SI-Einheiten


Tabelle 1: SI-Basiseinheiten


Größe Symbol Name Einheit Definition

Länge l Meter m Länge der Strecke, die das Licht im Vakuum während der Dauer von
1/299 792 458 Sekunde zurücklegt.
Masse m kilogram kg Das Kilogramm ist gleich der Masse des Internationalen Kilogrammprototyps.
Zeit t Sekunde s Periodendauer der Strahlung, entsprechend dem Übergang zwischen den beiden
Hyperfeinstrukturniveaus des Grundzustandes von Atomen
des Caesium-Isotops 133C
Stromstärke I Amper A Stärke eines konstanten elektrischen Stromes, der, durch zwei
parallele, geradlinige, unendlich lange und im Vakuum im Abstand von 1 Meter
voneinander angeordnete Leiter von vernachlässigbar kleinem, kreisförmigem
Querschnitt fließend, zwischen diesen Leitern die eine Kraft von 2 x 10-7 newton
pro Meter Leiterlänge erzeugen würde.
Thermodynamische
Temperatur
T Kelvin K Der Kelvin ist 1/273,16. der thermodynamischen
Temperatur des Tripelpunkts von Wasser
Stoffmenge n Mol mol Ein Mol ist die Stoffmenge eines Systems, das aus ebenso vielen
Einzelteilchen besteht, wie Atome in 12 Gramm des
Kohlenstoff-Nuklids 12C in ungebundenem Zustand enthalten sind
Lichtstärke IV Candela cd Der Candela ist die Lichtstärke in einer bestimmten Richtung einer Strahlungsquelle,
die monochromatische Strahlung der Frequenz 540 x 1012 hertz aussendet
und deren Strahlstärke in dieser Richtung 1/683 Watt pro Steradiant beträgt.

SI-abgeleitete Einheiten

Alle andere physikalischen Größen sind abgeleitete Größen und werden anhand der sieben Basisgrößen definiert.
Die SI-abgeleiteten EInheiten (auch kohärenten abgeleiteten SI-Einheiten genannt) für diese Größen werden daraus und mittels der sieben Basiseinheiten abgeleitet. Beispiele solcher SI-abgeleiteten Einheiten sind in der Tabelle 2 abgeblidet


Tabelle 2. Beispiele für kohärent abgeleitete SI-Einheiten s


  SI derived unit


Abgelietete Größe Name Symbol
Fläche square meter m2
volume cubic meter m3
speed, velocity meter per second m/s
acceleration meter per second squared   m/s2
wave number reciprocal meter m-1
mass density kilogram per cubic meter kg/m3
specific volume cubic meter per kilogram m3/kg
current density ampere per square meter A/m2
magnetic field
strength
ampere per meter A/m
amount-of-substance
concentration
mole per cubic meter mol/m3
luminance candela per square meter cd/m2
mass fraction kilogram per kilogram, which may be represented by the number 1 kg/kg = 1



Table 3.  SI derived units with special names and symbols


  SI derived unit


Derived quantity Name Symbol   Expression  
in terms of  
other SI units
Expression
in terms of
SI base units
plane angle radian (a) rad   – m·m-1 = 1 (b)
solid angle steradian (a) sr (c)   – m2·m-2 = 1 (b)
frequency hertz Hz   – s-1
force newton N   – m·kg·s-2
pressure, stress pascal Pa N/m2 m-1·kg·s-2
energy, work, quantity of heat   joule J N·m m2·kg·s-2
power, radiant flux watt W J/s m2·kg·s-3
electric charge, quantity of electricity coulomb C   – s·A
electric potential difference,
electromotive force
volt V W/A m2·kg·s-3·A-1
capacitance farad F C/V m-2·kg-1·s4·A2
electric resistance ohm Omega V/A m2·kg·s-3·A-2
electric conductance siemens S A/V m-2·kg-1·s3·A2
magnetic flux weber Wb V·s m2·kg·s-2·A-1
magnetic flux density tesla T Wb/m2 kg·s-2·A-1
inductance henry H Wb/A m2·kg·s-2·A-2
Celsius temperature degree Celsius °C   – K
luminous flux lumen lm cd·sr (c) m2·m-2·cd = cd
illuminance lux lx lm/m2 m2·m-4·cd = m-2·cd
activity (of a radionuclide) becquerel Bq   – s-1
absorbed dose, specific energy (imparted), kerma gray Gy J/kg m2·s-2
dose equivalent (d) sievert Sv J/kg m2·s-2
catalytic activity katal kat s-1·mol
(a) The radian
and steradian may be used advantageously in expressions for derived
units to distinguish between quantities of a different nature but
of the same dimension; some examples are given in Table 4.
(b) In practice, the symbols rad and sr are used where
appropriate, but the derived unit „1“ is generally omitted.
(c) In photometry, the unit name steradian and the unit
symbol sr are usually retained in expressions for derived units.
(d) Other quantities expressed in sieverts are ambient
dose equivalent, directional dose equivalent, personal dose equivalent,
and organ equivalent dose.

    Note on degree Celsius.
    The derived unit in Table 3 with the special name degree Celsius and
    special symbol °C deserves comment. Because of the way temperature
    scales used to be defined, it remains common practice to express a thermodynamic
    temperature, symbol T, in terms of its difference from the reference
    temperature T0 = 273.15 K, the ice point. This temperature
    difference is called a Celsius temperature, symbol t, and is
    defined by the quantity equation

    t= TT0.

    The unit of Celsius temperature is the degree Celsius, symbol °C. The
    numerical value of a Celsius temperature t expressed in degrees
    Celsius is given by

    t/°C = T/K – 273.15.

    It follows from the definition of t that the degree Celsius is equal
    in magnitude to the kelvin, which in turn implies that the numerical
    value of a given temperature difference or temperature interval whose
    value is expressed in the unit degree Celsius (°C) is equal to the
    numerical value of the same difference or interval when its value is
    expressed in the unit kelvin (K). Thus, temperature differences or temperature
    intervals may be expressed in either the degree Celsius or the kelvin
    using the same numerical value. For example, the Celsius temperature
    difference Deltat
    and the thermodynamic temperature difference DeltaT
    between the melting point of gallium and the triple point of water may
    be written as Deltat
    = 29.7546 °C = DeltaT
    = 29.7546 K.

22 kohärenten abgeleiteten SI-Einheiten wurden eigene Namen und Einheitenzeichen (Symbole) zugeordnet, die selbst wieder mit allen Basis- und abgeleiteten Einheiten kombiniert werden können, wie in Tabelle 4 ersichtlich


Tabelle 4.  Beispiele für Abgeleitete SI-Einheiten mit besonderem Namen


SI derived unit


Derived quantity Name Symbol
dynamic viscosity pascal second Pa·s
moment of force newton meter N·m
surface tension newton per meter N/m
angular velocity radian per second rad/s
angular acceleration radian per second squared rad/s2
heat flux density, irradiance watt per square meter W/m2
heat capacity, entropy joule per kelvin J/K
specific heat capacity, specific entropy joule per kilogram kelvin J/(kg·K)
specific energy joule per kilogram J/kg
thermal conductivity watt per meter kelvin W/(m·K)
energy density joule per cubic meter J/m3
electric field strength volt per meter V/m
electric charge density coulomb per cubic meter C/m3
electric flux density coulomb per square meter C/m2
permittivity farad per meter F/m
permeability henry per meter H/m
molar energy joule per mole J/mol
molar entropy, molar heat capacity joule per mole kelvin J/(mol·K)
exposure (x and gamma
rays)
coulomb per kilogram C/kg
absorbed dose rate gray per second Gy/s
radiant intensity watt per steradian W/sr
radiance watt per square meter steradian W/(m2·sr)
catalytic (activity) concentration katal per cubic meter kat/m3

Die 20 SI-Einheitenpräfixe, die dazu dienen, Vielfache oder Teile von Maßeinheiten zu bilden (um Zahlen mit vielen Stellen zu vermeiden) sind in Tabelle 5. abgebildet


Table 5.  SI prefixes


Faktor Name 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 deka 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

It is important to note that the kilogram is the only SI unit with a prefix
as part of its name and symbol. Because multiple prefixes may not be used,
in the case of the kilogram the prefix names of Table 5 are used
with the unit name "gram" and the prefix symbols are used with
the unit symbol "g." With this exception, any SI prefix may
be used with any SI unit, including the degree Celsius and its symbol
°C.

Example 1: 10-6 kg = 1 mg (one milligram), but not
10-6 kg = 1 µkg (one microkilogram)
Example 2: Consider the earlier example of the height of the Washington Monument.
We may write hW = 169 000 mm
= 16 900 cm = 169 m = 0.169 km
using the millimeter (SI prefix
milli, symbol m), centimeter (SI prefix centi, symbol c), or kilometer
(SI prefix kilo, symbol k).

Because the SI prefixes strictly represent powers of 10, they should not be used
to represent powers of 2. Thus, one kilobit, or 1 kbit, is 1000 bit and
not 210 bit = 1024 bit. To alleviate this
ambiguity, prefixes for binary multiples have
been adopted by the International Electrotechnical Commission (IEC) for
use in information technology.

Units outside the SI

Certain units are not part of the International System of Units,
that is, they are outside the SI, but are important and widely
used. Consistent with the recommendations of the International
Committee for Weights and Measures (CIPM, Comité International des Poids et Mesures), the units in this category that are accepted for use with the
SI are given in Table 6.


Table 6.  Units outside the SI that are accepted for
use with the SI


Name Symbol  Value in SI units
minute (time) min 1 min = 60 s
hour h 1 h = 60 min = 3600 s
day d 1 d = 24 h = 86 400 s
degree (angle) ° 1° = ( pi/180) rad
minute (angle) ' 1' = (1/60)° = (pi/10 800) rad
second (angle) '' 1'' = (1/60)' = (pi/648 000) rad
liter L 1 L = 1 dm3 = 10-3 m3
metric ton (a) t 1 t = 103 kg
neper Np 1 Np = 1
bel (b) B 1 B = (1/2) ln 10 Np (c)
electronvolt (d) eV 1 eV = 1.602 18 x 10-19 J, approximately
unified atomic mass unit (e) u 1 u = 1.660 54 x 10-27 kg, approximately
astronomical unit (f) ua 1 ua = 1.495 98 x 1011 m, approximately
(a) In many countries, this unit is called "tonne.“
(b) The bel is most commonly used with the SI prefix deci: 1 dB =
0.1 B.
(c) Although the neper is coherent with SI units and is accepted by
the CIPM, it has not been adopted by the General Conference on
Weights and Measures (CGPM, Conférence Générale des Poids et Mesures) and is thus not an SI unit.
(d) The electronvolt is the kinetic energy acquired by an electron
passing through a potential difference of 1 V in vacuum. The value
must be obtained by experiment, and is therefore not known exactly.
(e) The unified atomic mass unit is equal to 1/12 of the mass of an
unbound atom of the nuclide 12C, at rest and in its ground state. The value must be obtained
by experiment, and is therefore not known exactly.
(f)
The astronomical unit is a unit of length. Its value is such that,
when used to describe the motion of bodies in the solar system,
the heliocentric gravitation constant is (0.017 202 098 95)2 ua3·d-2. The value must be obtained by experiment, and is therefore not
known exactly.


The liter in Table 6 deserves comment. This unit and its symbol l
were adopted by the CIPM in 1879. The alternative symbol for the liter, L,
was adopted by the CGPM in 1979 in order to avoid the risk of
confusion between the letter l &nbsp and the number 1 .
Thus, although both  l and L are internationally accepted symbols
for the liter, to avoid this risk, the preferred symbol for use is L.
Neither a lowercase script letter l nor an uppercase script letter L
are approved symbols for the liter.

Other units outside the SI that are currently accepted for use
with the SI by NIST are given in Table 7. These units, which are
subject to future review, should be defined in relation to the
SI in every document in which they are used; their continued use
is not encouraged. The CIPM currently accepts the use of all of the units given in
Table 7 with the SI except for the curie, roentgen, rad, and rem.
Because of the continued wide use of these units in the United
States, NIST still accepts their use with the SI.



Table 7.  Other units outside the SI that are currently accepted
for use with the SI, subject to further review


Name Symbol    Value in SI units
nautical mile   1 nautical mile = 1852 m
knot   1 nautical mile per hour = (1852/3600) m/s
are a 1 a = 1 dam2 = 102 m2
hectare  ha 1 ha = 1 hm2 = 104 m2
bar bar 1 bar = 0.1 MPa = 100 kPa = 1000 hPa = 105 Pa
ångström Å 1 Å = 0.1 nm = 10-10 m
barn b 1 b = 100 fm2 = 10-28 m2
curie Ci 1 Ci = 3.7 x 1010 Bq
roentgen R 1 R = 2.58 x 10-4 C/kg
rad rad 1 rad = 1 cGy = 10-2 Gy
rem rem 1 rem = 1 cSv = 10-2 Sv