SI derived unit
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SI derived units are part of the SI system of measurement units and are derived from the seven SI base units.
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Dimensionless derived units
The following SI units are actually dimensionless ratios, formed by dividing two identical SI units. They are therefore considered by the BIPM to be derived. Formally, their SI unit is simply the number 1, but they are given these special names, for use whenever the lack of a unit might be confusing.
SI dimensionless units | ||||
---|---|---|---|---|
Name | Symbol | Quantity | Definition | |
radian | rad | Angle | The unit of angle is the angle subtended at the centre of a circle by an arc of the circumference equal in length to the radius of the circle. There are 2π radians in a circle. | |
steradian | sr | Solid angle | The unit of solid angle is the solid angle subtended at the centre of a sphere of radius r by a portion of the surface of the sphere having an area r2. There are 4π steradians on a sphere. |
Derived units with special names
Base units can be put together to derive units of measurement for other quantities. Some have been given names.
SI derived units with special names | ||||
---|---|---|---|---|
Name | Symbol | Quantity | Expression in terms of other units |
Expression in terms of SI base units |
hertz | Hz | Frequency | s−1 | s−1 |
newton | N | Force, Weight | m·kg·s−2 | m·kg·s−2 |
joule | J | Energy, Work, Heat | N·m | m2·kg·s−2 |
watt | W | Power, Radiant flux | J/s | m2·kg·s−3 |
pascal | Pa | Pressure, Stress | N/m2 | m−1·kg·s−2 |
lumen | lm | Luminous flux | cd·sr = m2·m−2·cd | cd |
lux | lx | Illuminance | lm/m2 = m2·m−4·cd | m−2·cd |
coulomb | C | Electric charge or flux | s·A | s·A |
volt | V | Electrical potential difference, Electromotive force | W/A = J/C | m2·kg·s−3·A−1 |
ohm | Ω | Electric resistance, Impedance, Reactance | V/A | m2·kg·s−3·A−2 |
farad | F | Electric capacitance | C/V | m−2·kg−1·s4·A2 |
weber | Wb | Magnetic flux | m2·kg·s−2·A−1 | m2·kg·s−2·A−1 |
tesla | T | Magnetic flux density, Magnetic inductivity | V·s·m−2 = Wb/m2 | kg·s−2·A−1 |
henry | H | Inductance | V·s·A−1 = Wb/A | m2·kg·s−2·A−2 |
siemens | S | Electric conductance | Ω−1 | m−2·kg−1 s3·A2 |
becquerel | Bq | Radioactivity (decays per unit time) | s−1 | s−1 |
gray | Gy | Absorbed dose (of ionising radiation) | J/kg | m2·s−2 |
sievert | Sv | Equivalent dose (of ionising radiation) | J/kg | m2·s−2 |
katal | kat | Catalytic activity | mol/s | s−1·mol |
degree Celsius | °C | Thermodynamic temperature | t°C = tK - 273.15 |
Other quantities and units
Other derived SI units | ||||
---|---|---|---|---|
Name | Symbol | Quantity | Expression in terms of SI base units |
|
square metre | m² | area | m² | |
cubic metre | m³ | volume | m³ | |
metre per second | m·s-1 | speed, velocity | m·s-1 | |
metre per second squared | m·s-2 | acceleration | m·s-2 | |
radian per second | rad·s-1 | angular velocity | s-1 | |
newton second | N·s | momentum | kg·m·s-1 | |
newton metre second | N·m·s | angular momentum | kg·m²·s-1 | |
newton metre | N·m | torque, moment of force | kg·m²·s-2 | |
reciprocal metre | m-1 | wavenumber | m-1 | |
kilogram per cubic metre | kg·m-3 | density, mass density | kg·m-3 | |
cubic metre per kilogram | kg-1·m³ | specific volume | kg-1·m³ | |
mole per cubic metre | m-3·mol | amount (-of-substance) concentration | m-3·mol | |
cubic metre per mole | m³·mol-1 | molar volume | m³·mol-1 | |
joule per kelvin | J·K-1 | heat capacity, entropy | kg·m²·s-2·K-1 | |
joule per kelvin mole | J·K-1·mol-1 | molar heat capacity, molar entropy | kg·m²·s-2·K-1·mol-1 | |
joule per kilogram kelvin | J·K-1·kg-1 | specific heat capacity, specific entropy | m²·s-2·K-1 | |
joule per mole | J·mol-1 | molar energy | kg·m²·s-2·mol-1 | |
joule per kilogram | J·kg-1 | specific energy | m²·s-2 | |
joule per cubic metre | J·m-3 | energy density | kg·m-1·s-2 | |
newton per metre | N·m-1 = J·m-2 | surface tension | kg·s-2 | |
watt per square metre | W·m-2 | heat flux density, irradiance | kg·s-3 | |
watt per metre kelvin | W·m-1·K-1 | thermal conductivity | kg·m·s-3·K-1 | |
square metre per second | m²·s-1 | kinematic viscosity, diffusion coefficient | m²·s-1 | |
pascal second | Pa·s = N·s·m-2 | dynamic viscosity | kg·m-1·s-1 | |
coulomb per cubic metre | C·m-3 | electric charge density | m-3·s·A | |
ampere per square metre | A·m-2 | electric current density | A·m-2 | |
siemens per metre | S·m-1 | conductivity | kg-1·m-3·s³·A² | |
siemens square metre per mole | S·m²·mol-1 | molar conductivity | kg-1·s³·mol-1·A² | |
farad per metre | F·m-1 | permittivity | kg-1·m-3·s4·A² | |
henry per metre | H·m-1 | permeability | kg·m·s-2·A-2 | |
volt per metre | V·m-1 | electric field strength | kg·m·s-3·A-1 | |
ampere per metre | A·m-1 | magnetic field strength | A·m-1 | |
candela per square metre | cd·m-2 | luminance | cd·m-2 | |
coulomb per kilogram | C·kg-1 | exposure (X and gamma rays) | kg-1·s·A | |
gray per second | Gy·s-1 | absorbed dose rate | m²·s-3 |
Conversion between kelvins and degrees Celsius
A change in temperature of 1°C is equal to a change in temperature of 1K.
Temperature in °C = Temperature in kelvins - 273.15
Thus, one could think of the Kelvin scale as the same as the Celsius scale, with its zero point moved down to absolute zero. This perspecitive is historically accurate; however, it has become more convenient to fix the standard for the kelvin, and thus the Celsius scale is derived from that standard (i.e., it now depends on absolute zero and the triple point of water with a 0.01 K offset — the boiling point of water no longer has anything to do with the official definition of degrees Celsius).
Temperature differences are often measured in degrees Celsius; however, it doesn't matter: differences in temperature are equivalent whether kelvins or degrees Celsius are used.
Therefore, a change in temperature (ΔT), when expressed in an equation, can be calculated using either kelvins or degrees celsius so long as one is consistent.
See also
References
- I. Mills, Tomislav Cvitas, Klaus Homann, Nikola Kallay, IUPAC: Quantities, Units and Symbols in Physical Chemistry, 2nd edition (June 1993), Blackwell Science Inc (p. 72)