Dimensionless constant

A dimensionless constant has no residual physical dimensions, so changing units leaves its numerical value unchanged. The fine-structure constant $\alpha =e^2/(4\pi {ϵ}_0\hslash c)$ is an example: the dimensions carried by its constituent quantities cancel.

A dimensional constant such as the speed of light can be assigned the numerical value one through a unit convention; this cannot make an arbitrary dimensionless coupling equal one. Dimensionless ratios also distinguish physical regimes, but not every such ratio is a universal physical constant. A Reynolds number, for example, depends on the selected flow, length and material properties.