Standard physical units SI base units (SI = Système International d Unités) Basic quantity SI base unit Name Symbol Length metre m Mass kilogram kg Time second s Electric current ampere A Temperature (thermodynamic or temperature difference) kelvin K Amount of substance mole mol Luminous intensity candela cd Definition of SI base units metre The metre is the length equal to 1650763.73 wavelength in vacuum of the radiation corresponding to the transition between the levels 2 p 10 and 5 d 5 of the krypton-86 atom. kilogram The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. second The second is the duration of 9192 631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. ampere The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed one metre apart in vacuum, would produce between these conductors a force equal to 2 10-7 newton per metre of length. kelvin The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. Note: When expressed in Celsius temperature (symbol t), t = T T 0 where T 0 = 273.15 K, the unit degrees Celsius (symbol C) is used as a special name for the kelvin. 1
mole 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 particles. candela The candela is the luminous intensity, in the perpendicular direction, of a black body at the temperature of freezing platinum under a pressure of 101325 newtons per square metre. Decimal multiples and sub-multiples of SI units (Internationally adopted prefixes) Factor by which the unit is multiplied Prefix 10-18 atto a Symbol 10-15 femto f 10-12 piko p 10-9 nano n 10-6 micro µ 10-3 milli m 10-2 centi c 10-1 deci d 10 deca da 10 2 hecto h 10 3 kilo k 10 6 mega M 10 9 giga G 10 12 tera T 10 15 peta P 10 18 exa E 2
SI derived units with special names and symbols Quantity SI unit Relationship Name Symbol m Plane angle radian rad 1 rad = 1 m Solid angle steradian sr 1 sr = 1 1 Frequency of a hertz Hz 1 Hz = periodic occurrence s 1 Activity of a becquerel Bq 1 Bq = radioactive substance s kg m Force Newton N 1 N = 1 N kg Pressure, pascal Pa 1 Pa = 1 = 1 mechanical stress m s 2 J kg Energy, work, joule 1 J = 1Nm = 1 = 1 Ws quantity of heat s 2 J N m Power, heat flow watt W 1 W = 1 1 = = 1 VA s s J Energy dosage Grey Gy 1 Gy = 1 = 1 kg s 2 Electric charge, coulomb C 1 C = 1 As quantity of electricity J W Electric potential, volt V 1 V = 1 = 1 potential differences, C A electromotive force s 2 3
Quantity SI unit Relationship Name Symbol C As Electric capacitance farad F 1 F = 1 = 1 V V V 1 Electric resistance ohm Ω 1 Ω = 1 = A s Electric conductance 1 A siemens S 1 S = 1 = 1 Ω V Magnetic flux weber Wb 1 Wb = 1 Vs Wb Magnetic flux density, tesla T 1 T = 1 magnetic induction Wb Vs Inductance, henry H 1 H = 1 = 1 magnetic conductance A A Celsius degree C * temperature Celsius Luminous flux lumen lm 1 lm = 1 cdsr lm Illuminance lux lx 1 lx = 1 The SI derived units are expressed in terms of base units, either as a power of the base unit or as a compound unit formed by multiplication of two or more units. Example: for area; kg m/s 2 for force. The SI derived units form a coherent system together with the base units and supplementary units. They include the multiples and submultiples of the base unit obtained by attaching a prefix. Example: 1 J = 1 kg (m/s) 2 = 1 N m = 1 W s for work. *The Celsius temperature t is equal to the difference t = T T 0 between two thermodynamic temperatures T and T 0 where T 0 = 273.15 K. 4
Units outside the SI with special names and symbols Quantity SI unit Relationship Name Symbol Plane angle full ** 1 full angle = 2π rad angle π 90 gon gon 1 gon = rad = 200 100 degree π 0 * 1 = rad 180 1 π minute * 1 = = rad 60 10800 1' π second * 1 = 1 = rad 60 648000 Refractive power dioptre 1 of optical systems dioptrie dpt** 1 dpt** = 1 m Area of ground are a 1 a = 10 2 =1da =100 and floor sections hectare ha 1 ha = 10 4 1 Volume litre l 1 l = 1 dm 3 = m 3 1000 Mass tonne t 1 t = 1000 kg = 1 Mg in nuclear atomic u** 1 u = 1,660565 10-27 kg physics mass unit of precious metric Kt** 1 Kt = 0,2 10-3 kg = 0,2 g stones carat 5
Quantity SI unit Relationship Name Symbol Linear textile fibres tex tex kg g density and yarns 1 tex = 10-6 = 1 degree Ø* m km Time minute min* 1 min = 60 s hour h* 1 h = 60 min = 3600 s day d* 1 d = 24 h = 86400 s common a* 1 a = 365 d = 8760 h year Pressure liquids, gases bar bar N steams 1 bar = 10 5 Pa = 10 5 Energy Nuclear electron ev 1 ev = 1,60219 10-19 J physics volt Units outside the SI are all units derived from the base units with a factor deviating from 1 (see above table under relationship). Exceptions: dioptre (1/m),although coherent, not declared SI unit. kilogram (kg) although with decimal prefix, the kilogram (kg) is not a unit outside the SI, because it is a base unit. ** without prefix ** not internationally standardized 6
Definitions of various derived units Quantity Symbol Definition Force N The newton is the force which, applied to the mass of 1 kilogram, gives it an acceleration of 1 m/s 2. The hitherto used kilogram-force is the force of 1 kg mass on a gravitational basis (standard acceleration). m g = 9.80665 s 2 Pressure Pa The pascal is the pressure produced by a force of 1 N applied, uniformly distributed, over an area of 1. N bar 1 bar = 10 5 Pa = 10 5 Mechanical N N stress m One m is the stress exerted by a force of 1 N from a material cross-section of 1 m. Dynamic viscosity Pa s The pascal second is equal to the dynamic viscosity of a homogeneous fluid in which, two layers 1 m apart, the top layer is moving parallel to the bottom layer at a velocity of1 m/s, and a shearing stress of 1 Pa is required to maintain this motion. Kinematic The square metre/second is equal to the kinematic viscosity s viscosity of a homogeneous fluid of 1 Pa s and 1 kg/m3 density. Energy, work, quantity of heat J The joule is the work done when the point of application of a force of 1 N is displaced through a distance of 1 m in the direction of the force. Power W The watt is equal to 1 J per second. 7
Units of pressure Pa KPa MPa bar N/m N (= 1 ) 1 Pa = 1 10-3 10-6 10-5 1 kpa = 10 3 1 10 3 10-5 1 MPa = 1 N/m = 10 6 10 3 1 10 1 (= 0.1 MPa) = 105 105 10-1 1 Units of mechanical stress Pa N m N (= 1 ) 1 Pa = 1 10-8 N (= 1 MPa) 1 = 10 6 1 m Units of energy, work quantity of heat J kj kwh (= 1 Nm) 1 J = 1 Ws = 1 10-3 2.78 10-7 1 kj = 10 3 1 2.78 10-4 1 kwh = 3.60 106 3.60 103 1 Units of power, energy flow, heat flow W kw Nm 1 W = 1 10-3 J (= 1. 1 ) s s 1 kw = 10 3 1 8