Plane angle is defined as the ratio of arc length to the radius ($d\theta = ds/r$), and solid angle is defined as the ratio of the intercepted area to the square of the radius ($d\Omega = dA/r^2$). Being ratios of similar physical quantities (length/length and area/area), both are dimensionless quantities . However, they possess supplementary SI units: radian (rad) for plane angle and steradian (sr) for solid angle . Therefore, they have units but no dimensions.