gives the azimuthal direction from one latitude-longitude position on the Earth to another.


gives the azimuthal direction between locations specified by position objects or geographic entities.


  • Geo direction is also known as azimuth or bearing.
  • GeoDirection[loc1,loc2] gives the clockwise angle measured at loc1 between true north and the geodesic from loc1 to loc2. Heights are ignored.
  • The result is returned as a Quantity angle with "AngularDegrees" unit.
  • Latitudes and longitudes can be given as numbers in degrees, as DMS strings, or as Quantity angles.
  • Position objects in GeoDirection[loc1,loc2] can be given as GeoPosition, GeoPositionXYZ, GeoPositionENU, or GeoGridPosition objects.
  • GeoDirection[loc1,loc2] by default uses the reference ellipsoid associated with the datum for loc1.
  • GeoDirection and GeoDistance solve the geodetic inverse problem.


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Basic Examples  (2)

Forward azimuthal angle between two positions on the reference ellipsoid:

Azimuth angle between two fully specified geodetic positions:

Scope  (4)

Azimuth angle between any two points on the Earth, using the parameters of the default datum "ITRF00":

Angles can also be specified as DMS strings:

Direction between geodetic positions, in different formats:

Height and time information is ignored in GeoDirection computations:

Direction between points in different datums. The computation is performed after changing the datum of the second point to the datum of the first:

The difference is very small:

Properties & Relations  (8)

GeoDirection is not a symmetric function:

GeoDirection is a partial inverse of GeoDestination:

GeoDirection returns part of the information returned by GeoDisplacement:

Compute bearings between a list of points:

Construct points on a geodesic circle, starting with regular bearings:

Azimuths between points of the circle increase, modulo angle determination:

Construct multiple points along a geodesic, at regular distance intervals:

Bearing does not stay constant along a geodesic:

GeoDirection is not a smooth function for nearly antipodal points:

Compare with the corresponding results on the surface of a sphere:

Initial bearings of geodesics connecting antipodal pairs of points are complementary:


Wolfram Research (2008), GeoDirection, Wolfram Language function, (updated 2014).


Wolfram Research (2008), GeoDirection, Wolfram Language function, (updated 2014).


@misc{reference.wolfram_2020_geodirection, author="Wolfram Research", title="{GeoDirection}", year="2014", howpublished="\url{}", note=[Accessed: 15-January-2021 ]}


@online{reference.wolfram_2020_geodirection, organization={Wolfram Research}, title={GeoDirection}, year={2014}, url={}, note=[Accessed: 15-January-2021 ]}


Wolfram Language. 2008. "GeoDirection." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014.


Wolfram Language. (2008). GeoDirection. Wolfram Language & System Documentation Center. Retrieved from