GeoDisk
is a two-dimensional GeoGraphics primitive that represents a filled disk of radius r centered at the location loc on the surface of the Earth.
Details and Options

- A geo disk with center loc and radius r is defined as the area covered by all geodesics of length r starting from loc. Specifying bearings α1 and α2 restricts the set of geodesics.
- The location loc can be specified either as latitude and longitude coordinates {lat,lon} in degrees, GeoPosition[…], or as a named geographical Entity[…].
- The radius r can be given as a Quantity length or as a number in meters.
- Bearings α1 and α2 are measured clockwise from true north and can be given as Quantity angles, as numbers in degrees, as DMS strings, or as named compass points like "N" or "SouthWest".
- By default, GeoDisk is drawn partially transparent to allow the background map to show through.
- FaceForm, EdgeForm, and GeoStyling can be used to give directives specifying how the interiors and boundaries of geographic regions should be rendered. The opacity of the interior can only be modified using GeoStyling.
- GeoDisk[loc] represents a geo disk centered at loc, with an automatic choice of radius.
- GeoDisk[] is equivalent to GeoDisk[$GeoLocation].
Examples
open allclose allBasic Examples (2)Summary of the most common use cases
Scope (6)Survey of the scope of standard use cases
The center location of the geo disk can be specified in several ways:

https://wolfram.com/xid/0bdpsyujv-8fh7rr

The default location is the local geo position:

https://wolfram.com/xid/0bdpsyujv-5kh819


https://wolfram.com/xid/0bdpsyujv-z9s0ni

The geo disk radius can be specified as a Quantity object, or directly in meters:

https://wolfram.com/xid/0bdpsyujv-zgak94

Plot a disk with default size around Madrid:

https://wolfram.com/xid/0bdpsyujv-4l8yop

Bearings are given in degrees, clockwise with respect to true north:

https://wolfram.com/xid/0bdpsyujv-56far4


https://wolfram.com/xid/0bdpsyujv-nhacni

Use different stylings for geo disks:

https://wolfram.com/xid/0bdpsyujv-e8suiu

Applications (3)Sample problems that can be solved with this function
The Mercator projection is conformal because it preserves shapes, though not areas or distances:

https://wolfram.com/xid/0bdpsyujv-cw8u7m

Compare with the default equirectangular projection:

https://wolfram.com/xid/0bdpsyujv-v5vpa4


https://wolfram.com/xid/0bdpsyujv-h2e9k4

Plot various distances from the epicenter of the 1992 Landers earthquake:

https://wolfram.com/xid/0bdpsyujv-us772q

Properties & Relations (11)Properties of the function, and connections to other functions
A geo disk is the set of points whose distance to the center is at most its radius:

https://wolfram.com/xid/0bdpsyujv-1oa0pq

https://wolfram.com/xid/0bdpsyujv-mkuypz

The boundary of a geo disk is a geo circle:

https://wolfram.com/xid/0bdpsyujv-ydlvuh

https://wolfram.com/xid/0bdpsyujv-hlspt4

A GeoDisk object is described using coordinates and distances on the Earth, irrespective of the coordinates used in the final map. A Disk object is described using the coordinates of the final map:

https://wolfram.com/xid/0bdpsyujv-bez1gv

It is possible to use a GeoPosition object to specify the center of the Disk object. Its radius, however, cannot be specified as a length on the surface of the Earth:

https://wolfram.com/xid/0bdpsyujv-nsyr1b

As we get closer to the poles, geo disks look more distorted in the equirectangular projection:

https://wolfram.com/xid/0bdpsyujv-9lv2p0

A geo disk containing a pole spans all values of longitude:

https://wolfram.com/xid/0bdpsyujv-rf04q

https://wolfram.com/xid/0bdpsyujv-7w9hnp


https://wolfram.com/xid/0bdpsyujv-1ez9mj

Progressive distortion of concentric geo disks of increasing radius:

https://wolfram.com/xid/0bdpsyujv-vj2g64

Same disks (still concentric) in the Mercator projection:

https://wolfram.com/xid/0bdpsyujv-50gwsi

The complement of a geo disk is approximately another geo disk centered in the antipodal location:

https://wolfram.com/xid/0bdpsyujv-pf05w2


https://wolfram.com/xid/0bdpsyujv-c45tq2

A large geo disk covers most of the Earth, including both poles. Only a small area is left uncovered:

https://wolfram.com/xid/0bdpsyujv-34ukac

All three sides of a geo disk sector are generically curved in most projections. The radii spanning from the center are geodesics:

https://wolfram.com/xid/0bdpsyujv-jubcxx

Even starting from bearings and
, the sides are curved:

https://wolfram.com/xid/0bdpsyujv-8lshic

A geo disk sector centered at a pole may be projected onto a rectangle:

https://wolfram.com/xid/0bdpsyujv-nuy1vc

Bearing at the South Pole coincides with longitude. Bearing α at the North Pole is related to longitude by the relation
, taking both angles in degrees:

https://wolfram.com/xid/0bdpsyujv-7yfv6m

Large disks accumulating around the antipodal point, using a spherical model of the Earth:

https://wolfram.com/xid/0bdpsyujv-t438io

The default reference model is an ellipsoid:

https://wolfram.com/xid/0bdpsyujv-rx6dh5

Interactive Examples (2)Examples with interactive outputs
Interactively place a geo disk of fixed radius and observe how its form changes as a function of latitude:

https://wolfram.com/xid/0bdpsyujv-o5e2h7

Explore the arguments of GeoDisk:

https://wolfram.com/xid/0bdpsyujv-bhue5w

Neat Examples (1)Surprising or curious use cases
Show that the cities in the US farthest from the US boundary are in Kansas. Take the US polygon:

https://wolfram.com/xid/0bdpsyujv-b6vxcd
Compute the distances in miles between consecutive points and accumulate them:

https://wolfram.com/xid/0bdpsyujv-3ep8ui
This is the total estimated length of the boundary, in miles:

https://wolfram.com/xid/0bdpsyujv-mi6u4w

Construct a parametrization of the boundary:

https://wolfram.com/xid/0bdpsyujv-09ehal

Draw 300 geo disks of 650 miles of radius along equidistant points of the boundary. There is a small space left uncovered—the region of the US farther than such distance from the boundary—and it is in Kansas:

https://wolfram.com/xid/0bdpsyujv-h1bvzu

Wolfram Research (2014), GeoDisk, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoDisk.html.
Text
Wolfram Research (2014), GeoDisk, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoDisk.html.
Wolfram Research (2014), GeoDisk, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoDisk.html.
CMS
Wolfram Language. 2014. "GeoDisk." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GeoDisk.html.
Wolfram Language. 2014. "GeoDisk." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GeoDisk.html.
APA
Wolfram Language. (2014). GeoDisk. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeoDisk.html
Wolfram Language. (2014). GeoDisk. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeoDisk.html
BibTeX
@misc{reference.wolfram_2025_geodisk, author="Wolfram Research", title="{GeoDisk}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/GeoDisk.html}", note=[Accessed: 09-July-2025
]}
BibLaTeX
@online{reference.wolfram_2025_geodisk, organization={Wolfram Research}, title={GeoDisk}, year={2014}, url={https://reference.wolfram.com/language/ref/GeoDisk.html}, note=[Accessed: 09-July-2025
]}