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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 can be obtained as ratios of quantities that are not dimensionless, but whose dimensions cancel out in the mathematical operation. [19] [20] Examples of quotients of dimension one include calculating slopes or some unit conversion factors.
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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.
Derived quantities can be expressed in terms of the base quantities. Note that neither the names nor the symbols used for the physical quantities are international standards. Some quantities are known as several different names such as the magnetic B-field which is known as the magnetic flux density , the magnetic induction or simply as the ...
Dimensionless quantities, or quantities of dimension one, [2] are quantities implicitly defined in a manner that prevents their aggregation into units of measurement. [3] [4] Typically expressed as ratios that align with another system, these quantities do not necessitate explicitly defined units.
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