$atan
Definition
Computes inverse tangent.
Expression operator · Arithmetic · Studio Visual: available. Studio validates the complete expression separately.
Syntax
{ "$atan": <expression> }
Replace angle-bracket placeholders with expressions or values.
Expression supplying the value to process. A field reference such as "$price" reads from the current document.
The value goes directly after the operator name; do not add an input wrapper.
Behavior
The following observations use the example expression below. Each row substitutes one argument while retaining the other example arguments. A missing field differs from an explicit null; the result shown is what Core actually returned.
For the input argument:
| Input case | Supplied value | Result |
|---|---|---|
| null | null | Error — $atan expects a numeric argument. |
| missing | Field absent | Error — $atan expects a numeric argument. |
| decimal | 2.5 | 1.1902899496825317 (double) |
| numeric string | "12" | Error — $atan expects a numeric argument. |
| text | "hello" | Error — $atan expects a numeric argument. |
| boolean | true | Error — $atan expects a numeric argument. |
| typed date | {"$date":"2026-01-15T15:00:00Z"} | Error — $atan expects a numeric argument. |
| empty array | [] | Error — $atan expects a numeric argument. |
| numeric array | [1,2,3] | Error — $atan expects a numeric argument. |
| object | {"x":1} | Error — $atan expects a numeric argument. |
Argument handling
| Invocation | Result |
|---|---|
| {"$atan":[]} | Error — $atan expects a numeric argument. |
| {"$atan":{"unexpected":1}} | Error — $atan expects a numeric argument. |
Examples
Expression:
{
"$atan": 0
}
Input document:
{}
Observed SrotaX result: 0.0 (double).
Detailed input cases
Expand the complete argument-by-argument test matrix
Each table changes only the indicated argument from the example above. Other arguments retain their baseline values. Values normally come from the input field probe; literal configuration arguments are replaced directly. “Missing” means the field is absent, not explicitly null. Numeric strings are strings, not numbers.
Argument: input
| Input case | Supplied value | SrotaX result |
|---|---|---|
| null | null | Error — $atan expects a numeric argument. |
| missing | Field absent | Error — $atan expects a numeric argument. |
| zero | 0 | 0.0 (double) |
| negative | -2 | -1.1071487177940904 (double) |
| decimal | 2.5 | 1.1902899496825317 (double) |
| numeric string | "12" | Error — $atan expects a numeric argument. |
| text | "hello" | Error — $atan expects a numeric argument. |
| empty string | "" | Error — $atan expects a numeric argument. |
| boolean | true | Error — $atan expects a numeric argument. |
| false | false | Error — $atan expects a numeric argument. |
| typed date | {"$date":"2026-01-15T15:00:00Z"} | Error — $atan expects a numeric argument. |
| decimal128 | {"$numberDecimal":"1.25"} | 0.8960553845713439 (double) |
| empty array | [] | Error — $atan expects a numeric argument. |
| numeric array | [1,2,3] | Error — $atan expects a numeric argument. |
| mixed array | [1,null,"x",3] | Error — $atan expects a numeric argument. |
| nested array | [[1,2],[3]] | Error — $atan expects a numeric argument. |
| empty object | {} | Error — $atan expects a numeric argument. |
| object | {"x":1} | Error — $atan expects a numeric argument. |
| ISO date string | "2026-01-15T15:00:00Z" | Error — $atan expects a numeric argument. |
Verification
This page records 22 executed cases. It covers individual argument substitutions, not every cross-product of arguments, locale, daylight-saving transitions, numeric overflow, collation or resource limits. No untested behavior is guaranteed.
Download exact expressions, inputs and SrotaX results. Errors are observed messages, not stable public error codes. The reference generator reads the checked-in execution report; do not edit generated observations by hand.
MongoDB differences
Compared with MongoDB 9.0.4: 3 exact BSON matches, 15 both rejected, 4 value/type/acceptance differences, 0 object-field-order differences.
“Exact” includes numeric BSON types and object key order. A value of 3 as int32 differs from 3.0 as double. Object-field-order differences are reported separately; object key ordering is not enforced by the engine regression baseline. Both rejected does not mean the error codes or messages match. This is finite-case evidence, not full compatibility certification.
Show observed differences
| Tested case | SrotaX | MongoDB |
|---|---|---|
| input / null | Error — $atan expects a numeric argument. | null |
| input / missing | Error — $atan expects a numeric argument. | null |
| input / negative | -1.1071487177940904 (double) | -1.1071487177940906 (double) |
| input / decimal128 | 0.8960553845713439 (double) | 0.8960553845713439561748007180299378 (decimal128) |