# What are Measures of Compactness?

A district that is not compact may be considered gerrymandered. For this reason, a number of measures of compactness have been devised to assess or defend  the districts in a plan. These measures aim to quantify how compact or dispersed a district is.

### Software for Redistricting and Measuring Compactness

Maptitude for Redistricting is the easy to use, professional tool for political redistricting. Maptitude for Redistricting computes nine measures of compactness:

• Reock – an area-based measure that compares each district to a circle, which is considered to be the most compact shape possible.
• Schwartzberg – a perimeter-based measure that compares a simplified version of each district to a circle
• Perimeter – a test that lets you compare plans where the plan with the smallest perimeter is the most compact
• Polsby-Popper – a measure of the ratio of the district area to the area of a circle with the same perimeter
• Length-Width – computes the absolute difference between the width (east-west) and the height (north-south) of each district
• Population Polygon – computes the ratio of the district population to the approximate population of the convex hull of the district (minimum convex polygon which completely contains the district).
• Minimum Convex Polygon – similar to the Population Polygon, but without regard to population within the areas
• Population Circle – computes the ratio of the district population to the approximate population of the minimum enclosing circle of the district
• Ehrenburg – computes the ratio of the largest inscribed circle divided by the area of the district