Units of Measurements

Units of Measurements

Table of Contents

SI-Basic Units
Spelling conventions for SI Units
Legal Units
Conversion of the most common British (UK) and American (US) Units into SI Units

As a result of international agreements a unification of the measurement system has been achieved (International System of Units; Système international = SI-units). In Germany the “Law on Units in the Measurement System” was passed on 2 July 1969, the implementing ordinance concerning this Law was passed on 26 July 1970 and a Law for amending the Law on Units in the Measurement System on 6 July 1973. According to this legal framework the unitsdefined in these laws and regulations are obligatory for business and official transactions. Details have been defined in DIN 1301 “Units, unit names, unit symbols” (DIN Deutsches Institut für Normung e. V., Burggrafenstraße 6, 10787 Berlin, Tel.: +49 30 2601-0, Fax: +49 30 2601-1231 and in ISO 31, which is now superseded by the harmonized ISO/IEC 80000 standard (ISO copyright office, Case postale 56, CH-1211 Geneva 20, Tel. + 41 22 749 01 11, Fax + 41 22 749 09 47.

In the USA the same units etc. were first described in The Metric Conversion Act of 1975 (Public Law 94–168) (see also G.G. Stoner, Cosmet. Toiletries 93, No. 11, 57 [1978]) and are now harmonized in ISO 80000.

The new units have been taken into account in the present edition of the Handbook, when new documentation has been provided by the manufacturers of auxiliary substances. The new units have also been used in some revisions and additions by the editors. However, in the following the most important changes in the measurement system are given so that conversions from older unit systems may be performed, if required.

There are nine basic SI units, of which the following 7 are relevant:

SI-Basic Units

Basis physical quantity

Basic unit

Name

Symbol

length

meter

m

time

second

s

mass

kilogram

kg

temperature

kelvin

K

electrical current

ampere

A

luminous intensity

candela

cd

amount of substance

mole

mol

17 further units are derived from the nine basic units, of which the following derived SI units, with their names,are relevant:

Physical quantity

Unit

Expressed as basic units or derived units

Name

Symbol

work, energy, quantity of heat

joule

J

illuminance

lux

lx

force

Newton

N

pressure

Pascal

Pa

The following prefixes were established for decimal multiples and subdivisions of units:

Multiples

Prefix

Symbol

Subdivisions

Prefix

Symbol

101

deca

da

10–1

deci

d

102

hecto

h

10–2

centi

c

103

kilo

k

10–3

milli

m

106

mega

M

10–6

micro

µ

109

giga

G

10–9

nano

n

1012

tera

T

10–12

pico

p

1015

peta

P

10–15

femto

f

1018

exa

E

10–18

atto

a

Spelling conventions for SI Units

If derived units consist of several basic units in the numerator or denominator, these are written one after the other with some space in between (in the case of a typewriter a single space).

Examples: N s/m, not Ns/m; kg m/s, not kgm/s.

However, multiples or subdivisions are written together with the respective units.

Examples: MNm, not M N m; mm2/s, not m m2/s.

Indices must not be appended to unit symbols but should be added to the formula symbol giving the physical quantity. Hence e.g. the normal volume may no longer be given as Nm3 (normal cubic meter) but instead as: normal volume Vn=…m3 or better: volume V=…m3 in the normal state.

Variations are permissible in the names for physical quantities, but the standard form of the unit name should always be used. This principle helps to avoid misleading spellings.

Data for the various units relevant to the present Handbook, or the corresponding conversion factors for previously used units, are given in the following table:

Legal Units

Physical quantity

Legal units

 

Conversion

Comment

Symbol

SI Unit

Relationship

Recommended unit

Previous unit

Name

Symbol

mass

m

kilogram

kg

;

kg

 

SI basic unit

density

ρ

kilogram per cubic meter

;

 

 

specific volume

V

cubic meter per kilogram

;

 

 

amount of substance

n

mole

mol

 

kmol

 

 

mass related to amount of substance (molar mass)

M

kilogram per mol

 

 

volume related to amount of substanc (molar volume)

Vm

cubic meter per mole

 

 

surface tension and interfacial tension

 

milli-Newton per meter

 

for all liquids

thermodynamic or kelvin temperature, celsius temperature

T, Θ, t, ϑ

Kelvin

K

K ℃

°K

SI basic unit practical conversion:

dynamic viscosity

η

Pascal second

Pa·s

mPa·s

cP (centipoise)

 

kinematic viscosity

ν

square meter per second

 

st (stokes)

 

Conversion of the most common British (UK) and American (US) Units into SI Units

Physical quantity

Name of the unit

Symbol

Conversion into SI Units

 

length

inch

in

1in

=25.4mm

foot

ft

1ft=12in

=0.3048m

yard

yd

1yd=3ft

=0.9144m

mile (statute)

 

1mile=1760yd

=1.609344km

nautical mile (intern.)

n. mile

1n. mile

=1.852km

area

square inch

sq in

1sq in

=6.4516cm2

square foot

sq ft

1sq ft=144sq in

=929.030cm2

square yard

sq yd

1sq yd=9sq ft

=0.836127m2

rood

 

1rood=1210sq yd

=1011.71m2

acre

 

1acre=4roods

=4046.86m2

square mile

sq mile

1sq mile=640acres

=2.589988km2

volume

cubic inch

cu in

1cu in

=16.3871cm3

cubic foot

cu ft

1cu ft

=28.3168dm3

cubic yard

cu yd

1cu yd

=0.764555m3

British measure of capacity

UK fluid ounce

UK fl oz

1fl oz

=28.4131cm3

UK gill

 

1gill=5fl oz

=0.142065dm3

UK pint

UK pt

1pt=20fl oz

=0.568261dm3

UK quart

UK qt

1qt=2pt

=1.13652dm3

UK gallon

UK gal

1gal=4qt

=4.54609dm3

American measure of capacity (liquid)

US fluid ounce

US fl oz

1fl oz

=29.5735cm3

US gill

gi

1gi=4fl oz

=0.118294dm3

US liquid pint

liq pt

1liq pt=4gi

=0.473176dm3

US liquid quart

liq qt

1liq qt=2liq pt

=0.946353dm3

US gallon

US gal

1gal=4liq qt

=3.78541dm3

US barrel (oil)

bbl

1bbl=42gal

=158.987dm3

American measure of capacity (dry)

US dry pint

dry pt

1dry pt

=0.550610dm3

US dry quart

dry qt

1dry qt=2dry pt

=1.10122dm3

US peck

pk

1pk=8dry qt

=8.80976dm3

US bushel

bu

1bu=4pk

=35.2391dm3

mass

grain

gr

1gr

=0.064799g

dram (avoir dupois)

dr

1dr=27.34375gr

=1.77185g

ounce (avdp.)

oz

1oz=16dr

=28.3495g

troy ounce

oz tr

1oz tr=480gr

=31.1035g

pound (avdp.)

lb

1lb=16oz

=0.453592kg

troy pound

lb tr

1lb tr=12oz tr

=0.373242kg

stone (UK)

 

1stone=14lb

=6.35029kg

hundredweight (UK)

cwt

1cwt=112lb

=50.8023kg

(long) ton (UK)

ton

1ton=2240lb

=1016.05kg

Shorthundredweight (US)

sh cwt

1sh cwt=100lb

=45.3592kg

short ton (US)

sh ton

1sh ton=2000lb

=907.185kg

force

poundal

pdl

1pdl=1lb ft/s2

=0.138255N

pound-force

lbf

1lbf

=4.44822N

UK ton-force

UK tonf

1tonf=2240lbf

=9964.02N

US ton-force=2kip

US tonf

1tonf=2000lbf

=8896.44N

pressure

pound-force / sq ft

lbf / ft2

1lbf / ft2

=47.8803Pa

pound-force / sq in (p.s.i.)

lbf / in2

1lbf / in2

=6.89476kPa

energy, quantity of heat

foot pound-force

ft lbf

1ft lbf

=1.35582J

British thermal unit

Btu

1Btu

=1.05506kJ

 

therm

 

1therm=105 Btu

=105.506MJ

 

power

British thermal unit / hour

Btu / h

1Btu / h

=0.293071W

horsepower

hp

1hp=550ft lbf / s

=745.700W

temperature

degree Fahrenheit

°F

temp. in ℃ =(temp. in °F −32)·5/9

∆1°F=∆5/9℃