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GeoArea
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GeoArea

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GeoArea[g]

gives the area of the geo region g.

Details and Options

  • GeoArea[Polygon[…]] computes the area enclosed by the polygon, assuming that neighboring points of the polygon are joined by geodesic paths.
  • GeoArea[Polygon[entity]] and GeoArea[entity] compute the area enclosed by the polygon of the given geo entity.
  • GeoArea[{g1,g2,…}] returns {GeoArea[g1],GeoArea[g2],…}.
  • GeoArea["World"] returns the area of the surface of the Earth, using the ellipsoidal model "ITRF00".
  • Possible options of GeoArea include:
  • GeoModel Automaticmodel of the Earth or celestial body
    UnitSystem $UnitSystemunit system to use in the result

Examples

open allclose all

Basic Examples  (3)Summary of the most common use cases

Compute the area of the polygon of the United States:

In[1]:=1
✖
https://wolfram.com/xid/0bdpsyuw0-wyk4qz
Out[1]=1

Compute the area of the latitude-longitude rectangle enclosing the United States:

In[1]:=1
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https://wolfram.com/xid/0bdpsyuw0-fk5oxi
Out[1]=1

Compute the area of a geo disk centered at your geo location:

In[1]:=1
✖
https://wolfram.com/xid/0bdpsyuw0-qpjy30
Out[1]=1

Scope  (7)Survey of the scope of standard use cases

Compute the area of a polygonal region on Earth, assuming geodesic edges:

In[1]:=1
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https://wolfram.com/xid/0bdpsyuw0-bejaxw
Out[1]=1

Compute the area of the region enclosed by the polygon of a geo entity:

In[1]:=1
✖
https://wolfram.com/xid/0bdpsyuw0-3b7n05
Out[1]=1

That can also be expressed as follows:

In[2]:=2
✖
https://wolfram.com/xid/0bdpsyuw0-69d9hs
Out[2]=2

Areas of the entities of a class, in this case the countries of South America:

In[1]:=1
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https://wolfram.com/xid/0bdpsyuw0-fno722
Out[1]=1

Total area of the polygon enclosing those countries:

In[2]:=2
✖
https://wolfram.com/xid/0bdpsyuw0-sj0tpv
Out[2]=2

Surface area of the Earth:

In[1]:=1
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https://wolfram.com/xid/0bdpsyuw0-5wjqrz
Out[1]=1

Area of 2D geo primitives:

In[1]:=1
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https://wolfram.com/xid/0bdpsyuw0-9ctwe4
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bdpsyuw0-yml5yc
Out[2]=2

Area of a region with holes:

In[1]:=1
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https://wolfram.com/xid/0bdpsyuw0-w50o14
In[2]:=2
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https://wolfram.com/xid/0bdpsyuw0-y122n3
In[3]:=3
✖
https://wolfram.com/xid/0bdpsyuw0-oubm0a
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0bdpsyuw0-dq2ng3
Out[4]=4

It can also be obtained by subtracting the areas of the inner regions from that of the outer region:

In[5]:=5
✖
https://wolfram.com/xid/0bdpsyuw0-vbcy2y
Out[5]=5

Total area of a group of non-overlapping geo regions:

In[1]:=1
✖
https://wolfram.com/xid/0bdpsyuw0-ja5hao
Out[1]=1

It can also be obtained by computing the respective areas and adding them:

In[2]:=2
✖
https://wolfram.com/xid/0bdpsyuw0-b2t48b
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0bdpsyuw0-b12t85
Out[3]=3

Options  (2)Common values & functionality for each option

UnitSystem  (1)

Use the units determined by the value of $UnitSystem:

In[1]:=1
✖
https://wolfram.com/xid/0bdpsyuw0-d9qs04
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0bdpsyuw0-rfv5ov
Out[2]=2

Specify the unit system to use:

In[3]:=3
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https://wolfram.com/xid/0bdpsyuw0-50dh1l
Out[3]=3

GeoModel  (1)

Area of a region of Earth:

In[1]:=1
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https://wolfram.com/xid/0bdpsyuw0-q3qy45
Out[1]=1

Area of the area delimited by the same parallels and meridians on Mars:

In[2]:=2
✖
https://wolfram.com/xid/0bdpsyuw0-yf20tf
Out[2]=2

Properties & Relations  (3)Properties of the function, and connections to other functions

The ratio of area to squared radius decreases, due to the curvature of the Earth:

In[1]:=1
✖
https://wolfram.com/xid/0bdpsyuw0-0eo5vh
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0bdpsyuw0-zrntuj
Out[2]=2

GeoArea computes area on the surface of the ellipsoidal Earth:

In[1]:=1
✖
https://wolfram.com/xid/0bdpsyuw0-079r8u
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0bdpsyuw0-3rgfqq
Out[2]=2

Use Area with the projected polygon to compute area on the flat map:

In[3]:=3
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https://wolfram.com/xid/0bdpsyuw0-ip1mcq
In[4]:=4
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https://wolfram.com/xid/0bdpsyuw0-chnxy9
Out[4]=4

"UTMZone33" is an appropriate transverse Mercator projection for Austria, and produces a relative error smaller than :

In[5]:=5
✖
https://wolfram.com/xid/0bdpsyuw0-6m25hh
Out[5]=5

Using an inconvenient projection, like "UTMZone48", may result in large area errors:

In[6]:=6
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https://wolfram.com/xid/0bdpsyuw0-zi0jbx
In[7]:=7
✖
https://wolfram.com/xid/0bdpsyuw0-sirt3s
Out[7]=7
In[8]:=8
✖
https://wolfram.com/xid/0bdpsyuw0-fnerah
Out[8]=8

GeoArea returns Missing["NotAvailable"] for those entity objects with no polygon information:

In[1]:=1
✖
https://wolfram.com/xid/0bdpsyuw0-e4mvjk
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0bdpsyuw0-yzaig1
Out[2]=2

Missing expressions are propagated:

In[3]:=3
✖
https://wolfram.com/xid/0bdpsyuw0-p8b854
Out[3]=3
Wolfram Research (2015), GeoArea, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoArea.html.
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Wolfram Research (2015), GeoArea, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoArea.html.

Text

Wolfram Research (2015), GeoArea, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoArea.html.

✖
Wolfram Research (2015), GeoArea, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoArea.html.

CMS

Wolfram Language. 2015. "GeoArea." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GeoArea.html.

✖
Wolfram Language. 2015. "GeoArea." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GeoArea.html.

APA

Wolfram Language. (2015). GeoArea. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeoArea.html

✖
Wolfram Language. (2015). GeoArea. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeoArea.html

BibTeX

@misc{reference.wolfram_2025_geoarea, author="Wolfram Research", title="{GeoArea}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/GeoArea.html}", note=[Accessed: 28-May-2025 ]}

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@misc{reference.wolfram_2025_geoarea, author="Wolfram Research", title="{GeoArea}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/GeoArea.html}", note=[Accessed: 28-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_geoarea, organization={Wolfram Research}, title={GeoArea}, year={2015}, url={https://reference.wolfram.com/language/ref/GeoArea.html}, note=[Accessed: 28-May-2025 ]}

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@online{reference.wolfram_2025_geoarea, organization={Wolfram Research}, title={GeoArea}, year={2015}, url={https://reference.wolfram.com/language/ref/GeoArea.html}, note=[Accessed: 28-May-2025 ]}