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# Calculate Distance Using Spherical Geometry

## Warning

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:

## Note

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.

`$geoNear`

pipeline stage with the`spherical: true`

option

## Important

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 ] } } } )

## Note

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.