Physical quantity

A physical quantity can be expressed as a value, which is the algebraic multiplication of a numerical value and a unit of measurement.

For example, the physical quantity mass, symbol m, can be quantified as m=n kg, where n is the numerical value and kg is the unit symbol (for kilogram).

Quantities that are vectors have, besides numerical value and unit, direction or orientation in space.

The value of a physical quantity Z is expressed as the product of a numerical value {Z} (a pure number) and a unit [Z]: For example, let

Conversely, the numerical value expressed in an arbitrary unit can be obtained as: The multiplication sign is usually left out, just as it is left out between variables in the scientific notation of formulas.

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.

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: 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.

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

For example, the Cauchy stress tensor possesses magnitude, direction, and orientation qualities.

The notion of dimension of a physical quantity was introduced by Joseph Fourier in 1822.

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).

Dimensional homogeneity is not necessarily sufficient for quantities to be comparable;[1] for example, both kinematic viscosity and thermal diffusivity have dimension of square length per time (in units of m2/s).

Quantities of the same kind share extra commonalities beyond their dimension and units allowing their comparison; for example, not all dimensionless quantities are of the same kind.

For some relations, their units radian and steradian can be written explicitly to emphasize the fact that the quantity involves plane or solid angles.

Important applied base units for space and time are below.

To clarify these effective template-derived quantities, we use q to stand for any quantity within some scope of context (not necessarily base quantities) and present in the table below some of the most commonly used symbols where applicable, their definitions, usage, SI units and SI dimensions – where [q] denotes the dimension of q.

For time derivatives, specific, molar, and flux densities of quantities, there is no one symbol; nomenclature depends on the subject, though time derivatives can be generally written using overdot notation.

No symbol is necessarily required for the gradient of a scalar field, since only the nabla/del operator ∇ or grad needs to be written.

is a unit vector in the direction of flow, i.e. tangent to a flowline.

Notice the dot product with the unit normal for a surface, since the amount of current passing through the surface is reduced when the current is not normal to the area.