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$degreesToRadians (aggregation)

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New in version 4.2.

Converts an input value measured in degrees to radians.

$degreesToRadians has the following syntax:

{ $degreesToRadians: <expression> }

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

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

For more information on expressions, see Expressions.


null, NaN, and +/- Infinity

If the argument resolves to a value of null or refers to a field that is missing, $degreesToRadians returns null. If the argument resolves to NaN, $degreesToRadians returns NaN. If the argument resolves to negative or positive infinity, $degreesToRadians negative or positive infinity respectively.

Example Results
{ $degreesToRadians: NaN } NaN
{ $degreesToRadians: null } null
{ $degreesToRadians : Infinity} Infinity
{ $degreesToRadians : -Infinity } -Infinity


The trigonometry collection contains a document that contains three angles measured in degrees:

  "angle_a" : NumberDecimal("53.13010235415597870314438744090659"),
  "angle_b" : NumberDecimal("36.86989764584402129685561255909341"),
  "angle_c" : NumberDecimal("90")

The following aggregation operation uses the $degreesToRadians expression to convert each value to its radian equivalent and add them to the input document using the $addFields pipeline stage.

    $addFields: {
      "angle_a_rad" : { $degreesToRadians : "$angle_a"},
      "angle_b_rad" : { $degreesToRadians : "$angle_b"},
      "angle_c_rad" : { $degreesToRadians : "$angle_c"}

The operation returns the following document:

  "_id" : ObjectId("5c50aec71c75c59232b3ede4"),
  "angle_a" : NumberDecimal("53.13010235415597870314438744090660"),
  "angle_b" : NumberDecimal("36.86989764584402129685561255909341"),
  "angle_c" : NumberDecimal("90"),
  "angle_a_rad" : NumberDecimal("0.9272952180016122324285124629224290"),
  "angle_b_rad" : NumberDecimal("0.6435011087932843868028092287173227"),
  "angle_c_rad" : NumberDecimal("1.570796326794896619231321691639752")

Since angle_a, angle_b, and angle_c are stored as 128-bit decimals, the output of $degreesToRadians is a 128-bit decimal.