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.


gives a sector of a disk from bearing α1 to bearing α2.

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].


open allclose all

Basic Examples  (2)

A disk of 2000 kilometers around a geo location:

A sector of a disk centered at Paris:

Scope  (6)

The center location of the geo disk can be specified in several ways:

The default location is the local geo position:

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

Plot a disk with default size around Madrid:

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

Use different stylings for geo disks:

Applications  (3)

The Mercator projection is conformal because it preserves shapes, though not areas or distances:

Compare with the default equirectangular projection:

Plot sectors to find overlap:

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

Properties & Relations  (11)

A geo disk is the set of points whose distance to the center is at most its radius:

The boundary of a geo disk is a geo circle:

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:

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:

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

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

Progressive distortion of concentric geo disks of increasing radius:

Same disks (still concentric) in the Mercator projection:

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

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

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

Even starting from bearings and , the sides are curved:

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

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:

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

The default reference model is an ellipsoid:

Interactive Examples  (2)

Interactively place a geo disk of fixed radius and observe how its form changes as a function of latitude:

Explore the arguments of GeoDisk:

Neat Examples  (1)

Show that the cities in the US farthest from the US boundary are in Kansas. Take the US polygon:

Compute the distances in miles between consecutive points and accumulate them:

This is the total estimated length of the boundary, in miles:

Construct a parametrization of the boundary:

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

Wolfram Research (2014), GeoDisk, Wolfram Language function,


Wolfram Research (2014), GeoDisk, Wolfram Language function,


Wolfram Language. 2014. "GeoDisk." Wolfram Language & System Documentation Center. Wolfram Research.


Wolfram Language. (2014). GeoDisk. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_geodisk, author="Wolfram Research", title="{GeoDisk}", year="2014", howpublished="\url{}", note=[Accessed: 19-June-2024 ]}


@online{reference.wolfram_2024_geodisk, organization={Wolfram Research}, title={GeoDisk}, year={2014}, url={}, note=[Accessed: 19-June-2024 ]}