Dimensionless quantity
In dimensional analysis, a
dimensionless quantity or
quantity of dimension one is a quantity without an associated physical dimension. It is thus a "pure" number, and as such always has a dimension of 1. Dimensionless quantities are widely used in mathematics, physics, engineering, economics, and in everyday life. Numerous well-known quantities, such as π, e, and φ, are dimensionless. By contrast, non-dimensionless quantities are measured in units of length, area, time, etc. Dimensionless quantities are often defined as products or ratios of quantities that are not dimensionless, but whose dimensions cancel out when their powers are multiplied. This is the case, for instance, with the engineering strain, a measure of deformation. It is defined as change in length, divided by initial length, but since these quantities both have dimensions
L, the result is a dimensionless quantity.