[X1 ANNEX U.K.

Editorial Information

X1 Substituted by Corrigendum to Council Directive 80/181/EEC of 20 December 1979 on the aproximation of the laws of the Member States relating to units of measurement and on the repeal of Directive 71/354/EEC (Official Journal of the European Communities No L 39 of 15 February 1980).

CHAPTER I U.K. LEGAL UNITS OF MEASUREMENT REFERRED TO IN ARTICLE 1 (a)

1. SI UNITS AND THEIR DECIMAL MULTIPLES AND SUBMULTIPLES U.K.

[F1 1.1. SI base units U.K.

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 Δ ν _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 Δ ν _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 m ² s ^–1 , where the metre and the second are defined in terms of c and Δ ν _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 Δ ν _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 m ² s ^–2 K ^–1 , where the kilogram, metre and second are defined in terms of h , c and Δ ν _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 × 10 ²³ 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 × 10 ¹² 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 s ³ , where the kilogram, metre and second are defined in terms of h , c and Δ ν _Cs .

1.1.1. Special name and symbol of the SI derived unit of temperature for expressing Celsius temperature U.K.

Quantity	Unit
	Name	Symbol
Celsius temperature	degree Celsius	°C

Celsius temperature t is defined as the difference t = T – T ₀ 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 ’ .]

Textual Amendments

F1 Substituted by Commission Directive (EU) 2019/1258 of 23 July 2019 amending, for the purpose of its adaptation to technical progress, the Annex to Council Directive 80/181/EEC as regards the definitions of SI base units (Text with EEA relevance).

[F2 1.2. SI derived units] U.K.

F3 1.2.1. SI supplementary units U.K.

[ F3

F3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .]

F3 Definitions of SI supplementary units: U.K.

F3 Unit of plane angle U.K.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

F3 Unit of solid angle U.K.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Textual Amendments

F3 Deleted by Directive 2009/3/EC of the European Parliament and of the Council of 11 March 2009 amending Council Directive 80/181/EEC on the approximation of the laws of the Member States relating to units of measurement (Text with EEA relevance).

[F2 1.2.2. General rule for SI derived units U.K.

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 U.K.

a 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.
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		m 2 · 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	m 2 · kg · s –2
Power a , radiant flux	watt	W	J · s –1	m 2 · kg · s –3
Quantity of electricity, electric charge	coulomb	C		s · A
Electric potential, potential difference, electromotive force	volt	V	W · A –1	m 2 · kg · s –3 · A –1
Electric resistance	ohm	Ω	V · A –1	m 2 · kg · s –3 · A –2
Conductance	siemens	S	A · V –1	m –2 · kg –1 · s 3 · A 2
Capacitance	farad	F	C · V –1	m –2 · kg –1 · s 4 · A 2
Magnetic flux	weber	Wb	V · s	m 2 · kg · s –2 · A –1
Magnetic flux density	tesla	T	Wb · m –2	kg · s –2 · A –1
Inductance	henry	H	Wb · A –1	m 2 · 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	m 2 · s –2
Dose equivalent	sievert	Sv	J · kg –1	m 2 · s –2
Catalytic activity	katal	kat		mol · s –1

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.]

Textual Amendments

F2 Substituted by Directive 2009/3/EC of the European Parliament and of the Council of 11 March 2009 amending Council Directive 80/181/EEC on the approximation of the laws of the Member States relating to units of measurement (Text with EEA relevance).

1.3. Prefixes and their symbols used to designate certain decimal multiples and submultiples U.K.

[F4 Factor	Prefix	Symbol
10 24	yotta	Y
10 21	zetta	Z
10 18	exa	E
10 15	peta	P
10 12	tera	T
10 9	giga	G
10 6	mega	M
10 3	kilo	[X2 k]
10 2	hecto	[X2 h]
10 1	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 U.K.

a The two symbols ‘ I ’ and ‘ L ’ may be used for the litre unit. (Sixteenth CGPM (1979), resolution 6).
b Unit listed in the International Bureau of Weights and Measures booklet as among the units to be permitted temporarily.
Quantity	Unit
	Name	Symbol	Value
Volume	litre	1 or L a	1 l = 1 dm 3 = 10 -3 m 3
Mass	tonne	t	1 t = 1 Mg = 10 3 kg
Pressure, stress	bar	bar b	1 bar = 10 5 Pa

Note: U.K.

The prefixes and their symbols listed in 1.3 may be used in conjunction with the units and symbols contained in Table 1.4. U.K.

2. UNITS WHICH ARE DEFINED ON THE BASIS OF SI UNITS BUT ARE NOT DECIMAL MULTIPLES OR SUBMULTIPLES THEREOF U.K.

a 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.
b No international symbol exists.
Quantity	Unit
	Name	Symbol	Value
Plane angle	revolution* a b		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

Note: U.K.

The prefixes listed in 1.3 may only be used in conjunction with the names ‘ grade ’ or ‘ gon ’ and the symbol ‘ gon ’ . U.K.

[F4 3. UNITS USED WITH THE SI, WHOSE VALUES IN SI ARE OBTAINED EXPERIMENTALLY U.K.

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 12 C.

Note: U.K.

The prefixes and their symbols listed in 1.3 may be used in conjunction with these two units and with their symbols.] U.K.

4. UNITS AND NAMES OF UNITS PERMITTED IN SPECIALIZED FIELDS ONLY U.K.

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 = 10 2 m 2
Mass per unit length of textile yarns and threads	tex*	tex*	1 tex = 10 -6 kg · m -1
[F5 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 m 2]

Note: U.K.

[F6 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 10 ² a is, however, called a ‘ hectare ’ .] U.K.

5. COMPOUND UNITS U.K.

Combinations of the units listed in Chapter I form compound units.]