Finding how many holes are in polygon using ArcMap

Question

I have many polygons, and I want to know how many holes are in the polygon using field calculator. Like this polygon that has three holes.

Answer 1

ArcGIS Polygon objects can have one or more parts, with each part containing one or more subparts (rings).

There are a number of ways to extract the number of "holes" (interior subparts), but the easiest is to subtract the number of parts from the number of subparts. While there is a Polygon.partCount property, there isn't a subpartCount, but converting the Polygon to Polyline boundaries will generate the subparts, which can be counted. Thus the equation is:

Polygon.boundary().partCount - Polygon.partCount

We can see this work with the following script:

import arcpy

def num_holes(poly):
    return poly.boundary().partCount - poly.partCount

wkts = [
    'POLYGON ((0 0, 9 0, 9 9, 0 9, 0 0))',
    'POLYGON ((0 0, 9 0, 9 9, 0 9, 0 0),(2 2, 2 4, 4 4, 4 2, 2 2))',
    'POLYGON ((0 0, 9 0, 9 9, 0 9, 0 0),(2 2, 2 4, 4 4, 4 2, 2 2),(7 1, 7 8, 8 8, 8 1, 7 1))',
    'MULTIPOLYGON (((0 0, 5 0, 5 9, 0 9, 0 0)),((6 0, 9 0, 9 9, 6 9, 6 0)))',
    'MULTIPOLYGON (((0 0, 5 0, 5 9, 0 9, 0 0),(2 2, 4 2, 4 4, 2 4, 2 2)),((6 0, 9 0, 9 9, 6 9, 6 0)))',
    'MULTIPOLYGON (((0 0, 5 0, 5 9, 0 9, 0 0),(2 2, 4 2, 4 4, 2 4, 2 2)),((6 0, 9 0, 9 9, 6 9, 6 0),(7 1, 7 8, 8 8, 8 1, 7 1)))']

sr = arcpy.SpatialReference(4326)
for i,wkt in enumerate(wkts,start=1):
    shp = arcpy.FromWKT(wkt,sr)
    print("i={:d} parts={:d} subparts={:d} holes={:d}".format(
            i,shp.partCount,shp.boundary().partCount,num_holes(shp)))

Which displays:

i=1 parts=1 subparts=1 holes=0
i=2 parts=1 subparts=2 holes=1
i=3 parts=1 subparts=3 holes=2
i=4 parts=2 subparts=2 holes=0
i=5 parts=2 subparts=3 holes=1
i=6 parts=2 subparts=4 holes=2

In CalculateField, the syntax would be:

!shape!.boundary().partCount - !shape!.partCount