Excerpt from Microscope Image Processing by Qiang Wu, Fatima Aziz Merchant, Kenneth R. Castleman
Thinness Ratio
Thinness is typically used to define the regularity of an object. Having computed the area (A) and perimeter (P) of an object, we can define the thinness ratio as �?�. T = 4pi(A/P2)
This measure takes a maximum value of 1 for a circle. Objects of regular shape have a higher thinness ratio than similar irregular ones.
There is not a default value that I can recommend. That is dependent on each user's requirements. Generally, it is less than 1.
Microscope Image Processing (written by AvQiang Wu,Fatima Merchant,Kenneth Castleman). Excerpt:
Thinness is typically used to define the regularity of an object. Having computed the area (A) and perimeter (P) of an object, we can define the thinness ratio as T = 4pi(A/P^{2})
This measure takes a maximum value of 1 for a circle. Objects of regular shape have a higher thinness ratio than similar irregular ones.
So, you can calculate your new field in Field Calculator to be:
4 * 3.14 * [Shape_Area] / ([Shape_Length] * [Shape_Length])
Most sliver polygons would have the ratio really close to 0, but from what I've seen whatever that is lower than 0.3 might be a good candidate, too. However, consider the features areas first before running into any hasty conclusions. Large and/or multipart features with irregular shape might have a really low thinness ratio yet they are not even close to be sliver polygons. You would probably want to set a definition query on your feature class excluding most of the polygons with large area….”
Source: Fighting sliver polygons in ArcGIS: thinness ratio | Tereshenkov's Blog