These functions compute measurements of distance, area and angles.
There are also functions to compute geometry values determined by measurements.
Measurement Functions
ST_Area
Returns the area of a polygonal geometry.
float ST_Area
geometry g1
float ST_Area
geography geog
boolean use_spheroid=true
Description
Returns the area of a polygonal geometry.
For geometry types a 2D Cartesian (planar) area is computed, with units specified by the SRID.
For geography types by default area is determined on a spheroid with units in square meters.
To compute the area using the faster but less accurate spherical model use ST_Area(geog,false).
Enhanced: 2.0.0 - support for 2D polyhedral surfaces was introduced.
Enhanced: 2.2.0 - measurement on spheroid performed with GeographicLib for improved accuracy and robustness. Requires Proj >= 4.9.0 to take advantage of the new feature.
Changed: 3.0.0 - does not depend on SFCGAL anymore.
&sfs_compliant;
&sqlmm_compliant; SQL-MM 3: 8.1.2, 9.5.3
&P_support;
For polyhedral surfaces, only supports 2D polyhedral surfaces (not 2.5D). For 2.5D, may give a non-zero answer, but only for the faces that
sit completely in XY plane.
Examples
Return area in square feet for a plot of Massachusetts land and multiply by conversion to get square meters.
Note this is in square feet because EPSG:2249 is
Massachusetts State Plane Feet
select ST_Area(geom) sqft,
ST_Area(geom) * 0.3048 ^ 2 sqm
from (
select 'SRID=2249;POLYGON((743238 2967416,743238 2967450,
743265 2967450,743265.625 2967416,743238 2967416))' :: geometry geom
) subquery;
┌─────────┬─────────────┐
│ sqft │ sqm │
├─────────┼─────────────┤
│ 928.625 │ 86.27208552 │
└─────────┴─────────────┘
Return area square feet and transform to Massachusetts state plane meters (EPSG:26986) to get square meters.
Note this is in square feet because 2249 is
Massachusetts State Plane Feet and transformed area is in square meters since EPSG:26986 is state plane Massachusetts meters
select ST_Area(geom) sqft,
ST_Area(ST_Transform(geom, 26986)) As sqm
from (
select
'SRID=2249;POLYGON((743238 2967416,743238 2967450,
743265 2967450,743265.625 2967416,743238 2967416))' :: geometry geom
) subquery;
┌─────────┬─────────────────┐
│ sqft │ sqm │
├─────────┼─────────────────┤
│ 928.625 │ 86.272430607008 │
└─────────┴─────────────────┘
Return area square feet and square meters using geography data type. Note that we transform to our geometry to geography
(before you can do that make sure your geometry is in WGS 84 long lat 4326). Geography always measures in meters.
This is just for demonstration to compare. Normally your table will be stored in geography data type already.
select ST_Area(geog) / 0.3048 ^ 2 sqft_spheroid,
ST_Area(geog, false) / 0.3048 ^ 2 sqft_sphere,
ST_Area(geog) sqm_spheroid
from (
select ST_Transform(
'SRID=2249;POLYGON((743238 2967416,743238 2967450,743265 2967450,743265.625 2967416,743238 2967416))'::geometry,
4326
) :: geography geog
) as subquery;
┌──────────────────┬──────────────────┬──────────────────┐
│ sqft_spheroid │ sqft_sphere │ sqm_spheroid │
├──────────────────┼──────────────────┼──────────────────┤
│ 928.684405784452 │ 927.049336105925 │ 86.2776044979692 │
└──────────────────┴──────────────────┴──────────────────┘
If your data is in geography already:
select ST_Area(geog) / 0.3048 ^ 2 sqft,
ST_Area(the_geog) sqm
from somegeogtable;
See Also
, , , ,
ST_Azimuth
Returns the north-based azimuth as the angle in radians measured clockwise from the vertical on pointA to pointB.
float ST_Azimuth
geometry pointA
geometry pointB
float ST_Azimuth
geography pointA
geography pointB
Description
Returns the azimuth in radians of the segment defined by the given
point geometries, or NULL if the two points are coincident. The azimuth is angle is referenced from north, and is positive clockwise: North = 0; East = π/2; South = π; West = 3π/2.
For the geography type, the forward azimuth is solved as part of the inverse geodesic problem.
The azimuth is mathematical concept defined as the angle between a reference plane and a point, with angular units in radians.
Units can be converted to degrees using a built-in PostgreSQL function degrees(), as shown in the example.
Availability: 1.1.0
Enhanced: 2.0.0 support for geography was introduced.
Enhanced: 2.2.0 measurement on spheroid performed with GeographicLib for improved accuracy and robustness. Requires Proj >= 4.9.0 to take advantage of the new feature.
Azimuth is especially useful in conjunction with ST_Translate for shifting an object along its perpendicular axis. See
upgis_lineshift Plpgsqlfunctions PostGIS wiki section for example of this.
Examples
Geometry Azimuth in degrees
SELECT degrees(ST_Azimuth(ST_Point(25, 45), ST_Point(75, 100))) AS degA_B,
degrees(ST_Azimuth(ST_Point(75, 100), ST_Point(25, 45))) AS degB_A;
dega_b | degb_a
------------------+------------------
42.2736890060937 | 222.273689006094
Green: the start Point(25,45) with its vertical. Yellow: degA_B as the path to travel (azimuth).
Green: the start Point(75,100) with its vertical. Yellow: degB_A as the path to travel (azimuth).

See Also
, , , PostgreSQL Math Functions
ST_Angle
Returns the angle between 3 points, or between 2 vectors (4 points or 2 lines).
float ST_Angle
geometry point1
geometry point2
geometry point3
geometry point4
float ST_Angle
geometry line1
geometry line2
Description
For 3 points, computes the angle measured clockwise of P1P2P3.
If input are 2 lines, get first and last point of the lines as 4 points.
For 4 points,compute the angle measured clockwise of P1P2,P3P4.
Results are always positive, between 0 and 2*Pi radians.
Uses azimuth of pairs or points.
ST_Angle(P1,P2,P3) = ST_Angle(P2,P1,P2,P3)
Result is in radian and can be converted to degrees using a built-in PostgreSQL function degrees(), as shown in the example.
Availability: 2.5.0
Examples
Geometry Azimuth in degrees
WITH rand AS (
SELECT s, random() * 2 * PI() AS rad1
, random() * 2 * PI() AS rad2
FROM generate_series(1,2,2) AS s
)
, points AS (
SELECT s, rad1,rad2, ST_MakePoint(cos1+s,sin1+s) as p1, ST_MakePoint(s,s) AS p2, ST_MakePoint(cos2+s,sin2+s) as p3
FROM rand
,cos(rad1) cos1, sin(rad1) sin1
,cos(rad2) cos2, sin(rad2) sin2
)
SELECT s, ST_AsText(ST_SnapToGrid(ST_MakeLine(ARRAY[p1,p2,p3]),0.001)) AS line
, degrees(ST_Angle(p1,p2,p3)) as computed_angle
, round(degrees(2*PI()-rad2 -2*PI()+rad1+2*PI()))::int%360 AS reference
, round(degrees(2*PI()-rad2 -2*PI()+rad1+2*PI()))::int%360 AS reference
FROM points ;
1 | line | computed_angle | reference
------------------+------------------
1 | LINESTRING(1.511 1.86,1 1,0.896 0.005) | 155.27033848688 | 155
ST_ClosestPoint
Returns the 2D point on g1 that is closest to g2. This is the first point of
the shortest line.
geometry ST_ClosestPoint
geometry
g1
geometry
g2
Description
Returns the 2-dimensional point on g1 that is closest to g2. This is the first point of
the shortest line.
If you have a 3D Geometry, you may prefer to use .
Availability: 1.5.0
Examples
Closest between point and linestring is the point itself, but closest
point between a linestring and point is the point on line string that is closest.
SELECT ST_AsText(ST_ClosestPoint(pt,line)) AS cp_pt_line,
ST_AsText(ST_ClosestPoint(line,pt)) As cp_line_pt
FROM (SELECT 'POINT(100 100)'::geometry As pt,
'LINESTRING (20 80, 98 190, 110 180, 50 75 )'::geometry As line
) As foo;
cp_pt_line | cp_line_pt
----------------+------------------------------------------
POINT(100 100) | POINT(73.0769230769231 115.384615384615)
closest point on polygon A to polygon B
SELECT ST_AsText(
ST_ClosestPoint(
ST_GeomFromText('POLYGON((175 150, 20 40, 50 60, 125 100, 175 150))'),
ST_Buffer(ST_GeomFromText('POINT(110 170)'), 20)
)
) As ptwkt;
ptwkt
------------------------------------------
POINT(140.752120669087 125.695053378061)

See Also
,, , ,
ST_3DClosestPoint
Returns the 3D point on g1 that is closest to g2. This is the first point of
the 3D shortest line.
geometry ST_3DClosestPoint
geometry
g1
geometry
g2
Description
Returns the 3-dimensional point on g1 that is closest to g2. This is the first point of
the 3D shortest line. The 3D length of the 3D shortest line is the 3D distance.
&Z_support;
&P_support;
Availability: 2.0.0
Changed: 2.2.0 - if 2 2D geometries are input, a 2D point is returned (instead of old behavior assuming 0 for missing Z). In case of 2D and 3D, Z is no longer assumed to be 0 for missing Z.
Examples
linestring and point -- both 3d and 2d closest point
SELECT ST_AsEWKT(ST_3DClosestPoint(line,pt)) AS cp3d_line_pt,
ST_AsEWKT(ST_ClosestPoint(line,pt)) As cp2d_line_pt
FROM (SELECT 'POINT(100 100 30)'::geometry As pt,
'LINESTRING (20 80 20, 98 190 1, 110 180 3, 50 75 1000)'::geometry As line
) As foo;
cp3d_line_pt | cp2d_line_pt
-----------------------------------------------------------+------------------------------------------
POINT(54.6993798867619 128.935022917228 11.5475869506606) | POINT(73.0769230769231 115.384615384615)

linestring and multipoint -- both 3d and 2d closest point
SELECT ST_AsEWKT(ST_3DClosestPoint(line,pt)) AS cp3d_line_pt,
ST_AsEWKT(ST_ClosestPoint(line,pt)) As cp2d_line_pt
FROM (SELECT 'MULTIPOINT(100 100 30, 50 74 1000)'::geometry As pt,
'LINESTRING (20 80 20, 98 190 1, 110 180 3, 50 75 900)'::geometry As line
) As foo;
cp3d_line_pt | cp2d_line_pt
-----------------------------------------------------------+--------------
POINT(54.6993798867619 128.935022917228 11.5475869506606) | POINT(50 75)

Multilinestring and polygon both 3d and 2d closest point
SELECT ST_AsEWKT(ST_3DClosestPoint(poly, mline)) As cp3d,
ST_AsEWKT(ST_ClosestPoint(poly, mline)) As cp2d
FROM (SELECT ST_GeomFromEWKT('POLYGON((175 150 5, 20 40 5, 35 45 5, 50 60 5, 100 100 5, 175 150 5))') As poly,
ST_GeomFromEWKT('MULTILINESTRING((175 155 2, 20 40 20, 50 60 -2, 125 100 1, 175 155 1),
(1 10 2, 5 20 1))') As mline ) As foo;
cp3d | cp2d
-------------------------------------------+--------------
POINT(39.993580415989 54.1889925532825 5) | POINT(20 40)

See Also
, , ,
ST_Distance
Returns the distance between two geometry or geography values.
float ST_Distance
geometry
g1
geometry
g2
float ST_Distance
geography
geog1
geography
geog2
>boolean
use_spheroid=true
Description
For types returns the minimum 2D Cartesian (planar) distance between two geometries, in
projected units (spatial ref units).
For types defaults to return the minimum geodesic distance between two geographies in meters,
compute on the spheroid determined by the SRID.
If use_spheroid is
false, a faster spherical calculation is used.
&sfs_compliant;
&sqlmm_compliant; SQL-MM 3: 5.1.23
&curve_support;
Availability: 1.5.0 geography support was introduced in 1.5. Speed improvements for planar to better handle large or many vertex geometries
Enhanced: 2.1.0 improved speed for geography. See Making Geography faster for details.
Enhanced: 2.1.0 - support for curved geometries was introduced.
Enhanced: 2.2.0 - measurement on spheroid performed with GeographicLib for improved accuracy and robustness. Requires Proj >= 4.9.0 to take advantage of the new feature.
Changed: 3.0.0 - does not depend on SFCGAL anymore.
Basic Geometry Examples
Geometry example - units in planar degrees 4326 is WGS 84 long lat, units are degrees.
SELECT ST_Distance(
'SRID=4326;POINT(-72.1235 42.3521)'::geometry,
'SRID=4326;LINESTRING(-72.1260 42.45, -72.123 42.1546)'::geometry
);
st_distance
-----------------
0.00150567726382282
Geometry example - units in meters (SRID: 3857, proportional to pixels on popular web maps).
Although the value is off, nearby ones can be compared correctly,
which makes it a good choice for algorithms like KNN or KMeans.
SELECT ST_Distance(
ST_Transform('SRID=4326;POINT(-72.1235 42.3521)'::geometry, 3857),
ST_Transform('SRID=4326;LINESTRING(-72.1260 42.45, -72.123 42.1546)'::geometry, 3857)
);
st_distance
-----------------
167.441410065196
Geometry example - units in meters (SRID: 3857 as above, but corrected by cos(lat) to account for distortion)
SELECT ST_Distance(
ST_Transform('SRID=4326;POINT(-72.1235 42.3521)'::geometry, 3857),
ST_Transform('SRID=4326;LINESTRING(-72.1260 42.45, -72.123 42.1546)'::geometry, 3857)
) * cosd(42.3521);
st_distance
-----------------
123.742351254151
Geometry example - units in meters (SRID: 26986 Massachusetts state plane meters) (most accurate for Massachusetts)
SELECT ST_Distance(
ST_Transform('SRID=4326;POINT(-72.1235 42.3521)'::geometry, 26986),
ST_Transform('SRID=4326;LINESTRING(-72.1260 42.45, -72.123 42.1546)'::geometry, 26986)
);
st_distance
-----------------
123.797937878454
Geometry example - units in meters (SRID: 2163 US National Atlas Equal area) (least accurate)
SELECT ST_Distance(
ST_Transform('SRID=4326;POINT(-72.1235 42.3521)'::geometry, 2163),
ST_Transform('SRID=4326;LINESTRING(-72.1260 42.45, -72.123 42.1546)'::geometry, 2163)
);
st_distance
------------------
126.664256056812
Geography Examples
Same as geometry example but note units in meters - use sphere for slightly faster and less accurate computation.
SELECT ST_Distance(gg1, gg2) As spheroid_dist, ST_Distance(gg1, gg2, false) As sphere_dist
FROM (SELECT
'SRID=4326;POINT(-72.1235 42.3521)'::geography as gg1,
'SRID=4326;LINESTRING(-72.1260 42.45, -72.123 42.1546)'::geography as gg2
) As foo ;
spheroid_dist | sphere_dist
------------------+------------------
123.802076746848 | 123.475736916397
See Also
, , , ,
, , ,
ST_3DDistance
Returns the 3D cartesian minimum distance (based on spatial ref) between two geometries in
projected units.
float ST_3DDistance
geometry
g1
geometry
g2
Description
Returns the 3-dimensional minimum cartesian distance between two geometries in
projected units (spatial ref units).
&Z_support;
&P_support;
&sqlmm_compliant; SQL-MM ?
Availability: 2.0.0
Changed: 2.2.0 - In case of 2D and 3D, Z is no longer assumed to be 0 for missing Z.
Changed: 3.0.0 - SFCGAL version removed
Examples
-- Geometry example - units in meters (SRID: 2163 US National Atlas Equal area) (3D point and line compared 2D point and line)
-- Note: currently no vertical datum support so Z is not transformed and assumed to be same units as final.
SELECT ST_3DDistance(
ST_Transform('SRID=4326;POINT(-72.1235 42.3521 4)'::geometry,2163),
ST_Transform('SRID=4326;LINESTRING(-72.1260 42.45 15, -72.123 42.1546 20)'::geometry,2163)
) As dist_3d,
ST_Distance(
ST_Transform('SRID=4326;POINT(-72.1235 42.3521)'::geometry,2163),
ST_Transform('SRID=4326;LINESTRING(-72.1260 42.45, -72.123 42.1546)'::geometry,2163)
) As dist_2d;
dist_3d | dist_2d
------------------+-----------------
127.295059324629 | 126.66425605671
-- Multilinestring and polygon both 3d and 2d distance
-- Same example as 3D closest point example
SELECT ST_3DDistance(poly, mline) As dist3d,
ST_Distance(poly, mline) As dist2d
FROM (SELECT 'POLYGON((175 150 5, 20 40 5, 35 45 5, 50 60 5, 100 100 5, 175 150 5))'::geometry as poly,
'MULTILINESTRING((175 155 2, 20 40 20, 50 60 -2, 125 100 1, 175 155 1), (1 10 2, 5 20 1))'::geometry as mline) as foo;
dist3d | dist2d
-------------------+--------
0.716635696066337 | 0
See Also
, , , , ,
ST_DistanceSphere
Returns minimum distance in meters between two lon/lat
geometries using a spherical earth model.
float ST_DistanceSphere
geometry geomlonlatA
geometry geomlonlatB
Description
Returns minimum distance in meters between two lon/lat
points. Uses a spherical earth and radius derived from the spheroid
defined by the SRID.
Faster than , but less
accurate. PostGIS Versions prior to 1.5 only implemented for points.
Availability: 1.5 - support for other geometry types besides points was introduced. Prior versions only work with points.
Changed: 2.2.0 In prior versions this used to be called ST_Distance_Sphere
Examples
SELECT round(CAST(ST_DistanceSphere(ST_Centroid(the_geom), ST_GeomFromText('POINT(-118 38)',4326)) As numeric),2) As dist_meters,
round(CAST(ST_Distance(ST_Transform(ST_Centroid(the_geom),32611),
ST_Transform(ST_GeomFromText('POINT(-118 38)', 4326),32611)) As numeric),2) As dist_utm11_meters,
round(CAST(ST_Distance(ST_Centroid(the_geom), ST_GeomFromText('POINT(-118 38)', 4326)) As numeric),5) As dist_degrees,
round(CAST(ST_Distance(ST_Transform(the_geom,32611),
ST_Transform(ST_GeomFromText('POINT(-118 38)', 4326),32611)) As numeric),2) As min_dist_line_point_meters
FROM
(SELECT ST_GeomFromText('LINESTRING(-118.584 38.374,-118.583 38.5)', 4326) As the_geom) as foo;
dist_meters | dist_utm11_meters | dist_degrees | min_dist_line_point_meters
-------------+-------------------+--------------+----------------------------
70424.47 | 70438.00 | 0.72900 | 65871.18
See Also
,
ST_DistanceSpheroid
Returns the minimum distance between two lon/lat geometries
using a spheroidal earth model.
float ST_DistanceSpheroid
geometry geomlonlatA
geometry geomlonlatB
spheroid measurement_spheroid
Description
Returns minimum distance in meters between two lon/lat
geometries given a particular spheroid. See the explanation of spheroids given for
.
This function does not look at the SRID of the geometry.
It assumes the geometry coordinates are based on the provided spheroid.
Availability: 1.5 - support for other geometry types besides points was introduced. Prior versions only work with points.
Changed: 2.2.0 In prior versions this was called ST_Distance_Spheroid
Examples
SELECT round(CAST(
ST_DistanceSpheroid(ST_Centroid(the_geom), ST_GeomFromText('POINT(-118 38)',4326), 'SPHEROID["WGS 84",6378137,298.257223563]')
As numeric),2) As dist_meters_spheroid,
round(CAST(ST_DistanceSphere(ST_Centroid(the_geom), ST_GeomFromText('POINT(-118 38)',4326)) As numeric),2) As dist_meters_sphere,
round(CAST(ST_Distance(ST_Transform(ST_Centroid(the_geom),32611),
ST_Transform(ST_GeomFromText('POINT(-118 38)', 4326),32611)) As numeric),2) As dist_utm11_meters
FROM
(SELECT ST_GeomFromText('LINESTRING(-118.584 38.374,-118.583 38.5)', 4326) As the_geom) as foo;
dist_meters_spheroid | dist_meters_sphere | dist_utm11_meters
----------------------+--------------------+-------------------
70454.92 | 70424.47 | 70438.00
See Also
,
ST_FrechetDistance
Returns the Fréchet distance between two geometries.
float ST_FrechetDistance
geometry
g1
geometry
g2
float
densifyFrac = -1
Description
Implements algorithm for computing the Fréchet distance restricted to discrete points for both geometries, based on Computing Discrete Fréchet Distance.
The Fréchet distance is a measure of similarity between curves that takes into account the location and ordering of the points along the curves. Therefore it is often better than the Hausdorff distance.
When the optional densifyFrac is specified, this function performs a segment densification before computing the discrete Fréchet distance. The densifyFrac parameter sets the fraction by which to densify each segment. Each segment will be split into a number of equal-length subsegments, whose fraction of the total length is closest to the given fraction.
Units are in the units of the spatial reference system of the geometries.
The current implementation supports only vertices as the discrete locations. This could be extended to allow an arbitrary density of points to be used.
The smaller densifyFrac we specify, the more acurate Fréchet distance we get. But, the computation time and the memory usage increase with the square of the number of subsegments.
Performed by the GEOS module.
Availability: 2.4.0 - requires GEOS >= 3.7.0
Examples
postgres=# SELECT st_frechetdistance('LINESTRING (0 0, 100 0)'::geometry, 'LINESTRING (0 0, 50 50, 100 0)'::geometry);
st_frechetdistance
--------------------
70.7106781186548
(1 row)
SELECT st_frechetdistance('LINESTRING (0 0, 100 0)'::geometry, 'LINESTRING (0 0, 50 50, 100 0)'::geometry, 0.5);
st_frechetdistance
--------------------
50
(1 row)
See Also
ST_HausdorffDistance
Returns the Hausdorff distance between two geometries.
float ST_HausdorffDistance
geometry
g1
geometry
g2
float ST_HausdorffDistance
geometry
g1
geometry
g2
float
densifyFrac
Description
Returns the Hausdorff distance between two geometries, a measure of how similar or dissimilar 2 geometries are.
Implements algorithm for computing a distance metric which can be thought of as the "Discrete Hausdorff Distance".
This is the Hausdorff distance restricted to discrete points for one of the geometries. Wikipedia article on Hausdorff distance
Martin Davis note on how Hausdorff Distance calculation was used to prove correctness of the CascadePolygonUnion approach.
When densifyFrac is specified, this function performs a segment densification before computing the discrete hausdorff distance. The densifyFrac parameter sets the fraction by which to densify each segment. Each segment will be split into a number of equal-length subsegments, whose fraction of the total length is closest to the given fraction.
Units are in the units of the spatial reference system of the geometries.
The current implementation supports only vertices as the discrete locations. This could be extended to allow an arbitrary density of points to be used.
This algorithm is NOT equivalent to the standard Hausdorff distance. However, it computes an approximation that is correct for a large subset of useful cases.
One important part of this subset is Linestrings that are roughly parallel to each other, and roughly equal in length. This is a useful metric for line matching.
Availability: 1.5.0
Examples
For each building, find the parcel that best represents it. First we require the parcel intersect with the geometry.
DISTINCT ON guarantees we get each building listed only once, the ORDER BY .. ST_HausdorffDistance gives us a preference of parcel that is most similar to the building.
SELECT DISTINCT ON(buildings.gid) buildings.gid, parcels.parcel_id
FROM buildings INNER JOIN parcels ON ST_Intersects(buildings.geom,parcels.geom)
ORDER BY buildings.gid, ST_HausdorffDistance(buildings.geom, parcels.geom);
postgis=# SELECT ST_HausdorffDistance(
'LINESTRING (0 0, 2 0)'::geometry,
'MULTIPOINT (0 1, 1 0, 2 1)'::geometry);
st_hausdorffdistance
----------------------
1
(1 row)
postgis=# SELECT st_hausdorffdistance('LINESTRING (130 0, 0 0, 0 150)'::geometry, 'LINESTRING (10 10, 10 150, 130 10)'::geometry, 0.5);
st_hausdorffdistance
----------------------
70
(1 row)
See Also
ST_Length
Returns the 2D length of a linear geometry.
float ST_Length
geometry a_2dlinestring
float ST_Length
geography geog
boolean use_spheroid=true
Description
For geometry types: returns the 2D Cartesian length of the geometry if it is a LineString, MultiLineString, ST_Curve, ST_MultiCurve.
For areal geometries 0 is returned; use instead.
The units of length is determined by the
spatial reference system of the geometry.
For geography types: computation is performed using the inverse geodesic calculation. Units of length are in meters.
If PostGIS is compiled with PROJ version 4.8.0 or later, the spheroid is specified by the SRID, otherwise it is exclusive to WGS84.
If use_spheroid=false, then the calculation is based on a sphere instead of a spheroid.
Currently for geometry this is an alias for ST_Length2D, but this may change to support higher dimensions.
Changed: 2.0.0 Breaking change -- in prior versions applying this to a MULTI/POLYGON of type geography would give you the perimeter of the POLYGON/MULTIPOLYGON. In 2.0.0
this was changed to return 0 to be in line with geometry behavior. Please use ST_Perimeter if you want the perimeter of a polygon
For geography the calculation defaults to using a spheroidal model. To use the faster but less accurate spherical calculation use ST_Length(gg,false);
&sfs_compliant; s2.1.5.1
&sqlmm_compliant; SQL-MM 3: 7.1.2, 9.3.4
Availability: 1.5.0 geography support was introduced in 1.5.
&sfcgal_enhanced;
Geometry Examples
Return length in feet for line string. Note this is in feet because EPSG:2249 is
Massachusetts State Plane Feet
SELECT ST_Length(ST_GeomFromText('LINESTRING(743238 2967416,743238 2967450,743265 2967450,
743265.625 2967416,743238 2967416)',2249));
st_length
---------
122.630744000095
--Transforming WGS 84 LineString to Massachusetts state plane meters
SELECT ST_Length(
ST_Transform(
ST_GeomFromEWKT('SRID=4326;LINESTRING(-72.1260 42.45, -72.1240 42.45666, -72.123 42.1546)'),
26986
)
);
st_length
---------
34309.4563576191
Geography Examples
Return length of WGS 84 geography line
-- the default calculation uses a spheroid
SELECT ST_Length(the_geog) As length_spheroid, ST_Length(the_geog,false) As length_sphere
FROM (SELECT ST_GeographyFromText(
'SRID=4326;LINESTRING(-72.1260 42.45, -72.1240 42.45666, -72.123 42.1546)') As the_geog)
As foo;
length_spheroid | length_sphere
------------------+------------------
34310.5703627288 | 34346.2060960742
See Also
, , , ,
ST_Length2D
Returns the 2D length of a linear geometry. Alias for ST_Length
float ST_Length2D
geometry a_2dlinestring
Description
Returns the 2D length of the geometry if it is a
linestring or multi-linestring. This is an alias for ST_Length
See Also
,
ST_3DLength
Returns the 3D length of a linear geometry.
float ST_3DLength
geometry a_3dlinestring
Description
Returns the 3-dimensional or 2-dimensional length of the geometry if it is a
linestring or multi-linestring. For 2-d lines it will just return the 2-d length (same as ST_Length and ST_Length2D)
&Z_support;
Changed: 2.0.0 In prior versions this used to be called ST_Length3D
Examples
Return length in feet for a 3D cable. Note this is in feet because EPSG:2249 is
Massachusetts State Plane Feet
SELECT ST_3DLength(ST_GeomFromText('LINESTRING(743238 2967416 1,743238 2967450 1,743265 2967450 3,
743265.625 2967416 3,743238 2967416 3)',2249));
ST_3DLength
-----------
122.704716741457
See Also
,
ST_LengthSpheroid
Returns the 2D or 3D length/perimeter of a lon/lat geometry on a spheroid.
float ST_LengthSpheroid
geometry a_geometry
spheroid a_spheroid
Description
Calculates the length or perimeter of a geometry on an ellipsoid. This
is useful if the coordinates of the geometry are in
longitude/latitude and a length is desired without reprojection.
The spheroid is specified by a text value as follows:
SPHEROID[<NAME>,<SEMI-MAJOR AXIS>,<INVERSE FLATTENING>]
For example:
SPHEROID["GRS_1980",6378137,298.257222101]
Availability: 1.2.2
Changed: 2.2.0 In prior versions this was called ST_Length_Spheroid and had the alias ST_3DLength_Spheroid
&Z_support;
Examples
SELECT ST_LengthSpheroid( geometry_column,
'SPHEROID["GRS_1980",6378137,298.257222101]' )
FROM geometry_table;
SELECT ST_LengthSpheroid( the_geom, sph_m ) As tot_len,
ST_LengthSpheroid(ST_GeometryN(the_geom,1), sph_m) As len_line1,
ST_LengthSpheroid(ST_GeometryN(the_geom,2), sph_m) As len_line2
FROM (SELECT ST_GeomFromText('MULTILINESTRING((-118.584 38.374,-118.583 38.5),
(-71.05957 42.3589 , -71.061 43))') As the_geom,
CAST('SPHEROID["GRS_1980",6378137,298.257222101]' As spheroid) As sph_m) as foo;
tot_len | len_line1 | len_line2
------------------+------------------+------------------
85204.5207562955 | 13986.8725229309 | 71217.6482333646
--3D
SELECT ST_LengthSpheroid( the_geom, sph_m ) As tot_len,
ST_LengthSpheroid(ST_GeometryN(the_geom,1), sph_m) As len_line1,
ST_LengthSpheroid(ST_GeometryN(the_geom,2), sph_m) As len_line2
FROM (SELECT ST_GeomFromEWKT('MULTILINESTRING((-118.584 38.374 20,-118.583 38.5 30),
(-71.05957 42.3589 75, -71.061 43 90))') As the_geom,
CAST('SPHEROID["GRS_1980",6378137,298.257222101]' As spheroid) As sph_m) as foo;
tot_len | len_line1 | len_line2
------------------+-----------------+------------------
85204.5259107402 | 13986.876097711 | 71217.6498130292
See Also
,
ST_LongestLine
Returns the 2D longest line between two geometries.
geometry ST_LongestLine
geometry
g1
geometry
g2
Description
Returns the 2-D longest line between the points of two geometries.
The function returns the first longest line if more than one is found.
The line returned starts on g1 and ends on g2.
The length of the line is equal to the distance returned by .
Availability: 1.5.0
Examples
Longest line between point and line
SELECT ST_AsText(
ST_LongestLine('POINT(100 100)'::geometry,
'LINESTRING (20 80, 98 190, 110 180, 50 75 )'::geometry)
) As lline;
lline
-----------------
LINESTRING(100 100,98 190)
longest line between polygon and polygon
SELECT ST_AsText(
ST_LongestLine(
ST_GeomFromText('POLYGON((175 150, 20 40,
50 60, 125 100, 175 150))'),
ST_Buffer(ST_GeomFromText('POINT(110 170)'), 20)
)
) As llinewkt;
lline
-----------------
LINESTRING(20 40,121.111404660392 186.629392246051)

longest straight distance to travel from one part of an elegant city to the other
Note the max distance = to the length of the line.
SELECT ST_AsText(ST_LongestLine(c.the_geom, c.the_geom)) As llinewkt,
ST_MaxDistance(c.the_geom,c.the_geom) As max_dist,
ST_Length(ST_LongestLine(c.the_geom, c.the_geom)) As lenll
FROM (SELECT ST_BuildArea(ST_Collect(the_geom)) As the_geom
FROM (SELECT ST_Translate(ST_SnapToGrid(ST_Buffer(ST_Point(50 ,generate_series(50,190, 50)
),40, 'quad_segs=2'),1), x, 0) As the_geom
FROM generate_series(1,100,50) As x) AS foo
) As c;
llinewkt | max_dist | lenll
---------------------------+------------------+------------------
LINESTRING(23 22,129 178) | 188.605408193933 | 188.605408193933

See Also
, ,
ST_3DLongestLine
Returns the 3D longest line between two geometries
geometry ST_3DLongestLine
geometry
g1
geometry
g2
Description
Returns the 3-dimensional longest line between two geometries. The function will
only return the first longest line if more than one.
The line returned will always start in g1 and end in g2.
The 3D length of the line this function returns will always be the same as returns for g1 and g2.
Availability: 2.0.0
Changed: 2.2.0 - if 2 2D geometries are input, a 2D point is returned (instead of old behavior assuming 0 for missing Z). In case of 2D and 3D, Z is no longer assumed to be 0 for missing Z.
&Z_support;
&P_support;
Examples
linestring and point -- both 3d and 2d longest line
SELECT ST_AsEWKT(ST_3DLongestLine(line,pt)) AS lol3d_line_pt,
ST_AsEWKT(ST_LongestLine(line,pt)) As lol2d_line_pt
FROM (SELECT 'POINT(100 100 30)'::geometry As pt,
'LINESTRING (20 80 20, 98 190 1, 110 180 3, 50 75 1000)'::geometry As line
) As foo;
lol3d_line_pt | lol2d_line_pt
-----------------------------------+----------------------------
LINESTRING(50 75 1000,100 100 30) | LINESTRING(98 190,100 100)

linestring and multipoint -- both 3d and 2d longest line
SELECT ST_AsEWKT(ST_3DLongestLine(line,pt)) AS lol3d_line_pt,
ST_AsEWKT(ST_LongestLine(line,pt)) As lol2d_line_pt
FROM (SELECT 'MULTIPOINT(100 100 30, 50 74 1000)'::geometry As pt,
'LINESTRING (20 80 20, 98 190 1, 110 180 3, 50 75 900)'::geometry As line
) As foo;
lol3d_line_pt | lol2d_line_pt
---------------------------------+--------------------------
LINESTRING(98 190 1,50 74 1000) | LINESTRING(98 190,50 74)

Multilinestring and polygon both 3d and 2d longest line
SELECT ST_AsEWKT(ST_3DLongestLine(poly, mline)) As lol3d,
ST_AsEWKT(ST_LongestLine(poly, mline)) As lol2d
FROM (SELECT ST_GeomFromEWKT('POLYGON((175 150 5, 20 40 5, 35 45 5, 50 60 5, 100 100 5, 175 150 5))') As poly,
ST_GeomFromEWKT('MULTILINESTRING((175 155 2, 20 40 20, 50 60 -2, 125 100 1, 175 155 1),
(1 10 2, 5 20 1))') As mline ) As foo;
lol3d | lol2d
------------------------------+--------------------------
LINESTRING(175 150 5,1 10 2) | LINESTRING(175 150,1 10)

See Also
, , , ,
ST_MaxDistance
Returns the 2D largest distance between two geometries in
projected units.
float ST_MaxDistance
geometry g1
geometry g2
Description
Returns the 2-dimensional maximum distance between two geometries in
projected units. If g1 and g2 is the same geometry the function will return the distance between
the two vertices most far from each other in that geometry.
Availability: 1.5.0
Examples
Basic furthest distance the point is to any part of the line
postgis=# SELECT ST_MaxDistance('POINT(0 0)'::geometry, 'LINESTRING ( 2 0, 0 2 )'::geometry);
st_maxdistance
-----------------
2
(1 row)
postgis=# SELECT ST_MaxDistance('POINT(0 0)'::geometry, 'LINESTRING ( 2 2, 2 2 )'::geometry);
st_maxdistance
------------------
2.82842712474619
(1 row)
See Also
, ,
ST_3DMaxDistance
Returns the 3D cartesian maximum distance (based on spatial ref) between two geometries in
projected units.
float ST_3DMaxDistance
geometry
g1
geometry
g2
Description
Returns the 3-dimensional maximum cartesian distance between two geometries in
projected units (spatial ref units).
&Z_support;
&P_support;
Availability: 2.0.0
Changed: 2.2.0 - In case of 2D and 3D, Z is no longer assumed to be 0 for missing Z.
Examples
-- Geometry example - units in meters (SRID: 2163 US National Atlas Equal area) (3D point and line compared 2D point and line)
-- Note: currently no vertical datum support so Z is not transformed and assumed to be same units as final.
SELECT ST_3DMaxDistance(
ST_Transform(ST_GeomFromEWKT('SRID=4326;POINT(-72.1235 42.3521 10000)'),2163),
ST_Transform(ST_GeomFromEWKT('SRID=4326;LINESTRING(-72.1260 42.45 15, -72.123 42.1546 20)'),2163)
) As dist_3d,
ST_MaxDistance(
ST_Transform(ST_GeomFromEWKT('SRID=4326;POINT(-72.1235 42.3521 10000)'),2163),
ST_Transform(ST_GeomFromEWKT('SRID=4326;LINESTRING(-72.1260 42.45 15, -72.123 42.1546 20)'),2163)
) As dist_2d;
dist_3d | dist_2d
------------------+------------------
24383.7467488441 | 22247.8472107251
See Also
, , ,
ST_MinimumClearance
Returns the minimum clearance of a geometry, a measure of a geometry's robustness.
float ST_MinimumClearance
geometry g
Description
It is not uncommon to have a geometry that, while meeting the criteria for validity according to ST_IsValid (polygons)
or ST_IsSimple (lines), would become invalid if one of the vertices moved by a slight distance, as can happen during
conversion to text-based formats (such as WKT, KML, GML GeoJSON), or binary formats that do not use double-precision
floating point coordinates (MapInfo TAB).
A geometry's "minimum clearance" is the smallest distance by which a vertex of the geometry could be moved to produce
an invalid geometry. It can be thought of as a quantitative measure of a geometry's robustness, where increasing values
of minimum clearance indicate increasing robustness.
If a geometry has a minimum clearance of e, it can be said that:
No two distinct vertices in the geometry are separated by less than e.
No vertex is closer than e to a line segement of which it is not an endpoint.
If no minimum clearance exists for a geometry (for example, a single point, or a multipoint whose points are identical), then
ST_MinimumClearance will return Infinity.
Availability: 2.3.0
Examples
SELECT ST_MinimumClearance('POLYGON ((0 0, 1 0, 1 1, 0.5 3.2e-4, 0 0))');
st_minimumclearance
---------------------
0.00032
See Also
ST_MinimumClearanceLine
Returns the two-point LineString spanning a geometry's minimum clearance.
Geometry ST_MinimumClearanceLine
geometry
g
Description
Returns the two-point LineString spanning a geometry's minimum clearance. If the geometry does not have a minimum
clearance, LINESTRING EMPTY will be returned.
Performed by the GEOS module.
Availability: 2.3.0 - requires GEOS >= 3.6.0
Examples
SELECT ST_AsText(ST_MinimumClearanceLine('POLYGON ((0 0, 1 0, 1 1, 0.5 3.2e-4, 0 0))'));
st_astext
-------------------------------
LINESTRING(0.5 0.00032,0.5 0)
See Also
ST_Perimeter
Returns the length of the boundary of a polygonal geometry or geography.
float ST_Perimeter
geometry g1
float ST_Perimeter
geography geog
boolean use_spheroid=true
Description
Returns the 2D perimeter of the geometry/geography if it is a ST_Surface, ST_MultiSurface (Polygon, MultiPolygon). 0 is returned for
non-areal geometries. For linear geometries use . For geometry types, units for perimeter measures are specified by the
spatial reference system of the geometry.
For geography types, the calculations are performed using the inverse geodesic problem, where perimeter units are in meters.
If PostGIS is compiled with PROJ version 4.8.0 or later, the spheroid is specified by the SRID, otherwise it is exclusive to WGS84.
If use_spheroid=false, then calculations will approximate a sphere instead of a spheroid.
Currently this is an alias for ST_Perimeter2D, but this may change to support higher dimensions.
&sfs_compliant; s2.1.5.1
&sqlmm_compliant; SQL-MM 3: 8.1.3, 9.5.4
Availability 2.0.0: Support for geography was introduced
Examples: Geometry
Return perimeter in feet for Polygon and MultiPolygon. Note this is in feet because EPSG:2249 is
Massachusetts State Plane Feet
SELECT ST_Perimeter(ST_GeomFromText('POLYGON((743238 2967416,743238 2967450,743265 2967450,
743265.625 2967416,743238 2967416))', 2249));
st_perimeter
---------
122.630744000095
(1 row)
SELECT ST_Perimeter(ST_GeomFromText('MULTIPOLYGON(((763104.471273676 2949418.44119003,
763104.477769673 2949418.42538203,
763104.189609677 2949418.22343004,763104.471273676 2949418.44119003)),
((763104.471273676 2949418.44119003,763095.804579742 2949436.33850239,
763086.132105649 2949451.46730207,763078.452329651 2949462.11549407,
763075.354136904 2949466.17407812,763064.362142565 2949477.64291974,
763059.953961626 2949481.28983009,762994.637609571 2949532.04103014,
762990.568508415 2949535.06640477,762986.710889563 2949539.61421415,
763117.237897679 2949709.50493431,763235.236617789 2949617.95619822,
763287.718121842 2949562.20592617,763111.553321674 2949423.91664605,
763104.471273676 2949418.44119003)))', 2249));
st_perimeter
---------
845.227713366825
(1 row)
Examples: Geography
Return perimeter in meters and feet for Polygon and MultiPolygon. Note this is geography (WGS 84 long lat)
SELECT ST_Perimeter(geog) As per_meters, ST_Perimeter(geog)/0.3048 As per_ft
FROM ST_GeogFromText('POLYGON((-71.1776848522251 42.3902896512902,-71.1776843766326 42.3903829478009,
-71.1775844305465 42.3903826677917,-71.1775825927231 42.3902893647987,-71.1776848522251 42.3902896512902))') As geog;
per_meters | per_ft
-----------------+------------------
37.3790462565251 | 122.634666195949
-- MultiPolygon example --
SELECT ST_Perimeter(geog) As per_meters, ST_Perimeter(geog,false) As per_sphere_meters, ST_Perimeter(geog)/0.3048 As per_ft
FROM ST_GeogFromText('MULTIPOLYGON(((-71.1044543107478 42.340674480411,-71.1044542869917 42.3406744369506,
-71.1044553562977 42.340673886454,-71.1044543107478 42.340674480411)),
((-71.1044543107478 42.340674480411,-71.1044860600303 42.3407237015564,-71.1045215770124 42.3407653385914,
-71.1045498002983 42.3407946553165,-71.1045611902745 42.3408058316308,-71.1046016507427 42.340837442371,
-71.104617893173 42.3408475056957,-71.1048586153981 42.3409875993595,-71.1048736143677 42.3409959528211,
-71.1048878050242 42.3410084812078,-71.1044020965803 42.3414730072048,
-71.1039672113619 42.3412202916693,-71.1037740497748 42.3410666421308,
-71.1044280218456 42.3406894151355,-71.1044543107478 42.340674480411)))') As geog;
per_meters | per_sphere_meters | per_ft
------------------+-------------------+------------------
257.634283683311 | 257.412311446337 | 845.256836231335
See Also
, ,
ST_Perimeter2D
Returns the 2D perimeter of a polygonal geometry.
Alias for ST_Perimeter.
float ST_Perimeter2D
geometry geomA
Description
Returns the 2-dimensional perimeter of a polygonal geometry.
This is currently an alias for ST_Perimeter. In future versions ST_Perimeter may return the highest dimension perimeter for a geometry. This is still under consideration
See Also
ST_3DPerimeter
Returns the 3D perimeter of a polygonal geometry.
float ST_3DPerimeter
geometry geomA
Description
Returns the 3-dimensional perimeter of the geometry, if it
is a polygon or multi-polygon. If the geometry is 2-dimensional, then the 2-dimensional perimeter is returned.
&Z_support;
Changed: 2.0.0 In prior versions this used to be called ST_Perimeter3D
Examples
Perimeter of a slightly elevated polygon in the air in Massachusetts state plane feet
SELECT ST_3DPerimeter(the_geom), ST_Perimeter2d(the_geom), ST_Perimeter(the_geom) FROM
(SELECT ST_GeomFromEWKT('SRID=2249;POLYGON((743238 2967416 2,743238 2967450 1,
743265.625 2967416 1,743238 2967416 2))') As the_geom) As foo;
ST_3DPerimeter | st_perimeter2d | st_perimeter
------------------+------------------+------------------
105.465793597674 | 105.432997272188 | 105.432997272188
See Also
, ,
ST_Project
Returns a point projected from a start point by a distance and bearing (azimuth).
geography ST_Project
geography
g1
float
distance
float
azimuth
Description
Returns a point projected from a start point along a geodesic using
a given distance and azimuth (bearing).
This is known as the direct geodesic problem.
The distance is given in meters. Negative values are supported.
The azimuth (also known as heading or bearing) is given in radians.
It is measured clockwise from true north (azimuth zero).
East is azimuth π/2 (90 degrees);
south is azimuth π (180 degrees);
west is azimuth 3π/2 (270 degrees).
Negative azimuth values and values greater than 2π (360 degrees) are supported.
Availability: 2.0.0
Enhanced: 2.4.0 Allow negative distance and non-normalized azimuth.
Example: Projected point at 100,000 meters and bearing 45 degrees
SELECT ST_AsText(ST_Project('POINT(0 0)'::geography, 100000, radians(45.0)));
st_astext
--------------------------------------------
POINT(0.635231029125537 0.639472334729198)
(1 row)
See Also
, , PostgreSQL function radians()
ST_ShortestLine
Returns the 2D shortest line between two geometries
geometry ST_ShortestLine
geometry
g1
geometry
g2
Description
Returns the 2-dimensional shortest line between two geometries. The function will
only return the first shortest line if more than one, that the function finds.
If g1 and g2 intersects in just one point the function will return a line with both start
and end in that intersection-point.
If g1 and g2 are intersecting with more than one point the function will return a line with start
and end in the same point but it can be any of the intersecting points.
The line returned will always start in g1 and end in g2.
The length of the line this function returns will always be the same as ST_Distance returns for g1 and g2.
Availability: 1.5.0
Examples
Shortest line between point and linestring
SELECT ST_AsText(
ST_ShortestLine('POINT(100 100)'::geometry,
'LINESTRING (20 80, 98 190, 110 180, 50 75 )'::geometry)
) As sline;
sline
-----------------
LINESTRING(100 100,73.0769230769231 115.384615384615)
shortest line between polygon and polygon
SELECT ST_AsText(
ST_ShortestLine(
ST_GeomFromText('POLYGON((175 150, 20 40, 50 60, 125 100, 175 150))'),
ST_Buffer(ST_GeomFromText('POINT(110 170)'), 20)
)
) As slinewkt;
LINESTRING(140.752120669087 125.695053378061,121.111404660392 153.370607753949)

See Also
, , ,
ST_3DShortestLine
Returns the 3D shortest line between two geometries
geometry ST_3DShortestLine
geometry
g1
geometry
g2
Description
Returns the 3-dimensional shortest line between two geometries. The function will
only return the first shortest line if more than one, that the function finds.
If g1 and g2 intersects in just one point the function will return a line with both start
and end in that intersection-point.
If g1 and g2 are intersecting with more than one point the function will return a line with start
and end in the same point but it can be any of the intersecting points.
The line returned will always start in g1 and end in g2.
The 3D length of the line this function returns will always be the same as returns for g1 and g2.
Availability: 2.0.0
Changed: 2.2.0 - if 2 2D geometries are input, a 2D point is returned (instead of old behavior assuming 0 for missing Z). In case of 2D and 3D, Z is no longer assumed to be 0 for missing Z.
&Z_support;
&P_support;
Examples
linestring and point -- both 3d and 2d shortest line
SELECT ST_AsEWKT(ST_3DShortestLine(line,pt)) AS shl3d_line_pt,
ST_AsEWKT(ST_ShortestLine(line,pt)) As shl2d_line_pt
FROM (SELECT 'POINT(100 100 30)'::geometry As pt,
'LINESTRING (20 80 20, 98 190 1, 110 180 3, 50 75 1000)'::geometry As line
) As foo;
shl3d_line_pt | shl2d_line_pt
----------------------------------------------------------------------------+------------------------------------------------------
LINESTRING(54.6993798867619 128.935022917228 11.5475869506606,100 100 30) | LINESTRING(73.0769230769231 115.384615384615,100 100)

linestring and multipoint -- both 3d and 2d shortest line
SELECT ST_AsEWKT(ST_3DShortestLine(line,pt)) AS shl3d_line_pt,
ST_AsEWKT(ST_ShortestLine(line,pt)) As shl2d_line_pt
FROM (SELECT 'MULTIPOINT(100 100 30, 50 74 1000)'::geometry As pt,
'LINESTRING (20 80 20, 98 190 1, 110 180 3, 50 75 900)'::geometry As line
) As foo;
shl3d_line_pt | shl2d_line_pt
---------------------------------------------------------------------------+------------------------
LINESTRING(54.6993798867619 128.935022917228 11.5475869506606,100 100 30) | LINESTRING(50 75,50 74)

Multilinestring and polygon both 3d and 2d shortest line
SELECT ST_AsEWKT(ST_3DShortestLine(poly, mline)) As shl3d,
ST_AsEWKT(ST_ShortestLine(poly, mline)) As shl2d
FROM (SELECT ST_GeomFromEWKT('POLYGON((175 150 5, 20 40 5, 35 45 5, 50 60 5, 100 100 5, 175 150 5))') As poly,
ST_GeomFromEWKT('MULTILINESTRING((175 155 2, 20 40 20, 50 60 -2, 125 100 1, 175 155 1),
(1 10 2, 5 20 1))') As mline ) As foo;
shl3d | shl2d
---------------------------------------------------------------------------------------------------+------------------------
LINESTRING(39.993580415989 54.1889925532825 5,40.4078575708294 53.6052383805529 5.03423778139177) | LINESTRING(20 40,20 40)

See Also
, , , ,