Sphericity

Sphericity is a measure of how closely the shape of an object resembles that of a perfect sphere. For example, the sphericity of the balls inside a ball bearing determines the quality of the bearing, such as the load it can bear or the speed at which it can turn without failing. Sphericity is a specific example of a compactness measure of a shape. Defined by Wadell in 1935, the sphericity, ${\displaystyle \Psi }$, of an object is the ratio of the surface area of a sphere with the same volume to the object's surface area:

${\displaystyle \Psi ={\frac {\pi ^{\frac {1}{3}}(6V_{p})^{\frac {2}{3}}}{A_{p}}}}$

where ${\displaystyle V_{p}}$ is volume of the object and ${\displaystyle A_{p}}$ is the surface area. The sphericity of a sphere is unity by definition and, by the isoperimetric inequality, any shape which is not a sphere will have sphericity less than 1.

Sphericity applies in three dimensions; its analogue in two dimensions, such as the cross sectional circles along a cylindrical object such as a shaft, is called roundness.