce 1 oz tr = 31·10 × 10-3 kg pound 1 lb = 0·4536 kg Energy therm 1 therm = 105·506 × 106 J Until the date to be fixed under Article 1 (c), the units listed in Chapter III may be combined with each other or with those in Chapter I to form compound units. CHAPTER IV LEGAL UNITS OF MEASUREMENT REFERRED TO IN ARTICLE I (d), PERMITTED IN SPECIALIZED FIELDS ONLY Field of application Unit Name Approximate value Symbol Marine navigation fathom 1 fm = 1,829 m fm Beer, cider, waters, lemonades and fruit juices in returnable containers pint 1 pt = 0,5683 × 10-3 m3 pt fluid ounce 1 fl oz = 28,41 × 10-6 m3 fl. oz Spirit drinks gill 1 gill = 0,142 × 10-3 m3 gill Goods sold loose in bulk ounce (avoir dupois) 1 oz = 28,35 × 10-3 kg oz pound 1 lb = 0,4536 kg lb Gas supply therm 1 therm = 105,506 × 106 J therm Until the date to be fixed under Article 1 (d), the units listed in this Chapter may be combined with each other or with those in Chapter I to form compound units. ( 1 ) OJ L 202, 6.9.1971, p. 1. //</s