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ClickHouse/docs/en/sql-reference/functions/geo/polygon.md
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---
slug: /en/sql-reference/functions/geo/polygons
sidebar_label: Polygons
title: "Functions for Working with Polygons"
---
## WKT
Returns a WKT (Well Known Text) geometric object from various [Geo Data Types](../../data-types/geo.md). Supported WKT objects are:
- POINT
- POLYGON
- MULTIPOLYGON
- LINESTRING
- MULTILINESTRING
**Syntax**
```sql
WKT(geo_data)
```
**Parameters**
`geo_data` can be one of the following [Geo Data Types](../../data-types/geo.md) or their underlying primitive types:
- [Point](../../data-types/geo.md#point)
- [Ring](../../data-types/geo.md#ring)
- [Polygon](../../data-types/geo.md#polygon)
- [MultiPolygon](../../data-types/geo.md#multipolygon)
- [LineString](../../data-types/geo.md#linestring)
- [MultiLineString](../../data-types/geo.md#multilinestring)
**Returned value**
- WKT geometric object `POINT` is returned for a Point.
- WKT geometric object `POLYGON` is returned for a Polygon
- WKT geometric object `MULTIPOLYGON` is returned for a MultiPolygon.
- WKT geometric object `LINESTRING` is returned for a LineString.
- WKT geometric object `MULTILINESTRING` is returned for a MultiLineString.
**Examples**
POINT from tuple:
```sql
SELECT wkt((0., 0.));
```
```response
POINT(0 0)
```
POLYGON from an array of tuples or an array of tuple arrays:
```sql
SELECT wkt([(0., 0.), (10., 0.), (10., 10.), (0., 10.)]);
```
```response
POLYGON((0 0,10 0,10 10,0 10))
```
MULTIPOLYGON from an array of multi-dimensional tuple arrays:
```sql
SELECT wkt([[[(0., 0.), (10., 0.), (10., 10.), (0., 10.)], [(4., 4.), (5., 4.), (5., 5.), (4., 5.)]], [[(-10., -10.), (-10., -9.), (-9., 10.)]]]);
```
```response
MULTIPOLYGON(((0 0,10 0,10 10,0 10,0 0),(4 4,5 4,5 5,4 5,4 4)),((-10 -10,-10 -9,-9 10,-10 -10)))
```
## readWKTMultiPolygon
Converts a WKT (Well Known Text) MultiPolygon into a MultiPolygon type.
### Example
``` sql
SELECT
toTypeName(readWKTMultiPolygon('MULTIPOLYGON(((2 0,10 0,10 10,0 10,2 0),(4 4,5 4,5 5,4 5,4 4)),((-10 -10,-10 -9,-9 10,-10 -10)))')) AS type,
readWKTMultiPolygon('MULTIPOLYGON(((2 0,10 0,10 10,0 10,2 0),(4 4,5 4,5 5,4 5,4 4)),((-10 -10,-10 -9,-9 10,-10 -10)))') AS output FORMAT Markdown
```
| type | output |
|:-|:-|
| MultiPolygon | [[[(2,0),(10,0),(10,10),(0,10),(2,0)],[(4,4),(5,4),(5,5),(4,5),(4,4)]],[[(-10,-10),(-10,-9),(-9,10),(-10,-10)]]] |
### Input parameters
String starting with `MULTIPOLYGON`
### Returned value
MultiPolygon
## readWKTPolygon
Converts a WKT (Well Known Text) MultiPolygon into a Polygon type.
### Example
``` sql
SELECT
toTypeName(readWKTPolygon('POLYGON((2 0,10 0,10 10,0 10,2 0))')) AS type,
readWKTPolygon('POLYGON((2 0,10 0,10 10,0 10,2 0))') AS output
FORMAT Markdown
```
| type | output |
|:-|:-|
| Polygon | [[(2,0),(10,0),(10,10),(0,10),(2,0)]] |
### Input parameters
String starting with `POLYGON`
### Returned value
Polygon
## readWKTPoint
The `readWKTPoint` function in ClickHouse parses a Well-Known Text (WKT) representation of a Point geometry and returns a point in the internal ClickHouse format.
### Syntax
```sql
readWKTPoint(wkt_string)
```
### Arguments
- `wkt_string`: The input WKT string representing a Point geometry.
### Returned value
The function returns a ClickHouse internal representation of the Point geometry.
### Example
```sql
SELECT readWKTPoint('POINT (1.2 3.4)');
```
```response
(1.2,3.4)
```
## readWKTLineString
Parses a Well-Known Text (WKT) representation of a LineString geometry and returns it in the internal ClickHouse format.
### Syntax
```sql
readWKTLineString(wkt_string)
```
### Arguments
- `wkt_string`: The input WKT string representing a LineString geometry.
### Returned value
The function returns a ClickHouse internal representation of the linestring geometry.
### Example
```sql
SELECT readWKTLineString('LINESTRING (1 1, 2 2, 3 3, 1 1)');
```
```response
[(1,1),(2,2),(3,3),(1,1)]
```
## readWKTMultiLineString
Parses a Well-Known Text (WKT) representation of a MultiLineString geometry and returns it in the internal ClickHouse format.
### Syntax
```sql
readWKTMultiLineString(wkt_string)
```
### Arguments
- `wkt_string`: The input WKT string representing a MultiLineString geometry.
### Returned value
The function returns a ClickHouse internal representation of the multilinestring geometry.
### Example
```sql
SELECT readWKTMultiLineString('MULTILINESTRING ((1 1, 2 2, 3 3), (4 4, 5 5, 6 6))');
```
```response
[[(1,1),(2,2),(3,3)],[(4,4),(5,5),(6,6)]]
```
## readWKTRing
Parses a Well-Known Text (WKT) representation of a Polygon geometry and returns a ring (closed linestring) in the internal ClickHouse format.
### Syntax
```sql
readWKTRing(wkt_string)
```
### Arguments
- `wkt_string`: The input WKT string representing a Polygon geometry.
### Returned value
The function returns a ClickHouse internal representation of the ring (closed linestring) geometry.
### Example
```sql
SELECT readWKTRing('POLYGON ((1 1, 2 2, 3 3, 1 1))');
```
```response
[(1,1),(2,2),(3,3),(1,1)]
```
## polygonsWithinSpherical
Returns true or false depending on whether or not one polygon lies completely inside another polygon. Reference https://www.boost.org/doc/libs/1_62_0/libs/geometry/doc/html/geometry/reference/algorithms/within/within_2.html
### Example
``` sql
select polygonsWithinSpherical([[[(4.3613577, 50.8651821), (4.349556, 50.8535879), (4.3602419, 50.8435626), (4.3830299, 50.8428851), (4.3904543, 50.8564867), (4.3613148, 50.8651279)]]], [[[(4.346693, 50.858306), (4.367945, 50.852455), (4.366227, 50.840809), (4.344961, 50.833264), (4.338074, 50.848677), (4.346693, 50.858306)]]]);
```
```response
0
```
### Input parameters
### Returned value
UInt8, 0 for false, 1 for true
## polygonsDistanceSpherical
Calculates the minimal distance between two points where one point belongs to the first polygon and the second to another polygon. Spherical means that coordinates are interpreted as coordinates on a pure and ideal sphere, which is not true for the Earth. Using this type of coordinate system speeds up execution, but of course is not precise.
### Example
``` sql
SELECT polygonsDistanceSpherical([[[(0, 0), (0, 0.1), (0.1, 0.1), (0.1, 0)]]], [[[(10., 10.), (10., 40.), (40., 40.), (40., 10.), (10., 10.)]]])
```
```response
0.24372872211133834
```
### Input parameters
Two polygons
### Returned value
Float64
## polygonsDistanceCartesian
Calculates distance between two polygons
### Example
``` sql
SELECT polygonsDistanceCartesian([[[(0, 0), (0, 0.1), (0.1, 0.1), (0.1, 0)]]], [[[(10., 10.), (10., 40.), (40., 40.), (40., 10.), (10., 10.)]]])
```
```response
14.000714267493642
```
### Input parameters
Two polygons
### Returned value
Float64
## polygonsEqualsCartesian
Returns true if two polygons are equal
### Example
``` sql
SELECT polygonsEqualsCartesian([[[(1., 1.), (1., 4.), (4., 4.), (4., 1.)]]], [[[(1., 1.), (1., 4.), (4., 4.), (4., 1.), (1., 1.)]]])
```
```response
1
```
### Input parameters
Two polygons
### Returned value
UInt8, 0 for false, 1 for true
## polygonsSymDifferenceSpherical
Calculates the spatial set theoretic symmetric difference (XOR) between two polygons
### Example
``` sql
SELECT wkt(arraySort(polygonsSymDifferenceSpherical([[(50., 50.), (50., -50.), (-50., -50.), (-50., 50.), (50., 50.)], [(10., 10.), (10., 40.), (40., 40.), (40., 10.), (10., 10.)], [(-10., -10.), (-10., -40.), (-40., -40.), (-40., -10.), (-10., -10.)]], [[(-20., -20.), (-20., 20.), (20., 20.), (20., -20.), (-20., -20.)]])));
```
```response
MULTIPOLYGON(((-20 -10.3067,-10 -10,-10 -20.8791,-20 -20,-20 -10.3067)),((10 20.8791,20 20,20 10.3067,10 10,10 20.8791)),((50 50,50 -50,-50 -50,-50 50,50 50),(20 10.3067,40 10,40 40,10 40,10 20.8791,-20 20,-20 -10.3067,-40 -10,-40 -40,-10 -40,-10 -20.8791,20 -20,20 10.3067)))
```
### Input parameters
Polygons
### Returned value
MultiPolygon
## polygonsSymDifferenceCartesian
The same as `polygonsSymDifferenceSpherical`, but the coordinates are in the Cartesian coordinate system; which is more close to the model of the real Earth.
### Example
``` sql
SELECT wkt(polygonsSymDifferenceCartesian([[[(0, 0), (0, 3), (1, 2.9), (2, 2.6), (2.6, 2), (2.9, 1), (3, 0), (0, 0)]]], [[[(1., 1.), (1., 4.), (4., 4.), (4., 1.), (1., 1.)]]]))
```
```response
MULTIPOLYGON(((1 2.9,1 1,2.9 1,3 0,0 0,0 3,1 2.9)),((1 2.9,1 4,4 4,4 1,2.9 1,2.6 2,2 2.6,1 2.9)))
```
### Input parameters
Polygons
### Returned value
MultiPolygon
## polygonsIntersectionSpherical
Calculates the intersection (AND) between polygons, coordinates are spherical.
### Example
``` sql
SELECT wkt(arrayMap(a -> arrayMap(b -> arrayMap(c -> (round(c.1, 6), round(c.2, 6)), b), a), polygonsIntersectionSpherical([[[(4.3613577, 50.8651821), (4.349556, 50.8535879), (4.3602419, 50.8435626), (4.3830299, 50.8428851), (4.3904543, 50.8564867), (4.3613148, 50.8651279)]]], [[[(4.346693, 50.858306), (4.367945, 50.852455), (4.366227, 50.840809), (4.344961, 50.833264), (4.338074, 50.848677), (4.346693, 50.858306)]]])))
```
```response
MULTIPOLYGON(((4.3666 50.8434,4.36024 50.8436,4.34956 50.8536,4.35268 50.8567,4.36794 50.8525,4.3666 50.8434)))
```
### Input parameters
Polygons
### Returned value
MultiPolygon
## polygonsWithinCartesian
Returns true if the second polygon is within the first polygon.
### Example
``` sql
SELECT polygonsWithinCartesian([[[(2., 2.), (2., 3.), (3., 3.), (3., 2.)]]], [[[(1., 1.), (1., 4.), (4., 4.), (4., 1.), (1., 1.)]]])
```
```response
1
```
### Input parameters
Two polygons
### Returned value
UInt8, 0 for false, 1 for true
## polygonConvexHullCartesian
Calculates a convex hull. [Reference](https://www.boost.org/doc/libs/1_61_0/libs/geometry/doc/html/geometry/reference/algorithms/convex_hull.html)
Coordinates are in Cartesian coordinate system.
### Example
``` sql
SELECT wkt(polygonConvexHullCartesian([[[(0., 0.), (0., 5.), (5., 5.), (5., 0.), (2., 3.)]]]))
```
```response
POLYGON((0 0,0 5,5 5,5 0,0 0))
```
### Input parameters
MultiPolygon
### Returned value
Polygon
## polygonAreaSpherical
Calculates the surface area of a polygon.
### Example
``` sql
SELECT round(polygonAreaSpherical([[[(4.346693, 50.858306), (4.367945, 50.852455), (4.366227, 50.840809), (4.344961, 50.833264), (4.338074, 50.848677), (4.346693, 50.858306)]]]), 14)
```
```response
9.387704e-8
```
### Input parameters
Polygon
### Returned value
Float
## polygonsUnionSpherical
Calculates a union (OR).
### Example
``` sql
SELECT wkt(polygonsUnionSpherical([[[(4.3613577, 50.8651821), (4.349556, 50.8535879), (4.3602419, 50.8435626), (4.3830299, 50.8428851), (4.3904543, 50.8564867), (4.3613148, 50.8651279)]]], [[[(4.346693, 50.858306), (4.367945, 50.852455), (4.366227, 50.840809), (4.344961, 50.833264), (4.338074, 50.848677), (4.346693, 50.858306)]]]))
```
```response
MULTIPOLYGON(((4.36661 50.8434,4.36623 50.8408,4.34496 50.8333,4.33807 50.8487,4.34669 50.8583,4.35268 50.8567,4.36136 50.8652,4.36131 50.8651,4.39045 50.8565,4.38303 50.8429,4.36661 50.8434)))
```
### Input parameters
Polygons
### Returned value
MultiPolygon
## polygonPerimeterSpherical
Calculates the perimeter of the polygon.
### Example
This is the polygon representing Zimbabwe:
```
POLYGON((30.0107 -15.6462,30.0502 -15.6401,30.09 -15.6294,30.1301 -15.6237,30.1699 -15.6322,30.1956 -15.6491,30.2072 -15.6532,30.2231 -15.6497,30.231 -15.6447,30.2461 -15.6321,30.2549 -15.6289,30.2801 -15.6323,30.2962 -15.639,30.3281 -15.6524,30.3567 -15.6515,30.3963 -15.636,30.3977 -15.7168,30.3993 -15.812,30.4013 -15.9317,30.4026 -16.0012,30.5148 -16.0004,30.5866 -16,30.7497 -15.9989,30.8574 -15.9981,30.9019 -16.0071,30.9422 -16.0345,30.9583 -16.0511,30.9731 -16.062,30.9898 -16.0643,31.012 -16.0549,31.0237 -16.0452,31.0422 -16.0249,31.0569 -16.0176,31.0654 -16.0196,31.0733 -16.0255,31.0809 -16.0259,31.089 -16.0119,31.1141 -15.9969,31.1585 -16.0002,31.26 -16.0235,31.2789 -16.0303,31.2953 -16.0417,31.3096 -16.059,31.3284 -16.0928,31.3409 -16.1067,31.3603 -16.1169,31.3703 -16.1237,31.3746 -16.1329,31.3778 -16.1422,31.384 -16.1488,31.3877 -16.1496,31.3956 -16.1477,31.3996 -16.1473,31.4043 -16.1499,31.4041 -16.1545,31.4027 -16.1594,31.4046 -16.1623,31.4241 -16.1647,31.4457 -16.165,31.4657 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```
``` sql
SELECT round(polygonPerimeterSpherical([(30.010654, -15.646227), (30.050238, -15.640129), (30.090029, -15.629381), (30.130129, -15.623696), (30.16992, -15.632171), (30.195552, -15.649121), (30.207231, -15.653152), (30.223147, -15.649741), (30.231002, -15.644677), (30.246091, -15.632068), (30.254876, -15.628864), (30.280094, -15.632275), (30.296196, -15.639042), (30.32805, -15.652428), (30.356679, -15.651498), (30.396263, -15.635995), (30.39771, -15.716817), (30.39926, -15.812005), (30.401327, -15.931688), (30.402568, -16.001244), (30.514809, -16.000418), (30.586587, -16.000004), (30.74973, -15.998867), (30.857424, -15.998144), (30.901865, -16.007136), (30.942173, -16.034524), (30.958296, -16.05106), (30.973075, -16.062016), (30.989767, -16.06429), (31.012039, -16.054885), (31.023718, -16.045169), (31.042218, -16.024912), (31.056895, -16.017574), (31.065421, -16.019641), (31.073328, -16.025532), (31.080872, -16.025946), (31.089037, -16.01189), (31.1141, -15.996904), (31.15849, 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-16.388198), (28.857029, -16.36546), (28.840492, -16.323602), (28.836772, -16.306342), (28.840286, -16.284741), (28.86416, -16.231205), (28.847107, -16.202679), (28.852481, -16.162785), (28.8654, -16.121237), (28.870981, -16.087234), (28.868501, -16.08217), (28.86385, -16.076589), (28.859303, -16.069561), (28.857236, -16.060466), (28.860336, -16.049407), (28.874082, -16.028943), (28.877183, -16.022018), (28.898887, -15.995457), (28.932373, -15.963727), (28.946862, -15.957235), (28.951287, -15.955252), (28.972784, -15.951428), (29.018053, -15.950602), (29.042341, -15.946261), (29.055053, -15.934375), (29.076344, -15.895411), (29.086162, -15.884559), (29.102182, -15.870916), (29.121716, -15.859341), (29.141869, -15.854483), (29.150964, -15.848799), (29.186311, -15.812832), (29.406969, -15.714233), (29.422059, -15.711030000000001), (29.508462, -15.703588), (29.526239, -15.692839), (29.563446, -15.662144), (29.587217, -15.655736), (29.608559, -15.658422999999999), (29.62799, -15.663591), (29.648505, -15.666588), (29.672793, -15.663281), (29.73005, -15.644677), (29.773252, -15.638062), (29.814283, -15.619666), (29.837331, -15.614808), (29.881773, -15.618839), (29.967504, -15.641473), (30.010654, -15.646227)]), 6)
```
```response
0.45539
```
### Input parameters
### Returned value
## polygonsIntersectionCartesian
Calculates the intersection of polygons.
### Example
``` sql
SELECT wkt(polygonsIntersectionCartesian([[[(0., 0.), (0., 3.), (1., 2.9), (2., 2.6), (2.6, 2.), (2.9, 1.), (3., 0.), (0., 0.)]]], [[[(1., 1.), (1., 4.), (4., 4.), (4., 1.), (1., 1.)]]]))
```
```response
MULTIPOLYGON(((1 2.9,2 2.6,2.6 2,2.9 1,1 1,1 2.9)))
```
### Input parameters
Polygons
### Returned value
MultiPolygon
## polygonAreaCartesian
Calculates the area of a polygon
### Example
``` sql
SELECT polygonAreaCartesian([[[(0., 0.), (0., 5.), (5., 5.), (5., 0.)]]])
```
```response
25
```
### Input parameters
Polygon
### Returned value
Float64
## polygonPerimeterCartesian
Calculates the perimeter of a polygon.
### Example
``` sql
SELECT polygonPerimeterCartesian([[[(0., 0.), (0., 5.), (5., 5.), (5., 0.)]]])
```
```response
15
```
### Input parameters
Polygon
### Returned value
Float64
## polygonsUnionCartesian
Calculates the union of polygons.
### Example
``` sql
SELECT wkt(polygonsUnionCartesian([[[(0., 0.), (0., 3.), (1., 2.9), (2., 2.6), (2.6, 2.), (2.9, 1), (3., 0.), (0., 0.)]]], [[[(1., 1.), (1., 4.), (4., 4.), (4., 1.), (1., 1.)]]]))
```
```response
MULTIPOLYGON(((1 2.9,1 4,4 4,4 1,2.9 1,3 0,0 0,0 3,1 2.9)))
```
### Input parameters
Polygons
### Returned value
MultiPolygon
For more information on geometry systems, see this [presentation](https://archive.fosdem.org/2020/schedule/event/working_with_spatial_trajectories_in_boost_geometry/attachments/slides/3988/export/events/attachments/working_with_spatial_trajectories_in_boost_geometry/slides/3988/FOSDEM20_vissarion.pdf) about the Boost library, which is what ClickHouse uses.
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