$atan2 (aggregation)

• $atan2

New in version 4.2.

Returns the inverse tangent (arc tangent) of y / x,where y and x are the first and second values passed to theexpression respectively.

$atan2 has the following syntax:

{ $atan2: [ <expression 1>, <expression 2> ] }

$atan2 takes any valid expression that resolves to a number.

$atan2 returns values in radians. Use$radiansToDegrees operator to convert the output valuefrom radians to degrees.

By default $atan2 returns values as a double.$atan2 can also return values as a128-bit decimalas long as the <expression> resolves to a 128-bit decimal value.

For more information on expressions, seeExpressions.

Behavior

null and NaN

If the first argument to $atan2 is null,$atan2 returns null. If the first argument to$atan2 is NaN, $atan2 returns NaN.If the first argument resolves to a number and thesecond argument resolves to either NaN or null,$atan2 returns the NaN or null respectively.

Example

• Inverse Tangent of Value in Degrees
• Inverse Tangent of Value in Radians

The trigonometry collection contains a document thatstores three sides of a right-angle triangle:

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "side_a" : NumberDecimal("3"),
  "side_b" : NumberDecimal("4"),
  "hypotenuse" : NumberDecimal("5")
}

The following aggregation operation uses the$atan2 expression to calculate the angle adjacentto side_a and add it to the input document using the$addFields pipeline stage.

db.trigonometry.aggregate([
  {
    $addFields : {
      "angle_a" : {
        $radiansToDegrees : {
          $atan2 : [ "$side_b", "$side_a" ]
        }
      }
    }
  }
])

The $radiansToDegrees expression converts theradian value returned by $atan2 to the equivalentvalue in degrees.

The command returns the following output:

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "side_a" : NumberDecimal("3"),
  "side_b" : NumberDecimal("4"),
  "hypotenuse" : NumberDecimal("5"),
  "angle_a" : NumberDecimal("53.13010235415597870314438744090658")
}

Since side_b and side_a are stored as128-bit decimals, the output of$atan2 is a 128-bit decimal.

The trigonometry collection contains a document thatstores three sides of a right-angle triangle:

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "side_a" : NumberDecimal("3"),
  "side_b" : NumberDecimal("4"),
  "hypotenuse" : NumberDecimal("5")
}

The following aggregation operation uses the$atan2 expression to calculate the angle adjacentto side_a and add it to the input document using the$addFields pipeline stage.

db.trigonometry.aggregate([
  {
    $addFields : {
      "angle_a" : {
        $atan2 : [ "$side_b", "$side_a" ]
      }
    }
  }
])

The command returns the following output:

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "side_a" : NumberDecimal("3"),
  "side_b" : NumberDecimal("4"),
  "hypotenuse" : NumberDecimal("5"),
  "angle_a" : NumberDecimal("0.9272952180016122324285124629224287")
}

Since side_b and side_a are stored as128-bit decimals, the output of$atan2 is a 128-bit decimal.