A physical quantity that is dimensionless

A dimensionless physical quantity has the dimensional formula $[M^{0} L^{0} T^{0}]$.

Some dimensionless quantities are ratios of similar physical quantities and do not have units. Examples include strain, relative density, and refractive index.

However, certain dimensionless quantities possess units. For example, plane angle is the ratio of arc length to radius, making it dimensionless, but it has the unit radian. Similarly, solid angle is dimensionless but has the unit steradian.

Therefore, a physical quantity that is dimensionless may have a unit.