Calculate Distance Using Spherical Geometry


For spherical queries, use the 2dsphere index result.

The use of 2d index for spherical queries may lead to incorrect results, such as the use of the 2d index for spherical queries that wrap around the poles.

The 2d index supports queries that calculate distances on a Euclidean plane (flat surface). The index also supports the following query operators and command that calculate distances using spherical geometry:


While basic queries using spherical distance are supported by the 2d index, consider moving to a 2dsphere index if your data is primarily longitude and latitude.


The aforementioned operations use radians for distance. Other spherical query operators do not, such as $geoWithin.

For spherical query operators to function properly, you must convert distances to radians, and convert from radians to the distances units used by your application.

To convert:

  • distance to radians: divide the distance by the radius of the sphere (e.g. the Earth) in the same units as the distance measurement.
  • radians to distance: multiply the radian measure by the radius of the sphere (e.g. the Earth) in the units system that you want to convert the distance to.

The equatorial radius of the Earth is approximately 3,963.2 miles or 6,378.1 kilometers.

The following query would return documents from the places collection within the circle described by the center [ -74, 40.74 ] with a radius of 100 miles:

db.places.find( { loc: { $geoWithin: { $centerSphere: [ [ -74, 40.74 ] ,
                                                     100 / 3963.2 ] } } } )


If specifying latitude and longitude coordinates, list the longitude first and then latitude:

  • Valid longitude values are between -180 and 180, both inclusive.
  • Valid latitude values are between -90 and 90 (both inclusive).