# $atan (aggregation)¶

`$atan`

¶*New in version 4.2*.Returns the inverse tangent (arc tangent) of a value.

`$atan`

has the following syntax:{ $atan: <expression> } `$atan`

takes any valid expression that resolves to a number.`$atan`

returns values in radians. Use`$radiansToDegrees`

operator to convert the output value from radians to degrees.By default

`$atan`

returns values as a`double`

.`$atan`

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.

## Behavior¶

`null`

and `NaN`

¶

If the argument resolves to a value of `null`

or refers to a field
that is missing, `$atan`

returns `null`

. If the
argument resolves to `NaN`

, `$tan`

returns `NaN`

.

Example | Results |
---|---|

`{ $atan: NaN }` | `NaN` |

`{ $atan: null }` | `null` |

## Example¶

The `trigonometry`

collection contains a document that
stores 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
`$atan`

expression to calculate the angle adjacent
to `side_a`

and add it to the input document using the
`$addFields`

pipeline stage.

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

The `$radiansToDegrees`

expression converts the
radian value returned by `$atan`

to the equivalent
value 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 as
128-bit decimals, the output of
`$atan`

is a 128-bit decimal.