# pi



Use the `pi` function in APL to return the mathematical constant π (pi), approximately equal to 3.14159265358979. The function takes no arguments and always returns the same double-precision floating-point value.

`pi` is most commonly used to construct radian angle values for trigonometric functions. For example, you can encode the hour of day as a cyclic coordinate using `(hour * 2 * pi()) / 24`, or convert between degrees and radians using `radians = degrees * pi() / 180`.

## Usage [#usage]

### Syntax [#syntax]

```kusto
pi()
```

### Parameters [#parameters]

None.

### Returns [#returns]

The double-precision value of π: approximately 3.14159265358979.

## Example [#example]

Use `pi` to encode the hour of day as a cyclic angle for time-based analysis.

**Query**

```kusto
['sample-http-logs']
| extend hour_angle = (hourofday(_time) * 2 * pi()) / 24
| extend sin_hour = sin(hour_angle)
| extend cos_hour = cos(hour_angle)
| project _time, id, sin_hour, cos_hour
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%20%22%5B%27sample-http-logs%27%5D%20%7C%20extend%20hour_angle%20%3D%20%28hourofday%28_time%29%20%2A%202%20%2A%20pi%28%29%29%20/%2024%20%7C%20extend%20sin_hour%20%3D%20sin%28hour_angle%29%20%7C%20extend%20cos_hour%20%3D%20cos%28hour_angle%29%20%7C%20project%20_time%2C%20id%2C%20sin_hour%2C%20cos_hour%22%7D)

**Output**

| \_time              | id     | sin\_hour | cos\_hour |
| ------------------- | ------ | --------- | --------- |
| 2024-11-14 00:00:00 | user-1 | 0.0000    | 1.0000    |
| 2024-11-14 06:00:00 | user-2 | 1.0000    | 0.0000    |
| 2024-11-14 12:00:00 | user-3 | 0.0000    | -1.0000   |

## List of related functions [#list-of-related-functions]

* [sin](/apl/scalar-functions/mathematical-functions/sin): Returns the sine of an angle in radians. Combine with `pi` to encode cyclic signals.
* [cos](/apl/scalar-functions/mathematical-functions/cos): Returns the cosine of an angle in radians. Use together with `sin` and `pi` for cyclic coordinate encoding.
* [radians](/apl/scalar-functions/mathematical-functions/radians): Converts degrees to radians. Use it as an alternative to manually multiplying by `pi() / 180`.
* [degrees](/apl/scalar-functions/mathematical-functions/degrees): Converts radians to degrees. Use it to express results from inverse trig functions in degrees instead of radians.
* [atan2](/apl/scalar-functions/mathematical-functions/atan2): Returns the angle in radians between two coordinates. Its output range is (-π, π], so `pi` is a natural companion.

## Other query languages [#other-query-languages]

<LanguageComparisons>
  <Accordion title="Splunk SPL users">
    In Splunk SPL, `pi()` returns the same constant and works identically.

    <CodeGroup>
      ```sql Splunk example
      | eval angle = 2 * pi()
      ```

      ```kusto APL equivalent
      print angle = 2 * pi()
      ```
    </CodeGroup>
  </Accordion>

  <Accordion title="ANSI SQL users">
    In ANSI SQL, `PI()` is a standard function in SQL Server and PostgreSQL that returns π.

    <CodeGroup>
      ```sql SQL example
      SELECT PI() AS pi_value
      ```

      ```kusto APL equivalent
      print pi_value = pi()
      ```
    </CodeGroup>
  </Accordion>
</LanguageComparisons>