Dimensionless quantity

Dimensionless quantities, also known as quantities of dimension one are implicitly defined in a manner that prevents their aggregation into units of measurement. Typically expressed as ratios that align with another system, these quantities do not necessitate explicitly defined units. For instance, alcohol by volume (ABV) represents a volumetric ratio. Its derivation remains independent of the specific units of volume used; any common unit may be applied. Notably, ABV is never expressed as milliliters per milliliter, underscoring its dimensionless nature.

The number one is recognized as a dimensionless base quantity. Radians serve as dimensionless units for angular measurements, derived from the universal ratio of 2π times the radius of a circle being equal to its circumference.

Dimensionless quantities play a crucial role serving as parameters in differential equations in various technical disciplines. In calculus, concepts like the unitless ratios in limits or derivatives often involve dimensionless quantities. In differential geometry, the use of dimensionless parameters is evident in geometric relationships and transformations. Physics relies on dimensionless numbers like the Reynolds number in fluid dynamics, the fine-structure constant in quantum mechanics, and the Lorentz factor in relativity. In chemistry, state properties and ratios such as mole fractions concentration ratios are dimensionless.