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A physical quantity is a property of a material or system that can be quantified by measurement. A physical quantity can be expressed as the combination of a numerical value and a unit. For example, the physical quantity mass can be quantified as n kg, where n is the numerical value and kg is the unit. A physical quantity possesses at least two characteristics in common, one is numerical magnitude and other is the unit in which it is measured.

International recommendations for the use of symbols for quantities are set out in ISO/IEC 80000, the IUPAP red book and the IUPAC green book. For example, the recommended symbol for the physical quantity mass is m , and the recommended symbol for the quantity electric charge is Q .

Subscripts are used for two reasons, to simply attach a name to the quantity or associate it with another quantity, or represent a specific vector, matrix, or tensor component. clarification needed Name reference: The quantity has a subscripted or superscripted single letter, group of letters, or complete word, to label what concept or entity they refer to, often to distinguish it from other quantities with the same main symbol. These subscripts or superscripts tend to be written in upright roman typeface rather than italic while the main symbol representing the quantity is in italic. For instance E k or E kinetic is usually used to denote kinetic energy and E p or E potential is usually used to denote potential energy. Quantity reference: The quantity has a subscripted or superscripted single letter, group of letters, or complete word, to parameterize what measurement/s they refer to. These subscripts or superscripts tend to be written in italic rather than upright roman typefac

A scalar is a physical quantity that has magnitude but no direction. Symbols for physical quantities are usually chosen to be a single letter of the Latin or Greek alphabet, and are printed in italic type.

Vectors are physical quantities that possess both magnitude and direction. Symbols for physical quantities that are vectors are in bold type, underlined or with an arrow above. For example, if u is the speed of a particle, then the straightforward notations for its velocity are u , u , or u → {\displaystyle {\vec {u}}\,\!} .

Numerical quantities, even those denoted by letters, are usually printed in roman (upright) type, though sometimes in italic. Symbols for elementary functions (circular trigonometric, hyperbolic, logarithmic etc.), changes in a quantity like Δ in Δ y or operators like d in d x , are also recommended to be printed in roman type. Examples: Real numbers, such as 1 or √ 2 , e, the base of natural logarithms, i, the imaginary unit, π for the ratio of a circle's circumference to its diameter, 3.14159265358979323846264338327950288... δ x , Δ y , d z , representing differences (finite or otherwise) in the quantities x , y and z sin α , sinh γ , log x

Units edit There is often a choice of unit, though SI units (including submultiples and multiples of the basic unit) are usually used in scientific contexts due to their ease of use, international familiarity and prescription. For example, a quantity of mass might be represented by the symbol m , and could be expressed in the units kilograms (kg), pounds (lb), or daltons (Da). Dimensions edit The notion of dimension of a physical quantity was introduced by Joseph Fourier in 1822. By convention, physical quantities are organized in a dimensional system built upon base quantities, each of which is regarded as having its own dimension.

Base quantities are those quantities which are distinct in nature and in some cases have historically not been defined in terms of other quantities. Base quantities are those quantities on the basis of which other quantities can be expressed. The seven base quantities of the International System of Quantities (ISQ) and their corresponding SI units and dimensions are listed in the following table. Other conventions may have a different number of base units (e.g. the CGS and MKS systems of units). International System of Quantities base quantities Quantity SI unit Dimension symbol Name(s) (Common) symbol(s) Name Symbol Length, width, height, depth, distance a, b, c, d, h, l, r, s, w, x, y, z metre m L Time t , τ second s T Mass m kilogram kg M Absolute temperature T , θ kelvin K Θ Amount of substance n mole mol N Electric current i, I ampere A I Luminous intensity I v candela cd J Plane angle α , β , γ , θ , φ , χ radian r

Derived quantities are those whose definitions are based on other physical quantities (base quantities). Space edit Important applied base units for space and time are below. Area and volume are thus, of course, derived from the length, but included for completeness as they occur frequently in many derived quantities, in particular densities. Quantity SI unit Dimensions Description Symbols (Spatial) position (vector) r , R , a , d m L Angular position, angle of rotation (can be treated as vector or scalar) θ , θ rad None Area, cross-section A , S , Ω m2 L2 Vector area (Magnitude of surface area, directed normal to tangential plane of surface) A ≡ A n ^ , S ≡ S n ^ {\displaystyle \mathbf {A} \equiv A\mathbf {\hat {n}} ,\quad \mathbf {S} \equiv S\mathbf {\hat {n}} \,\!} m2 L2 Volume τ , V m3 L3 Densities, flows, gradients, and moments edit Important and convenient derived quantities such as densities, fluxes, flow