thumb|Ampèremetre (Ammeter)

A physical quantity (or simply quantity) By convention, physical quantities are organized in a dimensional system built upon base quantities, each of which is regarded as having its own dimension.

The dimension of a quantity Z is denoted or . any value of a physical quantity Z is expressed as the product of a numerical value {Z} (a pure number) and a unit [Z]:

:<math>Z = \{Z\} \times [Z]</math>

The value is sometimes called denominate number or magnitude (although "magnitude" typically refers to the absolute value or vector norm).

For example, let <math>Z</math> be "2 metres"; then, <math>\{Z\} = 2</math> is the numerical value and <math>[Z] = \mathrm{metre}</math> is the unit.

Conversely, the numerical value expressed in an arbitrary unit can be obtained as:

:<math>\{Z\} = Z / [Z]</math>

The multiplication sign is usually left out, just as it is left out between variables in the scientific notation of formulas. The convention used to express quantities is referred to as quantity calculus. In formulas, the unit [Z] can be treated as if it were a specific magnitude of a kind of physical dimension: see Dimensional analysis for more on this treatment.

Typography

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.

Physical quantities are normally typeset in italics.

Purely numerical quantities, even those denoted by letters, are usually printed in roman (upright) type, though sometimes in italics. Symbols for elementary functions (circular trigonometric, hyperbolic, logarithmic etc.), changes in a quantity like Δ in Δy or operators like d in dx, are also recommended to be printed in roman type.

Examples:

  • Real numbers, such as 1 or ,
  • e, the base of natural logarithms,
  • i, the imaginary unit,
  • π for the ratio of a circle's circumference to its diameter, 3.14159265...
  • δx, Δy, dz, representing differences (finite or otherwise) in the quantities x, y and z
  • sin &alpha;, sinh &gamma;, log x

Support

Scalars

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

Vectors are physical quantities that possess both magnitude and direction and whose operations obey the axioms of a vector space. 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>u</u>, or <math>\vec{u}</math>.

Tensors

Scalar and vector quantities are the simplest tensor quantities, which are tensors that can be used to describe more general physical properties. For example, the Cauchy stress tensor possesses magnitude, direction, and orientation qualities.

Base and derived quantities

Base quantities

A system of quantities relates physical quantities, and due to this dependence, a limited number of quantities can serve as a basis in terms of which the dimensions of all the remaining quantities of the system can be defined. A set of mutually independent quantities may be chosen by convention to act as such a set, and are called base quantities. 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).

{| class="wikitable"

|+ style="font-size:larger;font-weight:bold;"|International System of Quantities base quantities

! colspan=2|Quantity

! colspan=2|SI unit

! rowspan=2|Dimension<br>symbol

|-

! Name(s)

! (Common) symbol(s)

! Name

! Symbol

|-

| Length

| l, x, r

| metre

| m

| L

|-

| Time

| t

| second

| s

| T

|-

| Mass

| m

| kilogram

| kg

| M

|-

| Thermodynamic temperature

| T

| kelvin

| K

| Θ

|-

| Amount of substance

| n

| mole

| mol

| N

|-

| Electric current || i, I

| ampere

| A

| I

|-

| Luminous intensity || I<sub>v</sub>

| candela

| cd

| J

|}

The angular quantities, plane angle and solid angle, are defined as derived dimensionless quantities in the SI. For some relations, their units radian and steradian can be written explicitly to emphasize the fact that the quantity involves plane or solid angles.