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). 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.
General derived quantities Derived quantities are those whose definitions are based on other physical quantities (base quantities).
Space 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.
Densities, flows, gradients, and moments Important and convenient derived quantities such as densities,
fluxes,
flows,
currents are associated with many quantities. Sometimes different terms such as
current density and
flux density,
rate,
frequency and
current, are used interchangeably in the same context; sometimes they are used uniquely. 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. For generality we use
qm,
qn, and
F respectively. No symbol is necessarily required for the gradient of a scalar field, since only the
nabla/del operator ∇ or
grad needs to be written. For spatial density, current, current density and flux, the notations are common from one context to another, differing only by a change in subscripts. For current density, \mathbf{\hat{t}} 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. Only the current passing perpendicular to the surface contributes to the current passing
through the surface, no current passes
in the (tangential) plane of the surface. The calculus notations below can be used synonymously. :If
X is a
n-variable function X \equiv X \left ( x_1, x_2 \cdots x_n \right ) , then :
Differential The differential
n-space volume element is \mathrm{d}^n x \equiv \mathrm{d} V_n \equiv \mathrm{d} x_1 \mathrm{d} x_2 \cdots \mathrm{d} x_n , :
Integral: The
multiple integral of
X over the
n-space volume is \int X \mathrm{d}^n x \equiv \int X \mathrm{d} V_n \equiv \int \cdots \int \int X \mathrm{d} x_1 \mathrm{d} x_2 \cdots \mathrm{d} x_n . == See also ==