The compactness of a district, measured using the ratio of the district area to the area of a circle with the same perimeter, can serve as a useful proxy for how gerrymandered the district is. The map below colors Congressional districts according to their compactness, for states with at least three districts. Read the related blog post »

Gerrymander index scores, 113th Congress


METHODOLOGY
I grabbed district shapefiles from the U.S. Census, and calculated the area and perimeter for each district using QGIS. The Census files use simplified geometry for coastal regions, so that highly irregular coastlines (like Maryland's) don't have an outsized impact on the compactness measures. To arrive at the gerrymander scores, I compared the ratio of the district area to the area of a circle with the same perimeter, following the Polsby-Popper method. I inverted these values and multiplied by 100 to arrive at a 0-100 index, with the least compact districts receiving the highest scores. For the purposes of ranking state and district scores I omitted states with only one or two districts, as the former don't redistrict at all and the latter's district boundaries are more a factor of the state's boundaries than anything else.