A dimensionless quantity is a physical quantity without any physical dimension and expressed as a pure number without units. Examples of dimensionless quantities include:
- Pi (π), the ratio of the circumference of a circle to its diameter
- Reynolds number, a measure in fluid dynamics
- Strain, the ratio of change in length to original length
- Coefficient of friction, the ratio of friction force to normal force
- Relative density (specific gravity), the ratio of density of a substance to a reference substance such as water
- Refractive index, the ratio of the speed of light in vacuum to the speed of light in a material
Among these, the refractive index is a commonly given example of a dimensionless quantity because it is a ratio of two speeds, both having the same dimension (length/time), thus cancelling out all units resulting in a pure number.
