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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.
[19] [20] Examples of quotients of dimension one include calculating slopes or some unit conversion factors. Another set of examples is mass fractions or mole fractions, often written using parts-per notation such as ppm (= 10 −6), ppb (= 10 −9), and ppt (= 10 −12), or perhaps confusingly as ratios of two identical units (kg/kg or mol/mol).
Listed below are all conversion factors that are useful to convert between all combinations of the SI base units, and if not possible, between them and their unique elements, because ampere is a dimensionless ratio of two lengths such as [C/s], and candela (1/683 [W/sr]) is a dimensionless ratio of two dimensionless ratios such as ratio of two volumes [kg⋅m 2 /s 3] = [W] and ratio of two ...
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).
For example, if x is a quantity, then x c is the characteristic unit used to scale it. As an illustrative example, consider a first order differential equation with constant coefficients: + = (). In this equation the independent variable here is t, and the dependent variable is x.
Pages in category "Dimensionless quantities" The following 9 pages are in this category, out of 9 total. ... Rotation (quantity) This page was last ...
It is a dimensionless quantity (dimensionless physical constant), independent of the system of units used, which is related to the strength of the coupling of an elementary charge e with the electromagnetic field, by the formula 4πε 0 ħcα = e 2.
Any ratio between physical constants of the same dimensions results in a dimensionless physical constant, for example, the proton-to-electron mass ratio. The fine-structure constant α is the best known dimensionless fundamental physical constant. It is the value of the elementary charge squared expressed in Planck units. This value has become ...