I am using QGIS to calculate the form (or shape) factor of polygons following what Louf and Barthelemy did here: http://rsif.royalsocietypublishing.org/content/11/101/20140924
The form factor is defined as the ratio between the area of the block and the area of the circumscribed circle (something similar as a convex hull but with a circular buffer). The form factor is always smaller than 1 (since it is the area of the polygon divided by the area of the circumscribed circle).
To do so, I have a shapefile with the polygons of each block in several cities. I calculated the area of each polygon, but I need to find a way to calculate the area of the circumscribed circle. At the same time, it would be very useful if the calculation method can be repeated through a script or a function in the field calculator so it can be repeated for a large dataset of city blocks.