Fundamental units

A set of fundamental units is a set of units for physical quantities from which every other unit can be generated.

In the language of measurement, quantities are quantifiable aspects of the world, such as time, distance, velocity, mass, momentum, energy, and weight, and units are used to describe their measure. Many of these quantities are related to each other by various physical laws, and as a result the units of some of the quantities can be expressed as products (or ratios) of powers of other units (e.g., momentum is mass times velocity and velocity is measured in distance divided by time). These relationships are discussed in dimensional analysis. Those that cannot be so expressed can be regarded as "fundamental" in this sense.

There are other relationships between physical quantities which can be expressed by means of fundamental constants, and to some extent it is an arbitrary decision whether to retain the fundamental constant as a quantity with dimensions or simply to define it as unity or a fixed dimensionless number, and reduce the number of fundamental constants by one.

For instance, time and distance are related to each other by the speed of light, c, which is a fundamental constant. It is possible to use this relationship to eliminate either the fundamental unit of time or that of distance. Similar considerations apply to Planck's constant, h, which relates energy (with dimensions of mass, length and time) to frequency (dimensions of time). In theoretical physics it is customary to use such units (natural units) in which c = 1 and = 1.

Slightly different considerations apply to the so-called permittivity of free space, which historically has been regarded as a separate physical constant in some systems of measurement but not in others.

In the SI system there are 7 fundamental units: kilogram, meter, candela, second, ampere, kelvin, and mole.

In theory a system of fundamental quantities (or sometimes fundamental dimensions) would be such that every other physical quantity (or dimension of physical quantity) can be generated from them.