What is "dimensionless quantity"

n. (context physics English) a quantity lacking dimension, a pure number.

In dimensional analysis, a dimensionless quantity is a quantity to which no physical dimension is applicable. It is thus a bare number, and is therefore also known as a quantity of dimension one. Dimensionless quantities are widely used in many fields, such as mathematics, physics, engineering, and economics. Numerous well-known quantities, such as , , and , are dimensionless. By contrast, examples of quantities with dimensions are length, time, and speed, which are measured in dimensional units, such as metre, second and metre/second.

Dimensionless quantities are often obtained as products or ratios of quantities that are not dimensionless, but whose dimensions cancel out in the mathematical operation. An example of such a ratio is engineering strain, a measure of an object's deformation. It is defined as the object's change in length divided by its initial length, and because both these quantities have dimension L (length), their ratio is dimensionless. Another example is alcohol by volume, which characterizes the concentration of ethanol in an alcoholic beverage.