anx_1
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.
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