In MongoDB, the $atan aggregation pipeline operator returns the arctangent (inverse tangent) of a value.

The return value is in radians.

$atan accepts any valid expression that resolves to a number.

The $atan operator was introduced in MongoDB 4.2.

Example

Suppose we have a collection called test with the following document:

{ "_id" : 1, "data" : 2 }

We can use the $atan operator to return the arctangent of the data field:

db.test.aggregate(
  [
    { $match: { _id: 1 } },
    { $project: { 
        _id: 0,
        arctangent: { $atan: "$data" }
      }
    }
  ]
)

Result:

{ "arctangent" : 1.1071487177940906 }

Convert to Degrees

As mentioned, $atan returns its result in radians. You can use the $radiansToDegrees operator if you want the result in degrees.

Example:

db.test.aggregate(
  [
    { $match: { _id: 1 } },
    { $project: { 
        _id: 0,
        radians: { $atan: "$data" },
        degrees: { $radiansToDegrees: { $atan: "$data" } }
      }
    }
  ]
)

Result:

{ "radians" : 1.1071487177940906, "degrees" : 63.43494882292202 }

In this example, the first field presents the result in radians, and the second field presents it in degrees.

128-Bit Decimal Values

By default, the $atan operator returns values as a double, but it can also return values as a 128-bit decimal as long as the expression resolves to a 128-bit decimal value.

Suppose we add the following document to our collection:

{ "_id" : 2, "data" : NumberDecimal("2.1301023541559787031443874490659") }

Let’s run the the $atan operator against that document:

db.test.aggregate(
  [
    { $match: { _id: 2 } },
    { $project: { 
        _id: 0,
        arctangent: { $atan: "$data" }
      }
    }
  ]
)

Result:

{ "arctangent" : NumberDecimal("1.131877001503761613330938729211760") }

The output is 128-bit decimal.

Null Values

Null values return null when using the $atan operator.

Suppose we add the following document to our collection:

{ "_id" : 3, "data" : null }

Let’s run the the $atan operator against that document:

db.test.aggregate(
  [
    { $match: { _id: 3 } },
    { $project: { 
        _id: 0,
        result: { $atan: "$data" }
      }
    }
  ]
)

Result:

{ "result" : null }

We can see that the result is null.

NaN Values

If the argument resolves to NaN, $atan returns NaN.

Example:

db.test.aggregate(
  [
    { $match: { _id: 3 } },
    { $project: { 
        _id: 0,
        result: { $atan: 1 * "$data" }
      }
    }
  ]
)

Result:

{ "result" : NaN }

Non-Existent Fields

If the $atan operator is applied against a field that doesn’t exist, null is returned.

Example:

db.test.aggregate(
  [
    { $match: { _id: 3 } },
    { $project: { 
        _id: 0,
        result: { $atan: "$wrong" }
      }
    }
  ]
)

Result:

{ "result" : null }