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                                SI derived unit

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   SI derived units are units of measurement derived from the seven base
   units specified by the International System of Units (SI). They are either
   dimensionless or can be expressed as a product of one or more of the base
   units, possibly scaled by an appropriate power of exponentiation.

   The SI has special names for 22 of these derived units (for example,
   hertz, the SI unit of measurement of frequency), but the rest merely
   reflect their derivation: for example, the square metre (m^2), the SI
   derived unit of area; and the kilogram per cubic metre (kg/m^3 or
   kg⋅m^−3), the SI derived unit of density.

   The names of SI derived units, when written in full, are always in
   lowercase. However, the symbols for units named after persons are written
   with an uppercase initial letter. For example, the symbol for hertz is
   "Hz", but the symbol for metre is "m".^[1]

Contents

     * 1 Derived units with special names
     * 2 Examples of derived quantities and units
     * 3 Other units used with SI
     * 4 Supplementary units
     * 5 See also
     * 6 References
     * 7 Bibliography
     * 8 External links

Derived units with special names[edit]

   The International System of Units assigns special names to 22 derived
   units, which includes two dimensionless derived units, the radian (rad)
   and the steradian (sr).

                   Named units derived from SI base units^[2]
   Name       Symbol Quantity               Equivalents    SI base unit       
                                                           Equivalents        
   hertz        Hz   frequency                   1/s              s^−1        
   radian      rad   angle                       m/m               1          
   steradian    sr   solid angle               m^2/m^2             1          
   newton       N    force, weight             kg⋅m/s^2        kg⋅m⋅s^−2      
   pascal       Pa   pressure, stress           N/m^2         kg⋅m^−1⋅s^−2    
   joule        J    energy, work, heat     m⋅N, C⋅V, W⋅s     kg⋅m^2⋅s^−2     
   watt         W    power, radiant flux       J/s, V⋅A       kg⋅m^2⋅s^−3     
                     electric charge or                                       
   coulomb      C    quantity of               s⋅A, F⋅V           s⋅A
                     electricity            
                     voltage, electrical                                      
   volt         V    potential difference,     W/A, J/C     kg⋅m^2⋅s^−3⋅A^−1
                     electromotive force    
   farad        F    electrical capacitance    C/V, s/Ω    kg^−1⋅m^−2⋅s^4⋅A^2 
   ohm          Ω    electrical resistance,    1/S, V/A     kg⋅m^2⋅s^−3⋅A^−2  
                     impedance, reactance   
   siemens      S    electrical conductance    1/Ω, A/V    kg^−1⋅m^−2⋅s^3⋅A^2 
   weber        Wb   magnetic flux          J/A, T⋅m^2,V⋅s  kg⋅m^2⋅s^−2⋅A^−1  
                     magnetic induction,       V⋅s/m^2,                       
   tesla        T    magnetic flux density     Wb/m^2,        kg⋅s^−2⋅A^−1
                                               N/(A⋅m)     
   henry        H    electrical inductance   V⋅s/A, Ω⋅s,    kg⋅m^2⋅s^−2⋅A^−2  
                                                 Wb/A      
   degree       °C   temperature relative         K                K          
   Celsius           to 273.15 K            
   lumen        lm   luminous flux              cd⋅sr              cd         
   lux          lx   illuminance                lm/m^2          cd⋅m^−2       
   becquerel    Bq   radioactivity (decays       1/s              s^−1        
                     per unit time)         
   gray         Gy   absorbed dose (of           J/kg           m^2⋅s^−2      
                     ionizing radiation)    
   sievert      Sv   equivalent dose (of         J/kg           m^2⋅s^−2      
                     ionizing radiation)    
   katal       kat   catalytic activity         mol/s           s^−1⋅mol      

Examples of derived quantities and units[edit]

                           Kinematic SI derived units
   Name                      Symbol  Quantity             Expression in terms 
                                                          of SI base units    
   metre per second          m/s     speed, velocity      m⋅s^−1              
   metre per second squared  m/s^2   acceleration         m⋅s^−2              
   metre per second cubed    m/s^3   jerk, jolt           m⋅s^−3              
   metre per second to the   m/s^4   snap, jounce         m⋅s^−4              
   fourth                    
   radian per second         rad/s   angular velocity     s^−1                
   radian per second squared rad/s^2 angular acceleration s^−2                
   hertz per second          Hz/s    frequency drift      s^−2                
   cubic metre per second    m^3/s   volumetric flow      m^3⋅s^−1            

                          Mechanical SI derived units
                                                             Expression in    
   Name                Symbol         Quantity               terms            
                                                             of SI base units 
   square metre        m^2            area                   m^2              
   cubic metre         m^3            volume                 m^3              
   newton-second       N⋅s            momentum, impulse      m⋅kg⋅s^−1        
   newton metre second N⋅m⋅s          angular momentum       m^2⋅kg⋅s^−1      
   newton-metre        N⋅m = J/rad    torque, moment of      m^2⋅kg⋅s^−2      
                                      force                  
   newton per second   N/s            yank                   m⋅kg⋅s^−3        
                                      wavenumber, optical                     
   reciprocal metre    m^−1           power, curvature,      m^−1
                                      spatial frequency      
   kilogram per square kg/m^2         area density           m^−2⋅kg          
   metre               
   kilogram per cubic  kg/m^3         density, mass density  m^−3⋅kg          
   metre               
   cubic metre per     m^3/kg         specific volume        m^3⋅kg^−1        
   kilogram            
   joule-second        J⋅s            action                 m^2⋅kg⋅s^−1      
   joule per kilogram  J/kg           specific energy        m^2⋅s^−2         
   joule per cubic     J/m^3          energy density         m^−1⋅kg⋅s^−2     
   metre               
   newton per metre    N/m = J/m^2    surface tension,       kg⋅s^−2          
                                      stiffness              
   watt per square     W/m^2          heat flux density,     kg⋅s^−3          
   metre                              irradiance             
   square metre per                   kinematic viscosity,                    
   second              m^2/s          thermal diffusivity,   m^2⋅s^−1
                                      diffusion coefficient  
   pascal-second       Pa⋅s = N⋅s/m^2 dynamic viscosity      m^−1⋅kg⋅s^−1     
   kilogram per metre  kg/m           linear mass density    m^−1⋅kg          
   kilogram per second kg/s           mass flow rate         kg⋅s^−1          
   watt per steradian  W/(sr⋅m^2)     radiance               kg⋅s^−3          
   square metre        
   watt per steradian  W/(sr⋅m^3)     spectral radiance      m^−1⋅kg⋅s^−3     
   cubic metre         
   watt per metre      W/m            spectral power         m⋅kg⋅s^−3        
   gray per second     Gy/s           absorbed dose rate     m^2⋅s^−3         
   metre per cubic     m/m^3          fuel efficiency        m^−2             
   metre               
   watt per cubic      W/m^3          spectral irradiance,   m^−1⋅kg⋅s^−3     
   metre                              power density          
   joule per square    J/(m^2⋅s)      energy flux density    kg⋅s^−3          
   metre second        
   reciprocal pascal   Pa^−1          compressibility        m⋅kg^−1⋅s^2      
   joule per square    J/m^2          radiant exposure       kg⋅s^−2          
   metre               
   kilogram square     kg⋅m^2         moment of inertia      m^2⋅kg           
   metre               
   newton metre second N⋅m⋅s/kg       specific angular       m^2⋅s^−1         
   per kilogram                       momentum               
   watt per steradian  W/sr           radiant intensity      m^2⋅kg⋅s^−3      
   watt per steradian  W/(sr⋅m)       spectral intensity     m⋅kg⋅s^−3        
   metre               

                             Molar SI derived units
   Name             Symbol      Quantity              Expression in terms     
                                                      of SI base units        
   mole per cubic               molarity, amount of                           
   metre            mol/m^3     substance             m^−3⋅mol
                                concentration         
   cubic metre per  m^3/mol     molar volume          m^3⋅mol^−1              
   mole             
   joule per kelvin J/(K⋅mol)   molar heat capacity,  m^2⋅kg⋅s^−2⋅K^−1⋅mol^−1 
   mole                         molar entropy         
   joule per mole   J/mol       molar energy          m^2⋅kg⋅s^−2⋅mol^−1      
   siemens square   S⋅m^2/mol   molar conductivity    kg^−1⋅s^3⋅A^2⋅mol^−1    
   metre per mole   
   mole per         mol/kg      molality              kg^−1⋅mol               
   kilogram         
   kilogram per     kg/mol      molar mass            kg⋅mol^−1               
   mole             
   cubic metre per  m^3/(mol⋅s) catalytic efficiency  m^3⋅s^−1⋅mol^−1         
   mole second      
   reciprocal mole  mol^−1      Avogadro constant     mol^−1                  

                        Electromagnetic SI derived units
   Name               Symbol    Quantity                  Expression in terms 
                                                          of SI base units    
   coulomb per square           electric displacement                         
   metre              C/m^2     field, polarization       m^−2⋅s⋅A
                                density                   
   coulomb per cubic  C/m^3     electric charge density   m^−3⋅s⋅A            
   metre              
   ampere per square  A/m^2     electric current density  m^−2⋅A              
   metre              
   siemens per metre  S/m       electrical conductivity   m^−3⋅kg^−1⋅s^3⋅A^2  
   farad per metre    F/m       permittivity              m^−3⋅kg^−1⋅s^4⋅A^2  
   henry per metre    H/m       magnetic permeability     m⋅kg⋅s^−2⋅A^−2      
   volt per metre     V/m       electric field strength   m⋅kg⋅s^−3⋅A^−1      
   ampere per metre   A/m       magnetization, magnetic   m^−1⋅A              
                                field strength            
   coulomb per        C/kg      exposure (X and gamma     kg^−1⋅s⋅A           
   kilogram                     rays)                     
   ohm metre          Ω⋅m       resistivity               m^3⋅kg⋅s^−3⋅A^−2    
   coulomb per metre  C/m       linear charge density     m^−1⋅s⋅A            
   joule per tesla    J/T       magnetic dipole moment    m^2⋅A               
   square metre per   m^2/(V⋅s) electron mobility         kg^−1⋅s^2⋅A         
   volt second        
   reciprocal henry   H^−1      magnetic reluctance       m^−2⋅kg^−1⋅s^2⋅A^2  
   weber per metre    Wb/m      magnetic vector potential m⋅kg⋅s^−2⋅A^−1      
   weber metre        Wb⋅m      magnetic moment           m^3⋅kg⋅s^−2⋅A^−1    
   tesla metre        T⋅m       magnetic rigidity         m⋅kg⋅s^−2⋅A^−1      
   ampere radian      A⋅rad     magnetomotive force       A                   
   metre per henry    m/H       magnetic susceptibility   m^−1⋅kg^−1⋅s^2⋅A^2  

                          Photometric SI derived units
   Name                     Symbol Quantity          Expression in terms 
                                                     of SI base units    
   lumen second             lm⋅s   luminous energy   s⋅cd                
   lux second               lx⋅s   luminous exposure m^−2⋅s⋅cd           
   candela per square metre cd/m^2 luminance         m^−2⋅cd             
   lumen per watt           lm/W   luminous efficacy m^−2⋅kg^−1⋅s^3⋅cd   

                         Thermodynamic SI derived units
   Name               Symbol   Quantity                   Expression in terms 
                                                          of SI base units    
   joule per kelvin   J/K      heat capacity, entropy     m^2⋅kg⋅s^−2⋅K^−1    
   joule per kilogram J/(K⋅kg) specific heat capacity,    m^2⋅s^−2⋅K^−1       
   kelvin                      specific entropy           
   watt per metre     W/(m⋅K)  thermal conductivity       m⋅kg⋅s^−3⋅K^−1      
   kelvin             
   kelvin per watt    K/W      thermal resistance         m^−2⋅kg^−1⋅s^3⋅K    
   reciprocal kelvin  K^−1     thermal expansion          K^−1                
                               coefficient                
   kelvin per metre   K/m      temperature gradient       m^−1⋅K              

Other units used with SI[edit]

   Some other units such as the hour, litre, tonne, bar, and electronvolt are
   not SI units, but are widely used in conjunction with SI units.

Supplementary units[edit]

   Until 1995, the SI classified the radian and the steradian as
   supplementary units, but this designation was abandoned and the units were
   grouped as derived units.^[3]

See also[edit]

     * International System of Quantities (ISQ)
     * International Vocabulary of Metrology
     * Metric prefix
     * Metric system

References[edit]

    1. ^ Suplee, Curt (2 July 2009). "Special Publication 811".
    2. ^
       Link: mw-deduplicated-inline-style
       International Bureau of Weights and Measures (2006), The International
       System of Units (SI) (PDF) (8th ed.), ISBN 92-822-2213-6, archived
       (PDF) from the original on 4 June 2021, retrieved 16 December 2021
    3. ^
       Link: mw-deduplicated-inline-style
       "Resolution 8 of the CGPM at its 20th Meeting (1995)". Bureau
       International des Poids et Mesures. Retrieved 23 September 2014.

Bibliography[edit]

     * Link: mw-deduplicated-inline-style
       I. Mills, Tomislav Cvitas, Klaus Homann, Nikola Kallay, IUPAC (June
       1993). Quantities, Units and Symbols in Physical Chemistry (2nd ed.).
       Blackwell Science Inc. p. 72.{{cite book}}: CS1 maint: multiple names:
       authors list (link)

External links[edit]

     * [IMG] Media related to SI derived units at Wikimedia Commons

     * v                
     * t                
     * e                
   SI units             
                          * ampere                                 
                          * candela                    
                          * kelvin                     
   Base units             * kilogram                   
                          * metre                      
                          * mole                       
                          * second                     
                          * becquerel                  
                          * coulomb                    
                          * degree Celsius             
                          * farad                      
                          * gray                       
                          * henry                      
                          * hertz                      
                          * joule                      
                          * katal                      
                          * lumen                      
   Derived units          * lux                        
   with special names     * newton                     
                          * ohm                        
                          * pascal                     
                          * radian                     
                          * siemens                    
                          * sievert                    The SI logo
                          * steradian                  
                          * tesla                      
                          * volt                       
                          * watt                       
                          * weber                      
                          * astronomical unit          
                          * dalton                     
                          * day                        
                          * decibel                    
                          * degree of arc              
                          * electronvolt               
   Other accepted units   * hectare                    
                          * hour                       
                          * litre                      
                          * minute                     
                          * minute and second of arc   
                          * neper                      
                          * tonne                      
                          * Conversion of units        
                          * Metric prefixes            
   See also               * 2005–2019 definition       
                          * 2019 redefinition          
                          * Systems of measurement     
     * Category         

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