Dimensionless quantity

Dimensionless quantities, or quantities of dimension one, are quantities with no associated units of measurement. These may be ratios of quantities with the same physical units or ratios of dimensionally equal products with identical units. For instance, alcohol by volume (ABV) represents a volumetric ratio; its value remains independent of the specific units of volume used, such as in milliliters per milliliter (mL/mL). The International Organization for Standardization calls a physical quantity with units of 'one' a characteristic number.

The number one has been suggested 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.

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 (as concentration ratios) are dimensionless. Mathematics texts commonly omit units, making quantities like area and length appear to be dimensionless.