Dimensionless quantity

A dimensionless quantity (also known as a bare quantity, pure quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Dimensionless quantities are distinct from quantities that have associated dimensions, such as time (measured for instance in seconds).

The corresponding unit of measurement is one (symbol 1), which is not explicitly shown. For any system of units, the number one is considered a base unit. Dimensionless units are special names that serve as units of measurement for expressing other dimensionless quantities. For example, in the SI, radians (rad) and steradians (sr) are dimensionless units for plane angles and solid angles, respectively. For example, optical extent is defined as having units of metres multiplied by steradians.

Some dimensionless quantities are called dimensionless numbers or characteristic numbers; they result from the product or quotient of other general quantities (e.g., characteristic lengths) and serve as parameters in equations and models. Characteristic numbers often carry the term "number" in their names (e.g., "Reynolds number") and may be denoted mathematically with a capitalized two-letter acronym (e.g., "Re" or "Re", italicized or not). Several such numbers are defined as part of the International System of Quantities (ISQ), as standardized in ISO 80000-11.

Dimensionless physical constants (e.g., fine-structure constant) and dimensionless material constants (e.g., refractive index) are dimensionless quantities having a fixed value for the whole universe or for a given material, respectively