The Legal Units
in Germany
Foreword
Laws, Directives and Standards
The International System of Units SI (Système
international d’unités) is a progeny of the Metric System
and was given this name by the 11th General Conference
for Weights and Measures in 1960. On the basis of this
system, the units in metrology have been rearranged.
Law on Units in Metrology and on the Determination
of Time (Units and Time Act)
Revised version of 22 February 1985, last amended by
the Law Modifying the Law on Units in Metrology, the
Law modifying the Verification Act, the Law on the
Abrogation of the Time Act, the Law modifying the
Unit Ordinance and the Summer Time Ordinance of
3 July 2008 (OJ I, p. 1185)
The SI is based on seven base units and numerous
“derived units” which are formed from the base units
by pure multiplication and division, always using the
factor 1.
The SI emanates from the needs of science, but has
meanwhile also become the metric system prevailing
in the international economy. In Germany, the
SI units have been adopted as legal units for official
and commercial transactions. To ensure the national
and international uniformity of measures, the tasks
of realizing, maintaining and disseminating the units
in metrology have been assigned to the PhysikalischTechnische Bundesanstalt (PTB). Relevant details are
formulated in the Units Act.
Literature
• Bureau international des poids et mesures (BIPM):
Le Système international d´unités (SI) –
The International System of Units (SI).
8e édition, 2006. Pavillon de Breteuil,
F-92312 Sèvres Cedex, France
• Ambler Thomson, Barry N. Taylor (ed.): Guide for the
use of the International System of Units (SI). National
Institute of Standards and Technology. NIST Special
Publication 811, 2008 Edition
Braunschweig, June 2012
Execution Ordinance on the Law on Units in
Metrology and on the Determination of Time
of 13 ­December1985 (OJ I, p. 2272), last amended by the
3rd Ordinance on the Law modifying the Unit Ordinance) of 25 September 2009 (OJ I, p. 3169)
Council Directive 80/181/EEC of 20 December 1979
on the approximation of the laws of the Member States
relating to units of measurement. Latest amendments:
• 85/1/EEC of 18 December 1984
(Official Journal L 2 of 3 January 1985)
• 89/617/EEC of 27 November 1989
(Official Journal L 357 of 7 December 1989)
• 1999/103/EC of 24 January 2000
(Official Journal L 34 of 9 February 2000)
• 2009/3/EC of 11 March 2009
(Official Journal L 114 of 7 May 2009)
DIN 1301 Part 1, 2010-10
Units; unit names, unit symbols
DIN 1301 Part 1 Supplemetary Sheet 1, 04.82
Units; names and symbols analogous to units
DIN 1301 Part 2, 02.78
Units; submultiples and multiples for general use
DIN 1301 Part 3, 10.79
Units; conversions of units no longer to be used
DIN 1304 Part 1, 03.94
Letter symbols for physical quantities; symbols for general use
DIN 5493 Part 1, 02.93
Logarithmic quantities and units
ISO 1000: 11.92
SI units and recommendations for the use of their multiples and of
certain other units
ISO 31-0 to ISO 31-XIII
(Principles of quantities and units and of units for special physical
quantities)
3
SI base units
Base quantity
Name
Base unit
Symbol
Definition
(cf. also DIN 1301)
length
metre
m
The metre is the length of the path travelled by light in
vacuum during a time interval of 1/299 792 458 of a second.
mass
kilogram
kg
The kilogram is equal to the mass of the international
prototype of the kilogram.
time
second
s
The second is the duration of 9 192 631 770 periods of the
radiation corresponding to the transition between the two
hyperfine levels of the ground state of the caesium 133 atom.
electric current
ampere
A
The ampere is that constant current which, if maintained in
two straight parallel conductors of infinite length, of
negligible circular cross-section, and placed 1 metre apart in
vacuum, would produce between these conductors a force
equal to 2 · 10–7 newton per metre of length.
temperature
kelvin
K
The kelvin is the fraction 1/273.16 of the thermodynamic
temperature of the triple point of water.
This definition refers to water having the isotopic
composition defined exactly by the following amount of
substance ratios: 0.000 155 76 mole of 2H per mole of 1H,
0.000 379 9 mole of 17O per mole of 16O and 0.002 005 2
mole of 18O per mole of 16O.
amount of substance
mole
mol
­
The mole is the amount of substance of a system which
contains as many elementary entities as there are atoms in
0.012 kilogram of carbon 12. When the mole is used, the
elementary entities must be specified and may be atoms,
molecules, ions, electrons, other particles, or specified
groups of such particles.
luminous intensity
candela
cd
The candela is the luminous intensity, in a given direction,
of a source that emits monochromatic radiation of
frequency 540 · 1012 hertz and that has a radiant intensity in
that direction of 1/683 watt per steradian.
SI prefixes
FactorPrefixSymbol
1024
yottaY
1021
zettaZ
1018
exaE
1015
petaP
1012
teraT
109
gigaG
106
megaM
103
kilok
102
hectoh
101
decada
4
FactorPrefixSymbol
10–1
decid
10–2
centic
10–3
millim
10–6
microμ
10–9
nanon
10–12
picop
10–15
femtof
10–18
attoa
10–21
zeptoz
10–24
yoctoy
5
Quantities and their units
Quantity
Name of unit
Symbol
Relation and Remarks
length
metre
astronomical unit
parsec
light year
ångström
typographical point
inch*
foot
yard
mile
international nautical mile
fathom
m
ua
pc
l. y.
Å
p
in
ft
yd
mile
n. m.
fm
SI base unit
1 ua
= 149.597 870 · 109 m•mean Earth-Sun distance
1 pc = 206 265 ua = 30.857 · 1015 m
1 l. y. = 9.460 530 · 1015 m = 63 240 ua = 0.306 59 pc
1Å
= 10–10 m
1p
= 0.376 065 mm •in the printing industry
1 in = 2.54 · 10–2 m = 25.4 mm**
1 ft = 0.3048 m = 30.48 cm
1 yd = 0.9144 m
1 mile = 1609,344 m
1 n. m. = 1852 m
1 fm = 1.829 m •in maritime shipping
plane angle
radian
rad
1 rad = 1 m/m •central angle r = 1 m,
arc = 1 m
perigon angle
= 2 π · rad = 360° = 400 gon
degree
°
1° = (π/180) rad = 1.1111 gon
minute
’
1’ = 1°/60 •also called “angular minute”
second
”
1” = 1’/60 = 1°/3600 •also called “angular second”
gon
gon
1 gon = (π/200) rad = 0.9° •referred to as “grade”
grade g
1g = 1 gon = 0.5 π · 10–2 rad
c
c
centesimal minute
1 = 10–2 gon = 0.5 π · 10–4 rad
cc
cc
centesimal second
1 = 10–4 gon = 0.5 π · 10–6 rad
solid angle
steradian
sr
1 sr = 1 m2/m2 • r = 1 m,
area of spherical cap = 1 m2
refractive power
dioptre
dpt
1 dpt = 1/m •in optical systems only
area
square metre
m
•do not use “qm”
are
a
1a
= 100 m2 •for real estate and parcels
of land only
hectare
ha
1 ha = 100 a = 104 m2 •for real estate and parcels
of land only
barn
b
1b
= 10–28 m2 •in atomic and nuclear physics
Morgen
1 Morgen = 0.25 ha = 2500 m2•varies from region to region
square foot
sq ft
1 sq ft = 0.092 903 06 m2
acre
ac
1 ac
= 4046.856 m2
square yard
sq yd
1 sq yd = 0.8361 m2
2
• Legal units: In official and commercial transactions, quantities
must be indicated in legal units
(Units and Time Act, Unit Ordinance).
• Common units: These may only be used if it is not stipulated that
the quantities have to be indicated in legal units (e. g. in the field of
research), or they may be used only in addition to these.
6
* in italics: permissible in some countries acc. to EC directive, in
special fields of application and use
**last digit in bold face: value considered to be exact (cf. also ISO 31)
7
Quantity
Name of unit
Symbol
Relation and Remarks
volume
cubic metre
litre
m
l or L
•do not use “cbm”
1 l = 1 L = 10–3 m3 = 1 dm3 = 103 cm3 •do not use “ccm”
barrel
gill
fluid ounce
pint
quart
gallon
bbl
gill
fl oz
pt
qt
gal
1 barrel = 158.988 l •for crude oil only
1 gill = 0.142 · 10–3 m3 •for spirits only
1 fl oz = 28.4131 · 10–6 m3 = 28.4131 ml 29.5735 ml (USA)
1 pt = 0.568 262 · 10–3 m3= 568.262 ml 473.176 ml (USA)
1 qt = 1.136 52 · 10–3 m3 = 1.136 52 l 0.946 353 l (USA)
1 gal = 4.546 09 · 10–3 m3 = 4.54 609 l 3.785 41 l (USA)
measure of
capacity
for ships
register ton
gross register ton
net register ton
R. T.
G. R. T.
N. R. T.
1 R. T. = 100 ft3 = 2.831 68 m3
a ship’s permanently closed-in spaces in R. T.
overall capacity less spaces required for running the ship, in R. T.
m3/s
m3/kg
1 m3/s = 60 · 103 l/min = 3600 m3/h
1 m3/kg = 1 l/g
volume flow rate
specific volume
3
mass
kilogram
kg
SI base unit
gram
g
1g
= 10–3 kg
•do not use “gr.” or “Gr.”
tonne
t
1t
= 103 kg
metric carat
1 carat = 0.2 g = 0.2 · 10–3 kg •for precious stones only
(symbols “Kt” and “ct” also used)
unified atomic
u
1u
= 1.660 565 5 · 10–27 kg •1/12 of the mass of an
mass unit atom of the nuclide 12C
Pfund 1 = 0.5 kg •since 1884 no longer a
legal unit
Zentner
ztr
1 ztr = 50 kg
quintal
q
1q
= 100 kg
ounce (avoirdupois)
oz
1 oz = 28.3495 · 10–3 kg = 28.3495 g
troy ounce
oz tr
1 oz tr = 31.10 · 10–3 kg = 31.10 g
• for gold
pound
lb
1 lb = 0.453 592 37 kg = 453.592 37 g
weight ton
tons/deadweight
ton dw
t dw
1 ton dw= 1016 kg 1 t dw = 1000 kg
mass per unit
length
tex
den
1 tex = 10–6 kg/m = 1 g/km •for textiles only
1 den = 1/9 tex = 1/9 g/km
1 kg/m2
kg/s
kg/m3
1 kg/m2 = 1 mg/mm2
1 kg/s = 60 kg/min = 3.6 t/h = 86.4 t/d
1 kg/m3 = 1 g/l = 10–3 kg/l
tex
denier
mass per unit area mass flow
density
specific gravity
degree Öchsle
Oe°
of the must
8
•tonnage of ships
The specific gravity of the must (in degree Öchsle) corresponds to the
numerical value of the density (of grape must) in kg/m3 minus 1000.
9
Quantity
Name of unit
Symbol
Relation and Remarks
time
second
s
SI base unit
• prefixes to be used with s only
space of time,
minute
min
1 min = 60 s
duration
hour
h
1h
= 60 min = 3600 s
day
d
1d
= 24 h = 1440 min = 86 400 s
frequency
hertz
Hz
1 Hz = 1/s
number of revolutions reciprocal second
1/s
• do not use “rps” or “rpm”
(per unit time),
reciprocal minute
1/min
1/min = 1/(60s)
rotational speed*
velocity
metre per second
m/s
1 m/s = 3.6 km/h
knot
kn
1 kn = 1 n. m./h = 0.5144 m/s
2
acceleration
m/s
9.806 65 m/s2 = standard acceleration due to gravity gn
gal
Gal
1 Gal = 10–2 m/s2 •in geodesy only
angular velocity
rad/s
force
newton
N
1N
= 1 kg · m/s2 dyne
dyn
1 dyn = 10–5 N
pond
p
1p
= 9.806 65 · 10–3 N •1 kp ≈10 N
pulse
N · s
1 N · s = 1 kg · m/s •mass times velocity
2
sound pressure**
pascal
Pa
1 Pa = 1 N/m
sound power***
W
•DIN 1332
sound intensity**,
sound energy flux
density
W/m2
•DIN 1332
noise dose***
Pa2 · s
•DIN 45 644
2
2
pressure,
pascal
Pa
1 Pa
= 1 N/m = 1 kg/(s · m) ≈ 0.75 · 10–2 mmHg
mechanical bar
bar
1 bar = 105 Pa = 103 mbar = 105 kg/(s2 · m)
stress
conventional milli-
mmHg
1 mmHg = 133.322 Pa = 1.333 22 mbar
metres of mercury
•permissible in medicine only
stand. atmosphere
atm
1 atm = 1.013 25 bar
techn. atmosphere
at
1 at = 1 kp/cm2 = 0.980 665 bar
torr
torr
1 torr = (101 325/760) Pa = 1.333 224 mbar
conventional metres
head of water
mWS
1 mWS = 9806.65 Pa = 98.0665 mbar
1 lb/in2 = 68.947 57 mbar = 6894.757 Pa
psilb/in2
* in electrical engineering: angular frequency
** In acoustics, logarithmic quantities acc. to DIN 5493 part 1,
are often used (e. g. sound power level).
***referred to as sound dose when related to the nominal value
10
11
Quantity
Name of unit
Symbol
Relation and Remarks
dynamic
pascal second
Pa · s
1 Pa · s
= 1 N · s/m2 = 1 kg/(s · m) •DIN 1342
viscosity
poise
P
1P
= 0.1 Pa · s = 0,1 N · s/m2
kinematic
m2/s
•DIN 1342
viscosity
stokes
St
1 St = 10–4 m2/s
energy, work,
joule
J
1J
= 1 N · m = 1 W · s = (1/3.6) · 10–6 kW · h = 1 kg · m2/s2
quantity of heat
kilowatt hour
kW · h
1 kW · h = 3.6 MJ = 860 kcal
electron volt
eV
1 eV = 160.218 92 · 10–21 J
erg
erg
1 erg = 10–7 J
calorie
cal
1 cal = 4.1868 J = 1.163 · 10–3 W · h
therm
therm
1 therm = 105.50 · 106 J
calorific value
kcal/l
1 kcal/l = 4.1868 kJ/l • also called “gross calorific value”
kcal/kg
1 kcal/kg = 4.1868 kJ/kg
coal equivalent
t C. E. 1 t C. E. = 7 · 106 kcal = 29.3076 · 109 J = 8.141 · 103 kW · h
• The unit “coal equivalent per ton” is based on
a calorific value of 7000 kcal/kg
heat capacity
J/K
1 J/K = 1 m2 · kg/(s2 · K) •entropy
energy density
J/m3
1 J/m3 = 1 kg/(m · s2)
specific energy
J/kg
1 J/kg = 1 m2/s2
molar energy
J/mol
1 J/mol = 1 W · s/mol = 1 m2 · kg/(s2 · mol)
molar heat capacity
J/(mol · K)
1 J/(mol · K)= 1 m2 · kg/(s2 · K · mol) •molar entropy
power, energy flux, watt
W
1W
= 1 J/s = 1 N · m/s = 1 V · A = 1 m2 · kg/s3
heat flux
volt-amperes
Va
1 Va = 1 W • apparent power in electrical power
VAr
VAr
1 VAr = 1 W • reactive power } engineering
horse power
hp
1 hp = 75 m · kp/s = 0.735 498 75 kW
heating power
kcal/h
1 kcal/h = 1.163 W
thermal
W/(m · K)
1 W/(m · K)= 1 m · kg/(s3 · K) ≈ 0.860 kcal/(m · h · °C)
conductivity
kcal/(m · h · °C) 1 kcal/(m · h · °C) = 1.163 W/(m · K)
heat transition
W/(m2 · K)
1 W/(m2 · K)= 1 m · kg/(s3 · m · K) ≈ 0.860 kcal/(m2 · h · °C)
coefficient
kcal/(m · h · °C) 1 kcal/(m2 · h · °C) = 1.163 W/(m2 · K)
heat flux density,
W/m2
1 W/m2 = 1 kg/s3
irradiance
radiant intensity
W/sr
1 W/sr = 1 m2 · kg/(s3 · sr)
2
radiance
W/(m · sr)
1 W/(m2 · sr)= 1 kg/(s3 · sr)
12
13
Quantity
Name of unit
Symbol
Relation and Remarks
electric current
ampere
A
SI base unit
voltage,
electric potential, electromotive force
volt
V
1 V
= 1 W/A = 1 kg · m2/(A · s3)
electric resistance
ohm
Ω
1Ω
= 1 V/A = 1/S = 1 W/A2 = 1 kg · m2/(A2 · s3)
electric conductance
siemens
S
1S
= 1 A/V = 1/Ω = 1 W/V2 = 1 A2 · s3/(kg · m2)
electric charge,
quantity of electricity
coulomb
ampere-hour
C
A · h
1C =1A·s
1 A · h = 3600 A · s = 3600 C
electric charge density
C/m3
1 C/m3 = 1 A · s/m3
electric flux density,
displacement
C/m2
1 C/m2 = 1 A · s/m2
capacitance
F
1F
permittivity
F/m
1 F/m = 1 A · s/(V · m) = 1 A2 · s4/(kg · m3)
electric field strength
V/m
1 V/m = 1 kg · m/(A · s3) magnetic flux
magnetic flux density,
weber
Wb
1 Wb = 1 V · s = 1 T · m = 1 A · H = 1 kg · m2/(A · s2)
magnetic induction
inductance,
tesla
T
1T
= 1 Wb/m2 = 1 V · s/m2 = 1 kg/(s2 · A)
magnetic conductance henry
H
1H
= 1 Wb/A = V · s/A = 1 kg · m2/(A2 · s2)
permeability
H/m
1 H/m = 1 V · s/(A · m) = 1 kg · m/(A2 · s2)
farad
= 1 C/V = 1 A · s/V = 1 A2 · s4/(kg · m2)
• DIN 1357
2
magn. field strength
A/m
oersted
Oe
1 Oe = [103/(4π)] · A/m ≈ 80 A/m
temperature T
kelvin
K
SI base unit
Celsius temperature t degree Celsius
°C
t/°C = T/K – 273.15 • triple point of H2O = 0.01 °C
temperature difference Kelvin, degree Celsius K, °C
degree Fahrenheit
°F
t/°C = (5/9) · (t/°F – 32)
luminous intensity
candela
luminance
stilb
luminous flux
lumen
illuminance
lux
14
cd
SI base unit
cd/m
sb
lm
lx
2
1 sb = 104 cd/m2
1 lm = 1 cd · sr 1 lx = 1 lm/m2 = 1 cd · sr/m2 • DIN 5031 part 3
• DIN 5031 part 3
• DIN 5031 part 3
15
Quantity
Name of unit
Symbol
Relation and Remarks
activity (of a radioactive substance)
becquerel
curie
Bq
Ci
1 Bq 1 Ci = 1/s = 37 GBq
absorbed dose,
kerma
gray
rad
Gy
rd
1 Gy 1 rd = 1 J/kg = 1 W · s/kg = 1 m2/s2
= 1 cGy = 0.01 Gy
dose equivalent
sievert
rem
gray per second
rad per second
Sv
rem
Gy/s
rd/s
1 Sv 1 rem 1 Gy/s 1 rd/s = 1 J/kg = 1 W · s/kg = 1 m2/s2
= 1 cSv = 0.01 Sv
= 1 W/kg = 1 m2/s3
= 0.01 Gy/s
dose equivalent
rate
sievert per second
rem per second
Sv/s
rem/s
1 Sv/s = 1 W/kg = 1 m2/s3
1 rem/s = 0.01 Sv/s
exposure
coulomb per kg
röntgen
C/kg
R
1 C/kg = l A · s/kg • do not use this quantity any longer
1R
= 258 · 10–6 C/kg
amount of substance mole
concentration (of
amount of substance)
mol
mol/l
SI base unit 1 mol/l = 103 mol/m3 molar volume
l/mol
1 l/mol = 10–3 m3/mol
molar mass
g/mol
1 g/mol = 10–3 kg/mol
molar entropy
J/(mol · K)
1 J/(mol · K) molar intrinsic energy
J/mol
• DIN 1345
volume concentration*,**
1
substance amount fraction**
1
• DIN 1310
mass fraction**,
1
• DIN 1310
volume fraction**,
1
• DIN 1310
mass per unit volume***,
partial density***
kg/l or g/l
1 kg/l = 103 kg/m3
• DIN 1310
particle concentration
1/m3
• e. g. dust particles per m3
kat
1 kat = mol · s–1
1 kat/m3 = mol · s–1 · m–3
• contained in Directive
2009/3/EC as SI derived unit
absorbed dose rate
catalytic activity
catalytic
concentration
*
** 16
katal
kat/m3
also called “volume fraction” if the mixing process does not
change the volume
The fraction can also be indicated in per cent (1 % = 1/100) or per
thousand (1 ‰ = 1/1000).
• DIN 6814 part 4
• DIN 1310
= 1 kg · m2/(s2 · mol · K)
*** do not refer to “g/(100 ml)” as “%” and to “mg/(100 ml)” as
“mg %” (DIN 1310)
17
Fundamental constants (selection)
Fundamental constants are essential elements for the
description of the world: they appear in physical theories
without the theories proper being able to indicate their
values. These constants must therefore be measured
on the basis of experiments – a fundamental task of
­metrology.
Avogadro constant Boltzmann constant Elementary charge Faraday constant Fine structure constant, inverse Electric field constant
Magnetic field constant
Magnetic flux quantum
Gravitation constant Josephson constant Speed of light (in vacuum) Atomic mass constant Planck constant Electron rest mass
Proton rest mass
Rydberg constant Stefan Boltzmann constant Universal gas constant von Klitzing constant The numerical values of this survey have been taken
from the CODATA data base.
[http://physics.nist.gov/cuu/Constants/]
The figures in brackets behind a numerical value relate
to the uncertainty in the last digits of the value. The
uncertainty is stated as simple standard deviation
(example: the indication 6.672 59 (85) is the same as
6.672 59 ± 0.000 85).
18
NA = 6.022 141 29 (27) · 1023 mol–1
k = 1.380 6488 (13) · 10–23 J · K–1
e = 1.602 176 565 (35) · 10–19 C
F = 96 485.3365 (21) · C · mol–1
α–1 = 137.035 999 074 (44)
ε0 = 1/(μ · c2) = 8.854 187 817... · 10–12 F · m (exact)
μ0 = 4π · 10–7 N · A–2 = 12.566 370 614... · 10–7 N · A–2 (exact)
Φ0 = 2.067 833 758 (46) · 10–15 Wb
G = 6.673 84 (80) · 10–11 m3 · kg–1 · s–2
KJ = 483 597.870 (11) · 109 Hz · V–1
c = 299 792 458 m · s-1 (exact)
u = 1.660 538 921 (73) · 10–27 kg
h = 6.626 069 57 (29) · 10–34 J · s
me = 9.109 382 91 (40) · 10–31 kg
mp = 1.672 621 777 (74) · 10–27 kg
R∞ = 10 973 731.568 539 (55) m–1
σ = 5.670 373 (21) · 10–8 W · m–2 · K–4
R = 8.314 4621 (75) · J · mol–1 · K–1
RK = 25 812.807 4434 (84) Ω
Literature
P. J. Mohr, B. N. Taylor, D. B. Newell: CODATA recommended values of the fundamental physical constants:
2006, Rev. Mod. Phys. 80, 2 (2008)
19
The Physikalisch-Technische Bundesanstalt,
Germany's national metrology institute, is a
scientific and technical higher federal authority
falling within the competence of the Federal
Ministry for Economic Affairs and Energy.
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Braunschweig und Berlin
National Metrology Institute
Bundesallee 100
38116 Braunschweig, Germany
Press and Information Office
phone: +49 531 592-3006
fax:
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As of: 05/2016