Andrew Walkingshaw J A Townsend Peter Murray-Rust Jim Downing Sam Adams Hannah Barjat A list of the SEVEN base units of the International System of Units and some commonly used derived units. The SEVEN BASE UNITS - (id in brackets) kilogram - mass (kg) second - time (s) metre - length (m) ampere - electrical current (ampere) kelvin - temperature (k) mole - amount of substance (mol) candela - luminous intensity (candela) All other units can be derived in terms of these. Units which are of unitType dimensionless, for example mg/kg should have that specific unit defined in the non SI dictionary. For pure numbers or concepts which cannot have dimensions such as method names you should use the unit "none". Wikipedia The SI base unit of time, equal to the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. The second has had many definitions throughout history; originally, it was one sixtieth of one twenty-fourth of a solar day (the factor of sixty coming from Babylonian counting and the factor of 24 from Ancient Egypt). The present definition dates from the Thirteenth General Conference on Weights and Measures, which took place in 1967. Wikipedia The SI base unit of length, defined as the length of the path travelled by light in absolute vacuum during 1/299792458 of a second. The modern metre dates from 1791, when it was defined one ten-millionth of the length of the earth's meridian along a quadrant; it became France's official unit of length in 1793. Until 1960, the metre (like the kilogram) was defined by a prototype - in this case, a platinum-iridium bar; in 1960, the SI defined the metre as 1650763.73 wavelengths of the orange-red emission line (the 2p10 - 5d5 transition) in the EM spectrum of Krypton-86 in vacuum. Since 1983, the present definition has been used. Wikipedia The SI unit of current, defined as that constant current which if maintained in two straight parallel conductors of infinite length and negligible circular cross-section, placed 1 metre apart in vacuum, would produce between those conductors a force of 2E-7 newton per metre length. This is equivalent to setting the permeability of vacuum to pi*4E-7 Hm^-1. Prior to 1948, the International Ampere (equal to 0.99985 A) was used; it was defined in terms of the electrolytic deposition rate of silver. Wikipedia The SI base unit of mass, defined as being equal to the mass of the international prototype of the kilogram. It is the only SI base unit that employs a prefix, and the only SI unit that is still defined in relation to an artifact (a platinum-iridium mass) rather than to a fundamental physical property. Wikipedia The SI unit of temperature, defined as 1/273.16 of the thermodynamic temperature of the triple point of water. A temperature in Kelvin is measured with respect to absolute zero - where, except for zero-point motion, molecular motion stops. The unit is named after William Thomson, first Baron Kelvin, a Scottish physicist and engineer. Wikipedia The SI unit identifying the number of particles in a given amount of matter, a dimensionless number equal to the number of elementary entities in 0.012 kilograms of carbon 12 where the carbon 12 atoms are unbound, at rest, and in their ground state. The number of atoms in 12 grams of carbon 12 is commonly known as Avogadro's number; it is approximately 6.0221415E23. Prior to 1959, IUPAP and IUPAC defined the mole in terms of oxygen (though the definitions were slightly different from each other); in 1959/1960, the two organizations unified on the present definition. Wikipedia The SI base unit of luminous intensity, defined as a radiant intensity of 1/683 watt per steradian in a given direction from a monochromatic source at 540E12 Hz. This is based on an older unit, the candlepower, which was referenced to the luminous intensity of a "standard candle" of known composition. The frequency chosen is in the visible spectrum near green, which is within the range where the human eye is most sensitive. A quantity that cannot have units Use for dictionary concepts that cannot carry units. These include methods, names of programs, authors. none MUST not be used for concepts which should carry units or which can be formally classified as dimensionless. J A Townsend Peter Murray-Rust Wikipedia Wikipedia m m -1 The SI unit of plane angle. A radian is equal to the angle subtended at the centre of a circle by an arc of circumference equal in length to the circle's radius. The radian is therefore formally dimensionless, as it is a ratio of two lengths. There are 2*pi radians in a complete circle. Wikipedia m 2 m -2 The SI unit of solid angle, defined as 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 r^2. Since the surface area of a sphere is 4*pi*r^2, a sphere measures 4*pi steradians. The steradian is the solid analogue of the radian, and like that unit, is formally dimensionless (in this case, being the ratio of two areas.) Wikipedia s -1 s -1 The SI derived unit of frequency, defined as one cycle per second. Periodically varying angles are typically not expressed in Hz, but instead in an appropriate angular unit (such as radians per second). Wikipedia m.kg.s -2 m.kg.s -2 The SI derived unit of force, defined as the force necessary to accelerate a mass of one kilogram at a rate of 1m s^-2. Named after Sir Isaac Newton, the Newton was adopted as the name for the MKS (direct predecessor of the SI) unit of force in 1948. A small apple, fittingly, exerts a gravitational force of about 1N on Earth. Sebastian Breuers m.kg.s-2.mole -1 The SI derived unit of force per mole, defined as the force necessary to accelerate a mass of one kilogram at a rate of 1m s^-2 in relation to one mole. Computational chemistry procedures like minimizations often need force per mole as abort criterion. Wikipedia N m m2.kg.s -2 The SI derived unit of energy, defined as the energy required to exert a force of one newton for a distance of one metre. This is dimensionally, but not semantically, equivalent to the newton metre, which is typically used as a unit of torque. It is also, significantly, the work required to move an electric charge of one coulomb through an electric potential difference of one volt. Wikipedia J/s m2.kg.s -3 The SI derived unit of power, defined as one joule of energy per second. The watt dates back to the Second Congress of the British Association of the Advancement of Science in 1889, and is named after James Watt, one of the key engineers to the development of the steam engine. Wikipedia N/m 2 m-1.kg.s -2 The SI derived unit of pressure, equal to one newton per square metre. The pascal, named after Blaise Pascal, is also used to measure stress, Young's modulus, and tensile strength. For atmospheric pressures, however, it is commonly regarded as an inconveniently small unit. Wikipedia s.A The SI unit of electric charge, defined as the amount of electric charge carried by a current of one ampere flowing for one second. Also the unit of electric flux. The Coulomb could, in principle, be defined in terms of the elementary charge of the electron and the Josephson and von Klitzing constants; in this case, the kilogram would become a derived rather than fundamental unit. Wikipedia W/A = J/C m2.kg.s-3.A -1 The SI unit of electric potential difference, defined as the potential difference across a conductor when a current of one ampere dissipates one watt of power. The number of volts is a measure of the strength of an electrical source in the sense of how much power is produced for a given current level. It is named in honor of Alessandro Volta (1745-1827), who invented the voltaic pile, the first chemical battery. Since 1990 the volt is maintained internationally for practical measurement using the Josephson effect. Wikipedia V/A m2.kg.s-3.A -2 The SI unit of electrical impedance/resistance; a resistance of one ohm produces a potential difference of one volt when one ampere of current flows through it. Named after Georg Ohm, the German physicist who discovered Ohm's Law; since 1990, the unit has been internationally maintained using the Quantum Hall Effect and a conventional value for the von Klitzing constant. Wikipedia C/V m-2.kg-1.s4.A 2 The SI derived unit of capacitance, equal to one coulomb of stored charge causing a potential difference of one volt across the terminals of the capacitor being measured. Capacitance is a measure of the total amount of electric charge stored for a given electric potential. The farad is a very large unit; typical capacitors are in the microfarad to picofarad range. Although the farad is named after Michael Faraday, it should not be confused with the Faraday - an older unit of capacitance. Wikipedia [Omega] -1 m-2.kg -1 s3.A 2 The SI derived unit of electrical conductance, defined as the reciprocal of the system's electrical resistance. This is equivalent to the obsolete "mho" unit (derived from spelling "ohm" backwards and written with an upside-down capital omega). Wikipedia m2.kg.s-2.A -1 m2.kg.s-2.A -1 The SI derived unit of magnetic flux; a change in flux of one weber per second through a loop will induce an electromotive force of one volt. The weber, like the farad, is a very large unit. Wikipedia V.s.m -2 = Wb/m 2 kg.s-2.A -1 The SI derived unit of magnetic flux density, defined as one weber per metre squared. The tesla is the value of the total magnetic flux (in some sense, the "power" of a magnet) over area; hence reducing the affected area generally increases the magnetic flux density. Like many of the other electromagnetic units, one tesla is very large. Wikipedia V.s.A -1 = Wb/A m2.kg.s-2.A -2 The SI derived unit of magnetic inductance; a circuit with an inductance of one henry gives rise to an EMF of one volt when the rate of change of current in the circuit is 1 A.s^-1. Inductance is a measure of how much magnetic flux is produced for a given circuit. Wikipedia s -1 s -1 The SI derived unit of radioactivity, defined as the activity of a quantity of radioactive material in which one nucleus decays per second. This, therefore, has the same dimensionality as the hertz (s^-1, reciprocal time) - a frequency, in other words. The reason for having a specific unit for radioactivity is slightly unusual; it was specifically introduced because of the dangers to human health which might arise from mistakes involving the units reciprocal second. Using the becquerel unit, a more active (and so, all the other things fixed, more dangerous) source has a higher number. Using 1/s or s as a second instead may lead to confusion. Wikipedia J/kg m2.s -2 The SI derived unit of absorbed radioactive dose, defined as the absorption of one joule of radiation energy by one kilogram of matter. Note that these are the same units as the sievert. To avoid any risk of confusion between the absorbed dose and the equivalent dose, one must use the corresponding special units, namely the gray instead of the joule per kilogram for absorbed dose and the sievert instead of the joule per kilogram for the dose equivalent. Wikipedia J/kg m2.s -2 The SI derived unit of equivalent radioactive dose, equal to the absorbed dose in grays multiplied by two dimensionless constants - Q, dependent on radiation type, and N dependent on all other factors. The sievert attempts to reflect the biological effects of radiation as opposed to the physical aspects, which are characterised by the absorbed dose, measured in grays. Note that these are the same units as the sievert. To avoid any risk of confusion between the absorbed dose and the equivalent dose, one must use the corresponding special units, namely the gray instead of the joule per kilogram for absorbed dose and the sievert instead of the joule per kilogram for the dose equivalent. Wikipedia mol/s s-1.mol The derived SI unit for expressing quantity values of catalytic activity, in mol s^-1. The katal is not used to express the rate of a reaction; that is expressed in moles per second. Rather, it is used to express catalytic activity which is a property of the catalyst. The katal is invariant of the measurement procedure, but the numerical quantity value is not and depends on the experimental conditions. Therefore, in order to define the quantity of a catalyst, the rate of conversion of a defined chemical reaction has to be specified, preferably of the first order, under strictly controlled conditions. Wikipedia Rate of change in concentration expressed in units of moles per cubic metre per second [moles m-3 s-1]. Rate of change in concentration expressed in units of moles per cubic metre per second [moles m-3 s-1]. Wikipedia Rate of change in concentration expressed in units of moles per cubic decimetre per second [moles dm-3 s-1]. Rate of change in concentration expressed in units of moles per cubic decimetre per second [moles dm-3 s-1]. Wikipedia Units of a bimolecular rate coefficient expressed in m3 mole-1 s-1. Wikipedia Units of a termolecular rate coefficient expressed in m6 mole-2 s-1. Wikipedia TO BE ADDED mol/L 103.m-3.mol Wikipedia mol/kg kg-1.mol TO BE ADDED not yet added Wikipedia m 2 TO BE ADDED not yet added Wikipedia m 3 TO BE ADDED not yet added Wikipedia m -3 TO BE ADDED not yet added Wikipedia m 3.m3 TO BE ADDED not yet added Wikipedia m -4 TO BE ADDED not yet added Wikipedia m.s -1 TO BE ADDED not yet added Wikipedia m.s -2 TO BE ADDED not yet added Wikipedia s -1 TO BE ADDED not yet added Wikipedia kg.m.s -1 TO BE ADDED not yet added Wikipedia kg.m2.s -1 TO BE ADDED not yet added Wikipedia kg.m2.s -2 The derived SI unit of torquw; cross-product of distance and force. The newton-metre is the SI unit of torque; although it has the same dimensionality as energy, it has a different origin, as energy is the scalar, rather than vector, product of distance and force. Wikipedia m -1 TO BE ADDED not yet added Wikipedia kg.m -3 Derived SI unit of density TO BE ADDED Wikipedia kg-1.m 3 TO BE ADDED not yet added Wikipedia m-3.mol TO BE ADDED not yet added Wikipedia m-3.mol TO BE ADDED not yet added Wikipedia m3.mol -1 TO BE ADDED not yet added Wikipedia kg.m2.s-2.K -1 Derived SI unit of absolute heat capacity. This should not be confused with molar heat capacity; this unit pays no regard to the quantity of material being heated. Wikipedia kg.m2.s-2.K-1.mol -1 Derived SI unit of heat capacity per mole Molar heat capacity is the standard unit for heat capacity measurements in chemistry; it should not be confused with absolute heat capacity. Wikipedia m2.s-2.K -1 Derived SI unit of specific heat capacity Heat capacity can be measured in three ways; per number (eg. per mole), per unit mass (as here), or in absolute terms. Care must be taken not to confuse which of these units is relevant to any given measurement! Wikipedia kg.m2.s-2.mol -1 TO BE ADDED not yet added Wikipedia m2.s -2 TO BE ADDED not yet added Wikipedia kg.m-1.s -2 TO BE ADDED not yet added Wikipedia kg.s -2 TO BE ADDED not yet added Wikipedia kg.s -3 TO BE ADDED not yet added Wikipedia kg.m.s-3.K -1 TO BE ADDED not yet added Wikipedia m2.s -1 TO BE ADDED not yet added Wikipedia m-2.s -1 Per metre squared per second Units of per area per time. Wikipedia mol.m-2.s -1 Moles per metre squared per second Units of molar flux over an area. In this case flux is defined as the amount that flows through a unit area per unit time. For an example of use see Fick's First Law. Wikipedia kg.m-2.s -1 Massin kg per metre squared per second Units of mass flux over an area. In this case flux is defined as the amount that flows through a unit area per unit time. Wikipedia kg.m-1.s -1 TO BE ADDED not yet added Wikipedia m-3.s.A TO BE ADDED not yet added Wikipedia A.m -2 TO BE ADDED not yet added Wikipedia kg-1.m-3.s3.A 2 TO BE ADDED not yet added Wikipedia kg-1.s3.mol-1.A 2 TO BE ADDED not yet added Wikipedia kg-1.m-3.s4.A 2 TO BE ADDED not yet added Wikipedia kg.m.s-2.A -2 TO BE ADDED not yet added Wikipedia kg.m.s-3.A -1 TO BE ADDED not yet added Wikipedia A.m -1 TO BE ADDED not yet added Wikipedia cd.m -2 TO BE ADDED not yet added Wikipedia kg-1.s.A TO BE ADDED not yet added Wikipedia m2.s -3 TO BE ADDED not yet added Wikipedia Gradient of energy with respect to length. Although formally identical to force, many authors report energy gradients as energy per unit length and this unitType preserves the dimensional representation. Specifically, forces are defined as -dE/dx for a given energy field and free coordinate x; this is a common source of sign error.