> ## Documentation Index
> Fetch the complete documentation index at: https://axiom.co/docs/llms.txt
> Use this file to discover all available pages before exploring further.

<AgentInstructions>

## Submitting Feedback

If you encounter incorrect, outdated, or confusing documentation on this page, submit feedback:

POST https://axiom.co/docs/feedback

```json
{
  "path": "/apl/scalar-functions/mathematical-functions/atan2",
  "feedback": "Description of the issue"
}
```

Only submit feedback when you have something specific and actionable to report.

</AgentInstructions>

# atan2

> This page explains how to use the atan2 function in APL.

Use the `atan2` function in APL to compute the angle, in radians, between the positive x-axis and the point (y, x). Unlike `atan`, which takes a single ratio, `atan2` takes separate y and x components, which avoids division-by-zero issues and preserves the correct quadrant information.

`atan2` is useful when you have two independent counts or values and want to express their ratio as an angle. For example, you can use `atan2` to encode the balance between error count and success count as a direction vector, or to analyze the ratio of two traffic volumes.

## For users of other query languages

If you come from other query languages, this section explains how to adjust your existing queries to achieve the same results in APL.

<AccordionGroup>
  <Accordion title="Splunk SPL users">
    In Splunk SPL, `atan2(y, x)` is available in the `eval` command with the same argument order and semantics.

    <CodeGroup>
      ```sql Splunk example theme={null}
      | eval angle = atan2(errors, successes)
      ```

      ```kusto APL equivalent theme={null}
      ['sample-http-logs']
      | extend angle = atan2(todouble(errors), todouble(successes))
      ```
    </CodeGroup>
  </Accordion>

  <Accordion title="ANSI SQL users">
    In ANSI SQL, the function is typically named `ATN2(y, x)` in SQL Server or `ATAN2(y, x)` in PostgreSQL. The argument order (y first, then x) is the same as in APL.

    <CodeGroup>
      ```sql SQL example theme={null}
      SELECT ATN2(errors, successes) AS angle FROM logs
      ```

      ```kusto APL equivalent theme={null}
      ['sample-http-logs']
      | extend angle = atan2(todouble(errors), todouble(successes))
      ```
    </CodeGroup>
  </Accordion>
</AccordionGroup>

## Usage

### Syntax

```kusto theme={null}
atan2(y, x)
```

### Parameters

| Name | Type | Required | Description                                  |
| ---- | ---- | -------- | -------------------------------------------- |
| `y`  | real | Yes      | The y-coordinate of the point (numerator).   |
| `x`  | real | Yes      | The x-coordinate of the point (denominator). |

### Returns

The angle in radians between the positive x-axis and the point (y, x), in the range (-π, π].

## Example

Use `atan2` to compute the angle between the positive x-axis and the point (x, y).

**Query**

```kusto theme={null}
print result = atan2(1, 1)
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%20%22print%20result%20%3D%20atan2%281%2C%201%29%22%7D)

**Output**

| result |
| ------ |
| 0.7854 |

## List of related functions

* [atan](/apl/scalar-functions/mathematical-functions/atan): Returns the arc tangent from a single ratio. Use it when you have a pre-computed ratio instead of separate y and x components.
* [asin](/apl/scalar-functions/mathematical-functions/asin): Returns the arc sine. Use it when the input maps to a sine value in \[-1, 1].
* [acos](/apl/scalar-functions/mathematical-functions/acos): Returns the arc cosine. Use it when the input maps to a cosine value in \[-1, 1].
* [tan](/apl/scalar-functions/mathematical-functions/tan): Returns the tangent. Use it to apply the forward transformation before using `atan2` as the inverse.
* [degrees](/apl/scalar-functions/mathematical-functions/degrees): Converts radians to degrees. Use it if you prefer the `atan2` result in degrees.