
Indicators 
Formula 
Range 
Significance/
Description 
Category : Patch area metrics 
1 
Built up (Total Land
Area) 
 
>0 
Total builtup land
(in ha) 
2 
Percentage of
Landscape
(PLAND) 
Pi = proportion of the landscape
occupied by patch type
(class) i.
aij = area (m^{2}) of patch ij.
A = total landscape area (m2). 
0 <
PLAND ≤
100 
PLAND
approaches 0
when the
corresponding
patch type (class)
becomes
increasingly rare
in the landscape.
PLAND = 100
when the entire
landscape consists
of a single patch
type; 
3 
Largest Patch
Index (Percenta
ge of
landscape) 
a ij = area (m^{2}) of patch ij
A= total landscape area 
0 ≤
LPI≤100 
LPI = 0 when
largest patch of
the patch type
becomes
increasingly
smaller.
LPI = 100 when
the entire
landscape consists
of a single patch
of, when the
largest patch
comprise 100% of
the landscape 
4 
Number of
Urban Patches 
N P U = n
NP equals the number of patches
in the landscape. 
NPU>0,
without
limit. 
It is a
fragmentation
Index. Higher the
value more the
fragmentation 
5 
Patch
density 
f(sample area) = (Patch
Number/Area) * 1000000 
PD>0, without limit 
Calculates patch
density index on a
raster map, using
a 4 neighbor
algorithm. Patch
density increases
with a greater number of patches
within a reference
area. 
6 
PerimeterArea Fractal
Dimension
PAFRAC 
PerimeterArea Fractal Dimension
aij = area (m^{2}) of patch ij.
pij = perimeter (m) of patch ij.
N = total number of patches in
the landscape 
1 ≤ PAFRAC ≤ 2 
It approaches 1
for shapes with
very simple
perimeters such as
squares, and
approaches 2 for
shapes with highly
convoluted,
perimeters.
PAFRAC requires
patches to vary in
size. 
7 
Landscape
Division Index
(DIVISION) 
a ij = area (m^{2}) of patch ij
A= total landscape area 
0≤DIVISION<1 
DIVISION =
0, when the
landscape consists
of single patch. It
approaches 1
when the
proportion of
landscape
comprising of the
focal patch type
decreases and as
those patches
decreases in size. 
Category : Edge/border metrics 
8 
Edge density 
k: patch type
m: number of patch type
n: number of edge segment of patch
type k
eik :total length of edge in
landscape involving patch type k
Area: total landscape area 
ED ≥ 0,
without
limit. ED =
0 when
there is no
class edge. 
ED measures
total edge of
urban boundary
used to compare
landscape of
varying sizes. 
9 
Area weighted
mean patch
fractal
dimension
(AWMPFD) 
Where si and pi are the area and
perimeter of patch i, and N is the
total number of patches 
1 ≤ AWMPFD ≤ 2 
AWMPFD
approaches 1 for
shapes with very
simple
perimeters, such
as circles or
squares, and
approaches 2 for
shapes with highly
convoluted
perimeter
AWMPFD
describes the
fragmentation of
urban patches. If
Sprawl is high
then the
AWMPFD value
is high 
10 
Perimeter Area
Weighted Mean
Ratio.
PARA_AM 
PARA _AM= Pij/Aij
Pij = perimeter of patch ij
Aij= area weighted mean of patch ij

≥ 0,
without
limit 
PARA AM is a
very useful
measure of
fragmentation; it
is a measure of
the amount of
'edge' for a
landscape or
class. PARA AM
value increased
with increasing
patch shape
complexity,
which precisely
characterized the
degree of patch
shape
complexity. 
11 
Mean Patch
Fractal
Dimension
(MPFD) 
pij = perimeter of patch ij
aij= area weighted mean of patch ij
N = total number of patches in
the landscape 
1<=MPFD<2 
Shape
Complexity.
MPFD is another
measure of shape
complexity,
approaches one
for shapes with
simple
perimeters and
approaches two
when shapes are
more complex. 
12 
Total Edge
(TE) 
eik = total length (m) of edge in
landscape involving patch
type (class) i; includes
landscape boundary and
background segments
involving patch type i. 
TE>0,
Without
limit 
TE equals the
sum of the
lengths (m) of all
edge segments
involving the
corresponding
patch type. TE
includes a userspecified
proportion of
internal
background edge
segments
involving the
corresponding
patch type 
Category : Shape metrics 
13 
NLSI(Normalized Landscape
Shape Index) 
Where si and pi are the area and
perimeter of patch i, and N is the
total number of patches. 
0≤NLSI<1 
NLSI = 0 when
the landscape
consists of single
square or
maximally
compact almost
square, it
increases when
the patch types
becomes
increasingly
disaggregated
and is 1 when the
patch type is
maximally
disaggregated 
14 
Landscape
Shape Index
(LSI) 
ei = total length of edge (or
perimeter) of class i
in terms of number
of cell surfaces;
includes all
landscape boundary
and background edge
segments involving
class i.
min ei = minimum total length of
edge (or perimeter)
of class i in terms of
number of cell surfaces (see below). 
LSI>1,
Without
Limit 
LSI = 1 when the
landscape
consists of a
single square or
maximally
compact (i.e.,
almost square)
patch of the
corresponding
type; LSI
increases without
limit as the patch
type becomes
more
disaggregated 
Category: Compactness/ contagion / dispersion metrics 
15 
Clumpiness 
gii =number of like adjacencies
(joins) between pixels of patch type
(class) I based on the doublecount
method.
gik =number of adjacencies (joins)
between pixels of patch types
(classes) i and k based on the
doublecount method.
minei
=minimum perimeter (in number of
cell surfaces) of patch type (class)i
for a maximally clumped class.
Pi =proportion of the landscape
occupied by patch type (class) i. 
1≤
CLUMPY
≤1 
It equals 0 when
the patches are
distributed
randomly, and
approaches 1
when the patch
type is
maximally
aggregated 
16 
Percentage of
Like
Adjacencies
(PLADJ) 
gii = number of like adjacencies
(joins) between pixels of
patch type (class) i based on
the doublecount method.
gik = number of adjacencies
(joins) between pixels of
patch types (classes) i and k
based on the doublecount
method. 
0<=PLADJ<=100 
The percentage
of cell
adjacencies
involving the
corresponding
patch type that
are like
adjacencies. Cell
adjacencies are
tallied using the
doublecount
method in which
pixel order is
preserved, at
least for all
internal
adjacencies 
17 
Total Core
Area (TCA) 

TCA>=0
Without
limit. 
TCA equals the
sum of the core
areas of each
patch (m^{2}) of the
corresponding
patch type, divided by
10,000 (to
convert to
hectares). 
18 
ENND
coefficient of
variation 
CV (coefficient of variation) equals
the standard deviation divided by
the mean, multiplied by 100 to
convert to a percentage, for the
corresponding patch metrics. 
It is
represented
in
percentage. 
In the analysis of
urban processes,
greater isolation
indicates greater
dispersion. 
19 
Aggregation
index 
gii =number of like adjacencies
(joins) between pixels of patch type
(class) i based on the single count
method.
maxgii = maximum number of like
adjacencies (joins) between pixels
of patch type class i based on single
count method.
Pi= proportion of landscape
comprised of patch type (class) i. 
1≤AI≤100 
AI equals when
the patches are
maximally
disaggregated
and equals 100
when the patches
are maximally
aggregated into a
single compact
patch.
Aggregation
corresponds to
the clustering of
patches to form
patches of a
larger size. 
20 
Interspersion
and
Juxtaposition 
eik = total length (m) of edge in
landscape between patch types
(classes) i and k.
E = total length (m) of edge in
landscape, excluding background
m = number of patch types
(classes) present in the landscape,
including the landscape border, if
present. 
0≤ IJI ≤100 
IJI is used to
measure patch
adjacency. IJI
approach 0 when
distribution of
adjacencies
among unique
patch types
becomes
increasingly
uneven; is equal
to 100 when all
patch types are
equally adjacent
to all other patch
types. 