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SE 012 400The Use of SI Units.British Standards Institution, London (England).Jan 6928p.British Standards Institution, 101-113 PentonvilleRoad, London, N.1, England

MF-$0.65 HC-$3.29*Mathematical Applications; *Mathematics;*Measurement; *Metric System; Physics; ResourceGuides; Technical Mathematics*International System of Units

This booklet (referred to as PD 5686:1969) replacesthe 1967 edition by including subsequent recommendations of theInternational Organization for Standardization (Is()) and the GeneralConference on Weights and Measures (CGPM). The International Systemof Units (SI) is described and rules are given for the formation ofderived units and decimal multiples and submultiples. The major partof this booklet is a list of the SI units for various physicalquantities, the recommended multiples and submultiples of theseunits, and the non-SI units which may also be used. Further tablesgive definitions of derived SI units with special names, the value ofsome imperial units in terms of SI units, and related BritishStandards-publications..(MM)

-

The Use of SI UnitsForewordThis booklet was first published in December 1965 to provide a simple accountof the units of the metric system and of the way the system has evolved in thepast few decades to produce the rational SI metric system now coming intoworld use.

It was revised in April 1967, and is now again revised to include the provisionsof the latest ISO Draft Recommendation No. 1557 for which it is known thatthere is.peteral international approval. The recommendation also embodies theup-to-date proposals of the General Conference on ,Weights and Measures(CGPM).

IntrooactionThe triAted Kingdom is changing to the metric system at a time when a rational-ized system of metric units, the Systeme International d'Unites (S1), is cominginto international use. The SI derives near17 all the quantities needed in alltechnologies from may six base-units which are arbitrarilY defined. This-contrastswith the metee systems currently used, in which many additional units (forinstance calorie ' and heraepower ') are arbitrarily and sometimes differentlydefined. Relationshir iaetween units are thus greatly simplified in the SI, theintroduction of which offers eXisting metric countries a uniqne opportunity toharmonize th9ir measurilig Practices,

"i tus opportunity is now being seiied:Already some 25 countries nave passedor are preparing legislation to make the SI the only legal system of measurement,and it is therefore a lopical choice for the UK. It involves the use of the newtonas the unit of force. which in some sectors may be less well known than themetric technical unit of force, the kilogramme-force.

The use of SI units instead of metric technical units will have little effectGn everyday life or trade. The metre and the Idlogramme remain thr> units oflinear measure and mass, and the litre, now accepted for most purposes as aspecial name for the cubic decimette, will be commonly uged as a unit of volume.

The SI is a coherent system of units, and this term should be ,:xplained.A syqtem of' units is coherent' if-the Product or, quotient of any two unit

quantiut in the system is the unit of the resultant quantity. For example, in'anycoherent system, unit area restilts when unit length is multiplied by unit lengthunit velocity when unit length is divided by unit time, and unit force When unitmass is multiplied by unit acceleration.

2

Historical noteThe idea of a decimal system of units was conceived by Simon Srevin (1548-1620)who also developed the even more important concept of decimal freDecimal units were also considered in the early days of the French Académie desSciences founded in 1666, but the adoption of the metric system as a practicalmeasure was part of the general increase in administrative activity in Europewhich followed the French Revolution. Aialvised by the scientists of his day, thestatezman Talkyrand aimed at the establishment of an interuatiaal decimalsystem of weights and measures tons les temps, a. tous les peuples '. It wasbased on the metre as the unit of length (it was intended to be one ten-millionthpart of the distance from the North Pole to the equator at sea level through Paris,but the circumstances did not permit this aim to be achieved with any greataccuracy) and the gramme as the unit of quantity of matter. The gramme wasto be the mass of one cubic centimetre of water at 0 °C.

Although the metric system was plimarily devised as a benefit to industryand commerce, physicists soon realized its advantages and it was adopted alsoin scientific and technical circles. In 1873 the British Association for theAdvancement of Science selected the centimetre and the gramme as basic unitsof length and mass for physical raposes.

Measurement of other quantities called for a base-unit of time and thn adop-tion of the second for this purpose gave the centimetre-gramme-second system(c.gs.). In about 1900 practical measurements in metric units began to be basedon the metre, the kilogramme and the second (the MKS system). In 1935, theInten.z.tional Electrotechnical Commission (IEC) accepted the recommendationof Professor Giorgi that this system of units of mechanics should be linked withthe electro-magnetic units by the adoption of any one of the latter as a fourthbase-unit The ampere, the unit of electriad current was adopted by the IECin 1950 as the fourth base-unit, giving the MKSA (or Giorgi) system.

Since 1875 all international matters concerning the metric system have beenthe responsibility of the Conf&ence Generale des Poids et Mesures (CGPM)which was constituted following the Convention held in Paris in that year. TheCGPM meets in Paris, and controls the Comite International des Poids et Mesures(CIPM) and various Sub-committees as well as the Bureau International desPoids et Mesures (BIPM).

The laboratories of BIPM at Sevres are the repository of the standard kilo-.gramme and the former standard metre. The kilogramme is still defined in termsof the international prototype at Sevres but the metre is now defined in terms ofa number of wavelengths of a particular radiation of light. The United Kingdomparticipates in CGPM work, the Government department responsible being theMinistry of Technology.

At its tenth meeting, in 1934, the CGPM adopted a rationalized and coherentsystem of units based on the four MKSA units, the kelvin as the unit of tempera-

3

ture and the candela as the unit of luminous intensity. The eleventh CGPM in1960 formally gave it the full title ' Système International d'Unités ' for whichthe abbreviation is ' SI ' in all languages.

The International System of Units (SI)At Appendices A and B to this document there is reproduced an exposition ofSI as it appears in the most recent ISO draft recommendation.

Attention is particularly drawn to the rules concerned with the formation ofmultiples and sub-multiples. These have as their object:

(1) Minimizing the variety of multiples and sub-multiples in common use.(2) Ensuring that their presentation is uniform.(3) Ensuring that their presentation is such that their relation to the coherent

unit is always simple and obvious.

It will be seen in Appendix A that ' in order to avoid errors in calculations,it is essential to use coherent units '. Obser vance of the above mentioned ruleswill considerably facilitate the transition from data expressed in decimal multiplesand sub-multiples to coherent units for the purpose of calculation. It is thereforerecommended that unless compelling rea ons to the contrary exist, the rulesshould be strictiN lbsere_

Appendix Latka from die annex to the ISO draft recommendation, liststhe SI units and a selection of their recommended multiples and sub-multiplestogether with other units or other names of units which may be used. Theappendix also includes some units-which are not contained in the ISO draft recorn-mendation but which may be used in the UK in addition to the internationallyagreed selection. These are marked with an asterisk.

Units of rnass, force and weight

The SI, being a coherent system of units, provides naturally for a coherent unitof force, namely the newton, and for the derivatives of tbrat unit for pnantitiessuch as pressure, stress, work and power.

In practical work it has been a common practice to use weight units as forceunits; in other words, the unit of force used has been that force which appliedto unit mass produces an acceleration g, rather than unit acceleration. This hasseveral disadvantages:

(1) The value of gravitational acceleration g varies across the earth'ssurface and so the weight of a given mass also varies. Some years ago anattempt was made to correct this minor error by introducing the concept

4

of the kgf or lbf, which were defined as the forces due to standardgravity ' acting on bodies of mass 1 kg or 1 lb respectively, standardgravitational acceleration being taken as 9-806 65 ra/s2 or 32-174 ft/s2.

(2) g is ' built-in' to the definition of the gravitational unit force, andwhen this unit is used it gives rise to the followingparadox in dynamics:that in those circumstances where the force of gravity plays a part, anymathematical expression will not contain g, whereas in circumstanceswhere the force of gravity is not at all a factor, the related mathctnaticalexpressions must contain g to compensate for the fact that the unit offorce used is g times greater than the coherent unit.The use of a mass unit sometimes, but not always, followed by the wordforce ' or abbreviation f ' in textual matter has often confused designers,

who have been uncertain whether the mass unit implied a force or wasmeant as a pure mass.

There is thus a powerful case for the adoption of the coherent unit whichobviates all of these disadvantages, being independent of g, and clear instatement.

(3)

Units of pressure and stressThe SI unit of pressure and stress is the newton per square metre. This unit andits recommended multiples and sub-muittules shotuld normally be used.

Notwithstanding the general principle,- lact -out.above, the bar and some ofits decimal multiples and sub-multiples V&A in certain fields and in particulaThave been adopted, on an interim baik fo i. the initial expression, of metricvalues of stress or pressure in certain ôbtsses of l'Iritish Standards. in all suchstandards and other publications the rèIatknship between the adopted unitand the SI unit should be given as a footnote or other note on eaCh relevantpage of the text or table (e.g. 1 bar ------ 111-1N.Pin2, 1 hbar 1(07 Mae, 1 mbar

102 N/m2).

Details of such Classes of British Statarlurds are given beliow:

(1) In British Standards specifying int r.tetric terms the strength of metallicmaterials, this property is express;Jr in hectobars.

(2) In British Standards specifying -=aetric values of pressure relating tovessels, plant ar d equipment, thihs is expressed in bars, Irectobars andmillibars. However, in high vacuum work, for pressures of about 1 N/m2or less, the N/rn2 with its deciung sub-multiples is currently acceptableand is to be recommended in prafeence to the torr or mmHg.

Conversion from imperial to metric unitsThe UK will not gain the full advantages of adopting the metric system by amere mathematical conversion of existing designs and products from, forinstance, inches to the equivalent in millimetres. For Britain, the essence of thechangeover operation is to line up with current international practice as a meansof improving our competitiveness in oversea markets, the great majority of whichare now metric. New designs will therefore have to be prepared on a metricbasis, using customary metric sizes and metric components, and taking accountof internationally agreed metric standards and the practice of the principalmetric countries.

In a w cases where, for instance, interchangeability must be maintained, itmay be necessary to carry out direct conversion kr to metric dimensions.Part 1 of BS 350 ' Conversion factors and taf. uasic :nfonnation onunits and a summary of the conversion factors, iEzIudizig those for SI units.Detailed conversion tables are contained in Part 2, a supplement to which(Supplement No. 1) includes tables for SI units where they are not already f,iven.Reference may also be usefully made to BS 2856 Precise conversion of inchand metric sizes on engineering drawings which recommends the conversionprocedure giving the essential accuracy required for precise dimensional inter-changeability.

Particulars of other British Standards concerned with units and conversionare given in Appendix E.

Appendix ARules for the use of units of the International System of Units

A.1 Scope. The purpose of this appendix is to give rules for the use of units ofthe International System of Units and for forming and selecting decimalmultiples and sub-multiples of the SI units for application in the variousfields of technology.

A.2 GeneralA.2.1 The name Sysame International d'Unites (International System of Units)and the international abbreviation SI are used for the systematically organizedsystem of units introduced by the Conference Generale des POds et Mesuresin 1960.

It includes the base-units of SI, supplementary SI units, derived SI units, andthe decimal multiples and sub-multi9leA of these units, formed by use of prefixes.

The name SI units ' is reserved- for the coherent units only.

A.2.2 The International System of Units is based on the following six base-unit: .

metre (m) ampere (A)kilogramme (kg) kelvin (K)second (s) candela (cd)

as units for the basic quantifes length, mass, time, electric current, thermo-dynamic temperature, and luminous intensity.

A.2.3 The SI units for plane angle and solid angle, the xadian (rad) and thesteradian (sr) respectively, are called supplementary units in the InternationalSystem of Units.

A.2.4 The expresslons fol the derived SI units are stated in terms of base-units,for example the SI unit for velocity is metre per second (mis).

For some of the derived SI units special names and symbols exist; thoseapproved by the Conference Generale des Poids et Mesures are listed below:

Quantity Name ofSI unit Symbol

Expres3ed in termsof SI base-units or

derived units

frequency hertz Hz 1 Hz .... 1/sforce newton N 1 N = 1 kg ra/s2work, energy, quantity of joule J 1 3 ,=, 1 N m

lltatpower watt W 1 W = 1 J/squantity of electricity coulomb C 1 C =, 1 A selectric potential, potential volt V I V =. / W/A

difference, tension,electromotive force

electric capacitance farad F 1 F = 1 A s/Velectric resistance ohm SI 1 I/ = 1 V/Aflux of magnetic induction, weber Wb 1 Wb =-- 1 V s

magnetic fluxmagnetic flux density, tesla T 1 T =-- 1 Wbini2

magnetic inductioninductance henry H 3 H --= 1 V s/Aluminous flux /tunen lin 1 Im ..--- 1 cd srillumination lux lx 1 lx .-- 1 lm/m1

It may sometimes be advantageous to express derivedderived units having special names, for example the SImoment (A s in) is usually expressed as C m.

A.2.5 Decimal multiples and sub-multiples of the SI unitof the prefixes given below:

units in terms of otherunit of electric dipole

s are formed by means

Factor by which the miltis multiplied Prefix Symbol

3.0111061061061021010-110-210-010-610-610 lo10-1610-10

teragigamegakilohectodecadecicentimillimicronanopicofeint°atto

0lc

da

IL

a

The symbol of a prefix is considered to be combined with the unit symbol towhich it is directly attached, forming with it a new unit symbol which can beraised to a positive or negative power and which can be combined with otherunit symbols to form symbols for compound units.

8

t8

Examp:es1 cm3 (10-.211)3 = 10-8 1n31 VS-1 = 00-8 0-1 = 108 S-11 rtim2/s = (10-'3 n1)2/S = 10-8 m2/s

Compound prefixes should not be used, for example write nm (nauometre)instead of mizin.

A.3 Rules for the use of SI units and their deemal multiples and sub-multiplesA.3.1 The SI units are preferred, but it will not be practical to Emit usage tothese; in addition, therefore, their dechnal multiples and sub-multiples, formedby using the prefixes, are required.

In order to avoid errors in calculations it is essential to use coherent units.Therefore, it is strongly recommended that in calculations only SI units themselvesbe used, and not their decimal multiples and sub-multiples.

A.3.2 The use of prefixes representing 10 raised to a power which is a multipleof 3 is especially recommended.NOTE. in certain cases, to ensure convenience in the use of the unit% this reccnnmenda-tion car-ssot be followed; Column 5 of the tables in Appendix S gives examples a theseexceptions.

A.3.3 It is recommended that only one prefix be used in forming the decimalmultiples or sub-me1tiples of a derived SI utit, and that this prefix be attached tea unit in the numerator.NOTE. in certain cases convenient>: in filo use requires attachment of a prefix to both thenumerator and the denominator at the same time, and sometimes only to the denominator.Column 5 of the tables in Appendix B gives examples of these exceptions.

A.4 Numerical valuesA.4.1 When expressing a quantity by a numerical value and a certain unit it hasbeen found suitable in most applications to use units resulting in numericalvalues between 0.1 and 1000.

The units which are decimal multiples and sub-multiples of the SI unitsshould therefore be chosen to provide values in this range, for example:

observed orcalculated values

12 000 N0.003 94 m14 010 N/m20.0003 s

can be expressed as

12 kN3-94 mm1401 kN/rna0-3 ms

A.4.2 The rule according to A.4.1 cannot, however, be consistently applied. Inone and the same context the numerical values expressed in a certain unit can

9

extend over a considerable range; this applies especially to tabulated numericalvalues. In such cases it is often appropriate to use the same unit, even when thismeans exceeding the preferred value range 0.1-1000.

A.5 List of units. Units for a number of commonly used quantities are git-enin Appendix B.

App

endi

x B

Lis

t of

SI u

nits

and

a s

elec

tion

of r

ecom

men

ded

deci

mal

mul

tiple

s an

d su

b-m

ultip

les

ofth

e SI

uni

ts

toge

ther

with

oth

er u

nits

or

othe

r na

mes

of u

nits

whi

ch m

ay b

e us

ed

An

aste

risk

aga

inst

a u

nit m

eans

that

the

unit

may

be u

sed

in th

e U

K b

ut is

not

yet

incl

uded

in th

e IF

0 d

raft

rec

omm

enda

tion.

Item

No.

InIS

O/R

31

Qua

ntity

s/ a

skSe

lect

ion

orde

nini

teci

/ain

nnar

dnid

edpi

es

and

Fab.

mni

tipie

sof

SI

milt

Oth

er d

ecim

alm

ultip

les

and

sub-

man

iple

s

of S

ilmit

Oth

er m

ilts

or o

ther

nam

es o

fun

its w

hich

may

be

used

Rem

arks

1-1.

1pl

ane

angl

era

d(r

adia

n)

mra

cl

grad

degr

ee (

-1, 1

° =

7r

rad

180 r

min

ute

(.. ,

'), 1

' =60 l'

seco

nd (

... ')

, r =

1-2.

1so

lid a

ngle

sr (ste

radi

an)

1-3.

1...7

leng

thm (m

etre

)

km mm

gm MI

dm C13

1

Inte

rnat

iona

l nau

tical

mile

(1 n

mile

= 1

852

m)

1-4.

1ar

eain

2km

2

dm2

cm2

hect

are

(ha)

, 1 h

a =

104

in2

are

(a),

1 a

= 1

02 m

2

Item

No.

inIS

OT

R 3

1Q

uant

itySI

uni

t

Sele

ctio

n of

reco

mm

ende

dde

cim

al m

ultip

les

and

sub-

mul

tiple

sof

SI

unit

1-5.

1vo

lum

e

1-6.

1tim

e

(sec

ond)

ms

as

1-8.

1an

gula

rve

loci

tyra

d/s

'

1-10

.1ve

loci

tym

/s'

Oth

er d

ecim

alm

ultip

les

and

sub-

mul

tiple

sof

SI

unit

Oth

er u

nits

or

othe

r na

mes

of

units

whi

ch m

ay b

e us

edR

emar

ks

dm3 3

hect

olitr

e (h

p,1

hl =

10-

1 m

3lit

re (

I),

1 I

= 1

0-3

m3

= 1

dm

3ce

ntili

tre

WI

1 cl

= 1

0-3

m3

mill

ilitr

e (m

1),

1 m

l = 1

0-3

m3

1 cm

3

In 1

964

the

Con

-fé

renc

e G

énér

ale

des

Poid

s et

Mes

ures

adop

ted

the

nam

elit

re (

I) a

s th

e sy

no-

nym

for

cub

icde

cim

etre

(dm

3) b

utdi

scou

rage

d th

e us

eof

the

nam

e lit

re f

orpr

ecis

ion

mea

sure

-m

ents

day

(d), ld=

24h

hour

(h)

,1

h =

60

min

min

ute

(min

),1

min

= 6

0 s

Oth

er u

nits

suc

h as

wee

k, m

onth

and

year

are

in c

omm

onus

e

kilo

met

re p

er h

our

(km

/h)

1 km

/h31

.-6

m/i

*kno

t (kn

)1

kn =

-1 n

mile

/h=

0.5

14 4

44 r

n/s

Part

ll: P

erio

dic

and

rela

ted

phen

omen

a

2-31

freq

uenc

y

Hz

(her

tz)

TH

zG

Hz

MH

zkH

z

Vid

gkaa

s:04

0c.

"

2-3.

2ro

tatio

nal

freq

uenc

y1/

sre

volu

tion

per

min

ute

(rev

/min

)re

volu

tion

per

seco

nd(r

ev/s

)

Part

Mec

hani

cs

3-1.

1m

ass

kg (kilo

gram

me)

Mg

mg

1.14

tonn

e (t

), 1

t =

10

kg

3-2,

1de

nsity

(mas

s de

nsity

)kg

/m3

Mg/

m'

1 kg

/dm

'=

1 g

/cm

31

t/m3

= 1

kg/

I =

1 g

/m1

1...1

mom

entu

mkg

m/s

KIA

) "4

3-6

1m

omen

t of

mom

entu

m,

angu

lar

mom

entu

m

kg in

s/s

3-7.

1m

omen

t of

iner

tiakg

m2

3-5.

1fo

rce

(new

ton)

MN

kN mN

p.N

daN

340.

1m

omen

t of

forc

e

N m

MN

mkN

m

pN m

daN

m

The

met

ric

cara

t(1

met

ric

cara

t=

2 x

10-

4 k

g) is

used

for

com

mer

cial

tran

sact

ions

indi

amon

ds, f

ine

pear

lsan

d pr

ecio

us s

tone

s

For

litre

(1)

see

item

1-5.

1

Ite

NO

.

iSO

/R 3

1Q

uant

itySI

tmit

Sele

ctio

n of

deci

mal

reco

mm

ende

mul

tipld

esan

d an

b.m

nitip

ies

of S

I un

it

0 er

dec

imal

mtli

tiltip

les

and

sob-

mul

tiple

of S

I un

it

Oth

er u

nits

or

othe

rna

time!

ofun

its w

hich

may

be

thR

elym

.ke

_ 3-11

.1pr

essu

reG

N/m

2an

dda

N/m

m2

1 hb

ar =

101

N/m

211

14 li

r,ol

obat

3-11

.2st

ress

MN

/m2

kN/m

2

Nfm

ni2

Nic

e1

bar

= 1

05 N

/rn2

11 la

Irti

III

k.al

110

fiel

ds in

som

eco

untr

ies.

The

nam

eN

/m2

mN

/m2

[LN

/m2

1 m

bar

= 1

02 N

/rn2

1 [L

bar

= 1

0-I

N/m

2

' pas

cal '

is g

iven

toth

e ne

wto

n pe

r sq

uare

met

re in

cer

tain

coun

trie

s

3-19

.1vi

scos

ity(d

ynam

ic)

N s

/rn2

mN

s/r

n2ce

n tip

oise

(cP

)1

cP =

10-

3 N

s/r

n241

LN

s/m

2

3-20

.1ki

nem

atic

visc

osity

m2/

s

mm

2/s

cent

isto

kes

(cSt

)1

cSt =

10-

6 m

2/s

3-21

.1su

rfac

e te

nsio

nN

/rn

mN

/m

3-.2

2.1

ener

gy,

wor

k

J (jou

le)

GJ

MJ

kJ mJ

kilo

wat

t hou

r (k

W h

)1

kW h

= 3

.6 x

105

J =

3.6

MJ

elec

tron

volt

(eV

)1

eV = (

1.60

2 10

10.0

00 0

7)x1

0-19

J

The

uni

ts W

h,

kW h

, MW

h, G

W h

and

TW

li k

ii in

Ted

inth

e el

ectr

ical

indu

stry

.T

he u

nits

keV

, MeV

and

GeV

are

use

din

acc

eler

ator

tech

nolo

gy

3-23

.1po

wer

(wat

t)

GW

MW

kW mW

ILW

impa

ct s

tren

gth

j/m2

002

daJf

cm2

J/cm

2

Part

IV

: Hea

t ther

mod

ynam

icte

mpe

ratu

re(k

elvi

n)

Cel

sius

tem

pera

ture

14-

1.1

4-2.

1te

mpe

ratu

rein

terv

alt

4-3,

1lin

ear

expa

nsio

nco

effi

cien

t11

K

4-4.

1he

at,

quan

tity

of h

eat

4-5.

1he

at f

low

rat

e

4-6.

1de

nsity

of

heat

flow

rat

eW

m'

degr

ee C

elsi

us (

°C)

°C1

°C =

1 K

11°C

t The

abb

revi

atio

n de

g' is

com

mon

ly u

sed

to e

xpre

ss a

tem

pera

ture

inte

rval

, but

is n

ow r

egar

ded

as o

bsol

esce

ntby

CG

PM. H

owev

er, i

t may

be

used

in te

xtua

l mat

ter,

e.g

. 'In

crea

se th

e te

mpe

ratu

re b

y 20

deg

C'.

Item

No.

inIS

O/R

31

Qua

ntity

s/ u

nit

Sele

ctio

n of

reco

mm

ende

dde

cim

alan

d au

b.m

nite

des

of S

I un

it

Oth

er d

ecim

alm

ultip

les

and

sub-

mul

tiple

sof

SI

unit

Oth

er u

nits

or

othe

r m

oles

of

mit

whi

ch m

ay b

e us

edR

emar

ks

4-7.

1th

erm

alco

nduc

tivity

W/m

KW

/m °

C

4-8.

1co

effi

cien

t of

heat

tran

sfer

W/m

2 K

W/m

2 °C

4-10

.1he

at c

apac

ityJ/

KIc

J/K

kJ/°

CJr

C

441.

1sp

ecif

ic h

eat

capa

city

J/kg

KkJ

/kg

Kky

kg o

c

jJ/

kg C

C

4-13

.1en

tsop

yJ/

KkJ

/K

4-14

.1sp

ecif

icen

troP

YJ/

kg K

kJfk

g K

1-16

.1sp

ecif

icen

ergy

.I/

kg

MI/

kgk.

/./kg

4-18

.1sp

ecif

icla

tent

hea

tIl

kg

MI/

kgk-

Tlk

g

Par

t V: E

lect

ricity

and

mag

netis

m(g

ee N

otes

1 a

nd 2

on

page

17)

5-1.

1el

ectr

ic c

urre

ntkA

(int

ensi

ty o

fA

elec

tric

cur

rent

)(a

mpe

re)

mA

gA nA pA.

,

NS

1

elec

tric

cha

rge,

quan

tity

ofel

ectr

icity

(cou

lom

b)

nC pC

5-3.

1vo

lum

e de

nsity

of c

harg

e,ch

arge

den

sity

C/m

a

MC

/ma

kC/m

5

C/m

ma

CO

O

1su

rfac

e de

nsity

of c

harg

e

C/m

2

MC

/ma

kC/m

2

C/m

ma

C/c

m2

elec

tric

fie

ldst

reng

th

V/m

MV

/mkV

/m

mV

/rn

V/m

mV

/cm

5-6.

1

5-6.

2

5-6.

3

elec

tic p

oten

tial

pote

ntia

ldi

ffer

ence

,te

nsio

n

elec

trom

otiv

efo

rce

(vol

t)

MV

kV mV

5-7.

1di

spla

cem

ent

CI&

kC/m

2C

/cm

a

NO

TE

I. I

n el

ectr

icity

and

mag

netis

m th

e SI

uni

ts a

ssum

e th

era

tiona

lized

for

m o

f th

e eq

uatio

ns b

etw

een

the

quan

titie

s. S

ee I

SO/R

31,

Par

t V.

NO

TE

2. T

he I

EC

has

not

con

side

red

the

rule

s gi

ven

in A

ppen

dix

A n

orth

e ar

rang

emen

t and

the

cont

ent o

f th

e lis

t. In

ord

er to

giv

e gu

idan

ce to

ISO

, IE

C/T

C 2

4 pr

ovid

ed th

e lis

t of

mul

tipIP

s an

d su

b-m

ultip

les

used

her

e, b

ut w

ithou

t div

isio

n in

to c

olum

ns.

'Item

No.

ISO

M 3

1Q

nant

itySI

(m

it

Sele

ctio

n of

reco

mm

ende

dde

cim

al m

ultip

les

and

sub-

mul

tiple

sof

SI

unit

5-9.

1el

ectr

ic f

lux,

flux

of

disp

lace

men

t

MC

kC mC

5-11

.1ca

paci

tanc

e(f

arad

)m

F

nF pF

5-12

.1pe

rmitt

ivity

F/m

(.1.

17/m

pFin

im

5-17

.2el

ectr

icpo

lari

zatio

n

C/m

2

MC

/m2

kC/m

2

5-18

.1el

ectr

ic d

ipol

em

omen

tC

m

5-19

.1cu

rren

t &w

hy

A/m

2

MA

/m2

kA/m

2

5-20

.1lin

ear

curr

ent

dens

ityA

/rn

kA/m

5-21

.1m

agne

tic f

ield

stre

ngth

A/r

n

kA/m

Oth

er d

ecim

alm

ultip

les

and

sub-

mul

tiple

sof

SI

unit

Oth

er u

nits

or

othe

r na

mes

of

units

whi

ch m

ay b

e us

edR

emar

ks

C/c

m2

A/m

m2

A/c

m2

Akm

A/c

m

A/m

mA

/cm

-

7St.1

1.1.

Vra

tnrW

0GIV

RI.T

enan

owsM

eWR

IMI..

....,.

.

5-23

.1m

agne

ticpo

tent

ial

diff

eren

ce

kA mA

5-24

.1m

agne

tic f

lux

dans

ity,

mag

netic

ir iu

ctio

n

T (tas

la)

mT

p.T

nT

5-25

1fl

ux o

f m

agne

ticin

duct

ion,

mar

etic

flu

x

Wb

(web

er)

mW

b

5-26

1m

agne

tic v

ecto

Pote

ntia

lW

b/m

kWb/

mW

b/m

m

5-27

.1

5-27

.2

self

indu

ctan

ce

mut

ual i

nduc

tanc

e

H (her

lrY

)m

lfpH nH pH

5-29

.1pe

rmea

bilit

yH

/mpH

/mnH

/m

5-34

.1el

ectr

omag

netic

mom

ent,

mag

netic

mom

ent

A m

2

5-35

.1m

agne

tizat

ion

Alm

kA/m

A/m

m

5-36

1m

agne

ticpo

lari

zatio

nT

mT

mag

antic

dip

ole

mom

ent

N m

2/A

Wb

m

Item

No.

ISO

/R 3

1Q

uant

itySI

uni

t

Sele

ctio

n of

reco

mm

ende

dde

cim

al m

ultip

les

and

anb.

nata

d,je

aof

s/ u

nity

'

Oth

er d

ecim

alm

ultip

les

and

sub-

mul

tiple

sof

SI

unit

Oth

er u

nits

or

othe

r na

mes

of

units

tibi

ch m

ay b

e us

edR

emar

kg

5-41

.1re

sist

ance

11 (ohm

)

GO

Mfl

ILO

mll

11-C

5-42

.1co

nduc

tanc

e11

S1Id s

(sie

men

s)m

Sp.

S

1 S

= 1

/fl

the

nam

e ' s

iem

ens

'an

d th

e sy

mbo

l ' S

'ar

e ad

opte

d by

IE

Can

d IS

O, b

ut n

ot s

ofa

r by

CG

PM

5-43

.1re

sist

ivity

a m

G11

mm

a m

kll m

mfl

mgn

mn1

2 m

(La

cm =

10-

9 a

mSI

mna

3SI

=10

-° m

m=

ppm

are

also

use

d

5-44

.1co

nduc

tivity

1/C

2m

MS/

inkS

/rn

Sfin

*IL

SIm

5-45

.1re

luct

ance

1111

5-46

.1ne

rmea

nce

1 H

5-49

.15-

49.2

5-49

.3

impe

danc

em

odul

us o

fim

peda

nce

'

reac

tanc

e

MQ

kQ mil

5-51

.1ad

mitt

ano.

vkS

5-51

2m

odul

us o

fad

mitt

ance

i/am

S

5-51

.3su

scep

tanc

e5-

51.4

cond

ucta

nce

5-52

.1ac

tive

pow

er*

TW GW

MW

kW mW

nW

5-53

.1ap

pare

nt p

ower

V A

*TV

A*G

V A

see

also

ISO

/It 3

1/Pa

rt V

*MV

A*k

V A

mV

Ar.

tV A

*nV

A

5-54

.1re

activ

e po

wer

*Tva

r*G

var

see

also

ISO

/It 3

1/Pa

rt V

*Mva

r*k

var

*var

*rnv

ar*p

.var

*nva

r

Item

No.

ISO

I/R

11 3

1Q

ualit

itY-

SI u

nit

Sele

ctio

n of

reco

mm

ende

dde

cim

al m

ultip

les

and

sub.

mm

ripi

enof

SI

um 't

Oth

er d

ecim

ala

mtiu

lple

s nd

sub-

mul

tiple

sof

SIu

nit

thr

oer

nam

es o

fO

er u

nits

oth

units

whi

ch m

ay b

e us

edR

emar

ks

Part

V1I

I: P

hysi

cal c

hem

istr

y an

d m

olec

ular

phy

sics

8-3.

1am

ount

of

subs

tanc

em

olt

kmol

8-5.

1m

olar

mis

skg

/mol

g/m

ol

8-6.

1m

olar

vol

ume

m3/

mol

m3/

kmol

; 1/m

ol

8-7,

1m

olar

inte

rnal

ener

8YJ/

mol

J/km

ol

8-8.

1

8-9.

1

mol

ar h

eat

capa

city

J/m

ol K

; Jum

ol T

J/kr

itol K

; J/k

mol

C

mol

ar e

ntro

py

8-13

.1m

olar

ity

J/m

ol K

mol

/m3

kmo1

/1km

ol/m

3m

o1/1

mol

/dm

3

8-15

.1m

olal

itym

ol/k

gkm

ol/k

g

8-36

.1di

ffus

ion

coef

fici

ent

m2/

s

8-38

.1th

erm

al d

iffu

sion

coef

fici

ent

m2/

s

In p

hysi

cal c

hem

istr

y an

d m

olec

ular

phy

sics

, the

intr

oduc

tion

of th

e ad

ditio

nal u

nit t

he m

ole

(mol

), c

orre

spon

ding

toth

e qu

antit

yam

ount

of

subs

tanc

eis

rec

omm

ende

d by

IU

PAP,

IU

PAC

and

ISO

/TC

12.

In

this

doc

umen

t the

mol

e is

not

list

ed in

Col

umn

3 (S

I un

it) b

ecau

se it

has

not s

o

far

been

app

rove

d by

the

CG

PM.

1 m

ol is

an

amou

nt o

f su

bsta

nce

of a

sys

tem

whi

ch c

onta

ins

as m

any

elem

enta

ry u

nits

as

ther

e ar

e ca

rbon

ato

ms

in 0

.012

kg

of "

C. T

heel

emen

tary

uni

t mus

t be

spec

ifie

d an

d m

ay b

e an

ato

m, a

mol

ecul

e, a

n io

n, a

n el

ectr

on, e

tc.,

or a

spe

cifi

ed g

roup

of s

uch

part

icle

s.

Appendix C

Definitions of derived SI units with special names

force The unit of force called the newton is that forcewhich, when applied to a body having a mass ofone kilogramme, gives it an acceleration of onemetre per second squared.The unit of energy called the joule is the work donewhen the point of application of a force of onenewton is displaced through a distance of one metrein the direction of the force.

power The unit of power called the watt is equal to onejoule per second.

electric charge The unit of electric charge called the coulomb is thequantity of electricity transported in one second bya current of one ampere.

electric potential The unit of electric potential called the volt is thedifference of potential between two points of aconducting wire carrying a constant current of oneampere, when the power dissipated between thesepoints is equal to one watt.

electric capacitance The unit of electric capacitance called the farad isthe capacitance of a capacitor between the platesof which there appears a difference of potential ofone volt when it is charged by a quantity of elec-tricity equal to one coulomb .

electric resistance The unit of electric resistance called the ohm is theresistance between two points of a conductor whena constant difference of potential of one volt,applied between these two points, produces in thisconductor a current of one ampere, this conductornot being the source of any electromotive force.The unit of frequency called the hertz is thefrequency of a periodic phenomenon of which theperiodic time is one second.The unit of magnetic flux called the weber is theflux which, linking a circuit of one turn, producesin it an electromotive force of one volt as it isreduced to zero at a uniform rate in one second.

energy

frequency

magnetic flux

23

234Z.3

magnetic flui density The unit of magnetic flux density called the tesla isthe density of one weber of magnetic flux persquare metre.

electric inductance The unit of electric inductance called the henry isthe inductance of a closed circuit in which anelectromotive force of one volt is produced whenthe electric current in the circuit varies uniformlyat the rate of one ampere per second.

The units of kelvin* and Celsius temperatureinterval are identical. A temperature expressedin degrees Celsius is equal to the temperatureexpressed in kelvin less 273-15t.

The unit of luminous flux called the lumen is theflux emitted within unit solid angle of onesteradiant by a point source having a uniformintensity of one candela.

illumination The unit of illumination called the lux is anillumination of one lumen per square metre.

temperature

luminous flux

The name degree Kelvin ' (symbol °K) was changed to kelvin ' (symbol K) at the 13thCGPM (1967).t This is true for the thermodynamic scale and for the international practical scale of 1968.There are, however, slight differences between thermodynamic scales and practical scales.# One steradian is the solid angle which, having its vertex at the centre of a sphere, cuts offan area of the surface of the sphere equal to that of a square with sides of length equal to theradius of the sphere.

Appendix DValues of some imperial units in ternis of SI units

Length Density

1 yd 0-9144 m 1 lb/in3 2-767 99 x 104 kg/m31 ft 304.8 mm 1 lb/ft3 16-0185 kg/rn3

1 in 254 mm 1 lb/UKgal 0.099 776 3 Mg/m31 mile 1-609 344 km (i.e. 0 -099 7763 kg/dm aro)

ForceI pdl 0-138 255 N

Area 1 lbf 4.448 22 N1 in2 645-16 nun21 ft2 0.092 903 0 m2 Pressure1 yd2 0-836 127 m2 1 lbf/in2 6-894 76 kN/m21 mile2 2-589 99 km2

Volume1 in3 16 387-1 mm31 ft3 0.028 316 8 m31 UKgal 4-546 09 dm3*

Velocity

ft/s 0.3048 m/s1 mile/h 0-447 04 m/s

Mass1 lb 0.453 592 37 kg

Energy (work, heat)1 ft pdl 0.042 140 1 31 ft lbf 1-355 821 calf 4-1868 J1 Btuf 1.055 06 kJ

Power1 hp 745-700 W

Temperature1 Rankine 5/9 of kelvin unit

unit(=I Fahren- (-5/9 of Celsius unit)

heit unit)

Numbers printed in bold type ar exact.

* By a resolution of the twelfth CGPM in 1964 the word litre ' (symbol 1) is now recognizedas a special name for the cubic decimetre, but is not used to express high precision measure-ments.

In 1901 the litre was defined as the volume of 1 kilogramme of pure water at normalatmospheric pressure and maximum density, equal therefore to 1.000 028 dm*. This 1901definition still-applies for the purposes of the 1963 Weights and Measures Act On the basisof the 1901 definition, 1 UKgal = 4-545 96 litres, but this small difference may be disregardedfor most purpose&

t As defined by the 5th International Conference on Properties of Steam, London, 1956,and used by ISO. The calorie referred to is the international table calorie, calrr

25

Appendix E

British Stagarlards concerned with units and ennwersionof units

BS 350 :

ES 1637 : 1950

BS 1957 : 1953

BS 1991 :

BS 2045 : 1965BS 2856 : 1957

BS 2990 : 1958

BS 3763 : 1964

Cmtversion factors and tables.Pacrt L : 1959 Basis of tables. Convenion factors (with Armmd-orenttrApril and Qrt. 1963, and Jan. 1965). 15s.

2 : 1962 Detailed conversion tables. 25s.Supplemen= No. 1.1967 (PD 6203) Additional tables for

,SI conversionn. 20s.lsiferguarandum on the:M.K.S. system of electrical and magizeticWrita. 3s.Pli=entation of numerical values (fineness of expression;rbunading of numbers). 5s.Letter symbols, signs and abbreviations.Part 1 : 1967 General. 15s.Part 2 : 1961 Chemical engineering, nuclear science andapplied chemistry. 10s.Pait 3 : 1961 Fluid mechanics. 7s. 6d.Part 4 : 1961 Structures, materials and soil mechanics. 12s. 6d.Part 5 : 1961 Applied thermodynamics. 75. 6d.Part 6 : 1963 Electrical science and engineering. 12s. 6d.Preferred numbers. 6s.Precise conversion of inch and metric sizes on engineeringdrawings (with Amendment Oct 1965). 5s.Rationalized and unrationalized formulae in electricalengineering (with Amendment Jan. 1960). 5s.International System (SI) units. 8s.

Metric conversion slide (in plastics case). 21s.

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