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This is a list of well-known dimensionless quantities illustrating their variety of forms and applications. The tables also include pure numbers, dimensionless ratios, or dimensionless physical constants; these topics are discussed in the article.
Dimensionless quantities, or quantities of dimension one, [1] are quantities implicitly defined in a manner that prevents their aggregation into units of measurement. [ 2 ] [ 3 ] Typically expressed as ratios that align with another system, these quantities do not necessitate explicitly defined units .
These include the Boltzmann constant, which gives the correspondence of the dimension temperature to the dimension of energy per degree of freedom, and the Avogadro constant, which gives the correspondence of the dimension of amount of substance with the dimension of count of entities (the latter formally regarded in the SI as being dimensionless).
A quantity of dimension one is historically known as a dimensionless quantity (a term that is still commonly used); all its dimensional exponents are zero and its dimension symbol is . Such a quantity can be regarded as a derived quantity in the form of the ratio of two quantities of the same dimension.
A United States Navy Aviation boatswain's mate tests the specific gravity of JP-5 fuel. Relative density, also called specific gravity, [1] [2] is a dimensionless quantity defined as the ratio of the density (mass of a unit volume) of a substance to the density of a given reference material.
Base quantity Symbol Description SI base unit Dimension Comments Amount of substance: n: The quantity proportional to the number of particles in a sample, with the Avogadro constant as the proportionality constant: mole (mol) N: extensive, scalar Length: l: The one-dimensional extent of an object metre (m) L: extensive: Time: t: The duration of ...
For example, if "x" represented mass, the letter "m" might be an appropriate symbol to represent the dimensionless mass quantity. In this article, the following conventions have been used: t – represents the independent variable – usually a time quantity.
Whereas the physical quantity indicated by a physical constant does not depend on the unit system used to express the quantity, the numerical values of dimensional physical constants do depend on choice of unit system. The term "physical constant" refers to the physical quantity, and not to the numerical value within any given system of units.