SI derived units
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Table 1. SI derived units expressed in terms of SI based units and SI supplementary units
- [TAB]
- Quantity |Name | Symbol
- acceleration | metre per second squared | m/s2
- angular acceleration | radian per second squared | rad/s2
- angular momentum | kilogram metre squared per second | kg·m2/s
- angular velocity | radian per second | rad/s
- area | square metre | m2
- coefficient of linear expansion | 1 per kelvin | K−1
- concentration (of amount of substance) | mole per cubic metre | mol/m3
- density | kilogram per cubic metre | kg/m3
- diffusion coefficient | metre squared per second | m2/s
- electric current density | ampere per square metre | A/m2
- exposure rate (ionizing radiation) | ampere per kilogram | A/kg
- cinematic viscosity | metre squared per second | m2/s
- luminance | candela per square metre | cd/m2
- magnetic field strength | ampere per metre | A/m
- magnetic moment | ampere metre squared | A·m2
- mass flow rate | kilogram per second | kg/s
- mass per unit area | kilogram per square metre | kg/m2
- mass per unit length | kilogram per metre | kg/m
- molality | mole per kilogram | mol/kg
- molar mass | kilogram per mole | kg/mol
- molar volume | cubic metre per mole | m3/mol
- moment of inertia | kilogram metre squared | kg·m2
- moment of momentum | kilogram metre squared per second | kg·m2/s
- momentum | kilogram metre per second | kg·m/s
- radioactivity (disintegration rate) | 1 per second | s−1
- rotational frequency | 1 per second | s−1
- specific volume | cubic metre per kilogram | m3/kg
- speed | metre per second | m/s
- velocity | metre per second | m/s
- volume | cubic metre | m3
- wave number | 1 per metre | m−1
Table 2. SI supplementary units
- [TAB]
- Quality | Name | Symbol | Definition
- plane angle | radian | rad | The radian is the plane angle between two radii of a circle which cut off on the circumference an arc equal in length to the radius
- solid angle | steradian | sr | The steradian is the solid angle which, having it's vertex in the centre of a sphere, cuts off an area of the surface of the sphere equal to that of a square with sides of length equal to the radius of the sphere.
Table 3. Derived units with special names
- [TAB]
- Quantity |Name | Symbol | Expression in terms of other SI units and definition of unit. | Expression in terms of SI Base units
- admittance | siemens | S | W−1 | m−2·kg−1·s3·A2
- capacitance | farad | F | C / V | m−2·kg−1·s4·A2
- conductance | siemens | S | W−1 | m−2·kg−1·s3·A2
- electrical resistance | ohm | W | V / A | m2·kg·s−3·A−2
- electric charge | coulomb | C | A·s | s·A
- electric flux | coulomb | C | A·s | s·A
- electric potential | volt | V | W / A | m2·kg·s−3·A−1
- electromotive force | volt | V | W / A | m2·kg·s−3·A−1
- energy | joule | J | N·m | m2·kg·s−2
- energy flux | watt | W | J/s | m2·kg·s−3
- flux of displacement | coulomb | C | A·s | s·A
- force | newton | N | kg·m/s2 | m·kg·s−2
- frequency | hertz | Hz | s−1 | s−1
- illuminance | lux | lx | lm/m2 | m−2·cd·sr
- impedance | ohm | W | V / A | m2·kg·s−3·A−2
- inductance | henry | H | Wb/A (V·s/A) | m2·kg·s−2·A−2
- luminous flux | lumen | lm | cd·sr | cd·sr
- magnetic flux | weber | Wb | V·s | m2·kg·s-2·A−1
- magnetic flux density | tesla | T | Wb/m2 | kg·s−2·A−1
- magnetic induction | tesla | T | Wb/m2 | kg·s−2·A−1
- magnetic polarization | tesla | T | Wb/m2 | kg·s−2·A−1
- permeance | henry | H | Wb/A (V·s/A) | m2·kg·s-2·A−2
- potential difference | volt | V | W / A | m2·kg·s−3·A−1
- power | watt | W | J/s | m2·kg·s-3
- pressure, stress | pascal | Pa | N/m2 | m−1·kg·s−2
- quantity of electricity | coulomb | C | A·s | s·A
- quantity of heat | joule | J | N·m | m2·kg·s−2
- reactance | ohm | W | V / A | m2·kg·s−3·A−2
- stress | pascal | Pa | N/m2 | m−1·kg·s−2
- susceptance | siemens | S | W−1 | m−2·kg−1·s 3·A2
- weight | newton | N | kg·m/s2 | m·kg·s−2
- work | joule | J | N·m | m2·kg·s−2
Notes to the above table
The expressions in the fourth column represent the definitions of the respective units in symbolic form. For instance, the quantity force is defined as the product of mass and acceleration (F = m·a) so the definition of the unit of force, the newton (N) is given by
1 N = 1 kg·m/s2.
Mechanical energy must not be expressed in newton metres (N·m) but only in joules (J).
The former unit is used only for torque or moment of force.
In the expressions for the lumen (lm) and lux (lx) in the fifth column, the steradian (sr) is treated as a base unit.
Table 4. SI derived units expressed in terms of SI derived units with special names as well as SI based units and SI supplementary units:
- [TAB]
- Quality |Name | Symbol | Expression in terms of SI Base units and SI Supplementary units
- absorbed dose | joul per kilogram | J/kg | m2·s−2
- coefficient of heat transfer | watt per metre squared kelvin | W/m2·K | kg·s−3·K−1
- conductivity | siemens per metre | S/m | m−3·kg−1·s 3·A2
- dialectric polarization | coulomb per square metre | C/m2 | m−2·s·A
- displacement | coulomb per square metre | C/m2 | m−2·s·A
- dynamic viscosity | pascal second | Pa·s | m−1·kg·s−1
- electric charge density | coulomb per cubic metre | C/m3 | m-3·s·A
- electric dipole moment | coulomb metre | C·m | m·s·A
- electric field strength | volt per metre | V /m | m·kg·s−3·A−1
- energy density | joul per cubic metre | J/m3 | m-1·kg·s−2
- entropy | joule per kelvin | J/K | m2·kg·s−2·K−1
- exposure (ionizing radiation) | coulomb per kilogram | C/kg | kg−1·s·A
- heat capacity | joule per kelvin | J/K | m2·kg·s−2·K−1
- heat flux density | watt per square metre | W /m2 | kg·s-3
- magnetic dipole moment | weber metre | Wb·m | m3·kg·s−2·A−1
- molar energy | joule per mole | J/mol | m2·kg·s−2·mol−1
- molar entropy | joule per mole kelvin | J/mol·K | m2·kg·s−2·K -1·mol−1
- molar heat capacity | joule per mole kelvin | J/mol·K | m2·kg·s−2·K -1·mol−1
- moment of force | newton metre | N·m | m2·kg·s−2
- permeability | henry per metre | H/m | m·kg·s−2·A−2
- permittivity | farad per metre | F/m | m−3·kg−1·A2
- radiant intensity | watt per steradian | W /sr | m2·kg·s−3·srl−1
- reluctance | 1 per henry | H−1 | m-2·kg−1·s 2·A2
- resistivity | ohm metre | Ω·m | m3·kg·s−3·A−2
- specific energy | joule per kilogram | J/kg | m2·s−2
- specific entropy | joule per kilogram kelvin | J/kg·K | m2·s−2·K−1
- specific heat capacity | joule per kilogram kelvin | J/kg·K | m2·s−2·K−1
- specific latent heat | joule per kilogram | J/kg | m2·s−2
- surface charge density | coulomb per square metre | C/m2 | m−2·s·A
- surface tension | newton per metre | N/m | kg·s−2
- thermal conductivity | watt per metre kelvin | W /m·K | m·kg·s-3·K−1
- torque | newton metre | N·m | m2·kg·s−2
Notes to the above table
In the interests of uniformity it is preferable to define, as far as possible, the SI (Systeme Internationale) derived units in accordance with the combinations given in the above tables. This does not, however, exclude the possibility of using other equivalent combinations in special cases. In education, for example, it may be convenient to define electric field strength initially in terms of the force experienced by unit charge and to use the corresponding unit newton per coulomb (N/C) instead of volt per metre (V/m).
Note that: 1 V/m = 1 W/A·m = 1 N·m/s·A·m = 1 N/C.
Torque of moment of force should not be expressed in joules (J) but only in newton metres (N·m).
The values of certain so-called dimensionless quantities such as index of refraction, relative permeability and relative permittivity are expressed as pure numbers. Each of these quantities does have an SI unit but this consists of the ratio of two identical SI units and thus may be expressed by the number 1.
SI Derived Units / Abgeleitete SI-Einheiten
English/German
Frequency / Frequenz
hertz: Hz = 1/s
Force / Kraft
newton: N = m kg/s2
Pressure, stress / Druck, mechanische Spannung
pascal: Pa = N/m2= kg/m s2
Energy, work, quantity of heat / Energie, Arbeit, Wärmemenge
joule: J = N m = m2kg/s2
Power, radiant flux / Leistung
watt: W = J/s = m2kg/s3
Quantity of electricity, electric charge / elektrische Ladung
coulomb: C = s A
Electric potential / elektrische Spannung
volt: V = W/A = m2kg/s3 A
Capacitance / Kapazität
farad: F = C/V = s4A2/m2 kg
Electric resistance / elektrischer Widerstand
ohm: Omega = V/A = m2kg/s3 A2
Conductance / elektr.Leitfähigkeit
siemens: S = A/V = s3A2/m2 kg
Magnetic flux / magnetischer Fluss
weber: Wb = V s = m2kg/s2 A
Magnetic flux density, magnetic induction / Magnetische Induktion
tesla: T = Wb/m2 = kg/s2 A
Inductance / Induktivität
henry: H = Wb/A = m2kg/s2 A2
Luminous flux / Lichtstrom
lumen:lm = cd sr
Illuminance / Beleuchtungsstärke
lux:lx = lm/m2 = cd sr/m2
Activity (ionizing radiations) / Radioaktivität
becquerel: Bq = 1/s
Absorbed dose / Absorbierte Strahlendosis
gray: Gy = J/kg = m2/s2
Dynamic viscosity / Dynamische Viskosität
pascal second: Pa s = kg/m s
Moment of force / Drehmoment
meter newton: N m = m2 kg/s2
Surface tension / Oberflächenspannung
newton per meter:N/m = kg/s2
Heat flux density, irradiance / Wärmeflussdichte
watt per squaremeter: W/m2 = kg/s3
Heat capacity, entropy / Wärmekapazität,Entropie
joule per kelvin:J/K = m2 kg/s2 K
Specific heat capacity, specific entropy /Spez. Wärmekapazität, spez. Entropie
joule per kilogramkelvin: J/kg K = m2/s2 K
Specific energy / Spezifische Energie
joule per kilogram:J/kg = m2/s2
Thermal conductivity / Thermische Leitfähigkeit
watt per meterkelvin: W/m K = m kg/s3 K
Energy density / Energiedichte
joule per cubicmeter: J/m3 = kg/m s2
Electric field strength / Elektrische Feldstärke
volt per meter: V/m = m kg/s3 A
Electric charge density / Elektrische Ladungsdichte
coulomb per cubicmeter: C/m3 = s A/m3
Electric displacement, electric flux density /Elektrische Flussdichte
coulomb per squaremeter: C/m2 = s A/m2
Permittivity / Influenz
farad per meter: F/m = s4 A2/m3 kg
Permeability / Permeabilität
henry per meter: H/m = m kg/s2 A2
Molar energy / Molare Energie
joule per mole:J/mol = m2 kg/s2 mol
Molar entropy, molar heat capacity / Molare Entropie, molare Wärmekapazität
joule per molekelvin: J/mol K = m2 kg/s2 K mol
Exposure (ionizing radiations) / Exposition
coulomb per kilogram: C/kg = s A/kg
Absorbed dose rate / Absorbierte Dosisrate
gray per second: Gy/s = m2/s3
Frequency / Frequenz
hertz: Hz = 1/s
Force / Kraft
newton: N = m kg/s2
Pressure, stress / Druck, mechanische Spannung
pascal: Pa = N/m2= kg/m s2
Energy, work, quantity of heat / Energie, Arbeit, Wärmemenge
joule: J = N m = m2kg/s2
Power, radiant flux / Leistung
watt: W = J/s = m2kg/s3
Quantity of electricity, electric charge / elektrische Ladung
coulomb: C = s A
Electric potential / elektrische Spannung
volt: V = W/A = m2kg/s3 A
Capacitance / Kapazität
farad: F = C/V = s4A2/m2 kg
Electric resistance / elektrischer Widerstand
ohm: Omega = V/A = m2kg/s3 A2
Conductance / elektr.Leitfähigkeit
siemens: S = A/V = s3A2/m2 kg
Magnetic flux / magnetischer Fluss
weber: Wb = V s = m2kg/s2 A
Magnetic flux density, magnetic induction / Magnetische Induktion
tesla: T = Wb/m2 = kg/s2 A
Inductance / Induktivität
henry: H = Wb/A = m2kg/s2 A2
Luminous flux / Lichtstrom
lumen:lm = cd sr
Illuminance / Beleuchtungsstärke
lux:lx = lm/m2 = cd sr/m2
Activity (ionizing radiations) / Radioaktivität
becquerel: Bq = 1/s
Absorbed dose / Absorbierte Strahlendosis
gray: Gy = J/kg = m2/s2
Dynamic viscosity / Dynamische Viskosität
pascal second: Pa s = kg/m s
Moment of force / Drehmoment
meter newton: N m = m2 kg/s2
Surface tension / Oberflächenspannung
newton per meter:N/m = kg/s2
Heat flux density, irradiance / Wärmeflussdichte
watt per squaremeter: W/m2 = kg/s3
Heat capacity, entropy / Wärmekapazität,Entropie
joule per kelvin:J/K = m2 kg/s2 K
Specific heat capacity, specific entropy /Spez. Wärmekapazität, spez. Entropie
joule per kilogramkelvin: J/kg K = m2/s2 K
Specific energy / Spezifische Energie
joule per kilogram:J/kg = m2/s2
Thermal conductivity / Thermische Leitfähigkeit
watt per meterkelvin: W/m K = m kg/s3 K
Energy density / Energiedichte
joule per cubicmeter: J/m3 = kg/m s2
Electric field strength / Elektrische Feldstärke
volt per meter: V/m = m kg/s3 A
Electric charge density / Elektrische Ladungsdichte
coulomb per cubicmeter: C/m3 = s A/m3
Electric displacement, electric flux density /Elektrische Flussdichte
coulomb per squaremeter: C/m2 = s A/m2
Permittivity / Influenz
farad per meter: F/m = s4 A2/m3 kg
Permeability / Permeabilität
henry per meter: H/m = m kg/s2 A2
Molar energy / Molare Energie
joule per mole:J/mol = m2 kg/s2 mol
Molar entropy, molar heat capacity / Molare Entropie, molare Wärmekapazität
joule per molekelvin: J/mol K = m2 kg/s2 K mol
Exposure (ionizing radiations) / Exposition
coulomb per kilogram: C/kg = s A/kg
Absorbed dose rate / Absorbierte Dosisrate
gray per second: Gy/s = m2/s3
cgs Units / cgs-Einheiten
erg
1erg = E-7 J
dyne
1 dyn = E-5 N
poise
1 P = 1 dyn s/cm2 = 0.1 Pa s
stokes
1 St = 1 cm2/s = E-4 m2/s
gauss
1G = E-4 T
oersted
1Oe = (1000/(4∙pi)) A/m
maxwell
1Mx = E-8 Wb
stilb
1sb = 1 cd/cm2 = E4 cd/m2
phot
1ph = E4 lx
1erg = E-7 J
dyne
1 dyn = E-5 N
poise
1 P = 1 dyn s/cm2 = 0.1 Pa s
stokes
1 St = 1 cm2/s = E-4 m2/s
gauss
1G = E-4 T
oersted
1Oe = (1000/(4∙pi)) A/m
maxwell
1Mx = E-8 Wb
stilb
1sb = 1 cd/cm2 = E4 cd/m2
phot
1ph = E4 lx