> ## Documentation Index
> Fetch the complete documentation index at: https://axiom-mano-sample-app.mintlify.site/llms.txt
> Use this file to discover all available pages before exploring further.

# Rounding functions

> Learn how to use and combine different rounding functions in APL

## Rounding functions

| **Function Name**        | **Description**                                                                                                           |
| ------------------------ | ------------------------------------------------------------------------------------------------------------------------- |
| [ceiling()](#ceiling)    | Calculates the smallest integer greater than, or equal to, the specified numeric expression.                              |
| [bin()](#bin)            | Rounds values down to an integer multiple of a given bin size.                                                            |
| [bin\_auto()](#bin-auto) | Rounds values down to a fixed-size "bin", with control over the bin size and starting point provided by a query property. |
| [floor()](#floor)        | Calculates the largest integer less than, or equal to, the specified numeric expression.                                  |

## ceiling()

Calculates the smallest integer greater than, or equal to, the specified numeric expression.

### Arguments

* x: A real number.

### Returns

* The smallest integer greater than, or equal to, the specified numeric expression.

### Examples

```kusto
ceiling(x)
```

```kusto
ceiling(25.43) == 26
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B'sample-http-logs'%5D%5Cn%7C%20project%20smallest_integer%20%3D%20ceiling%2825.43%29%22%7D)

## bin()

Rounds values down to an integer multiple of a given bin size.

The `bin()` function is used with [summarize operator](/apl/tabular-operators/summarize-operator). If your set of values are disorderly, they will be grouped into fractions.

### Arguments

* value: A date, number, or [timespan](/apl/data-types/scalar-data-types#timespan-literals)
* roundTo: The "bin size", a number or timespan that divides value.

### Returns

The nearest multiple of roundTo below value.

### Examples

```kusto
bin(value,roundTo)
```

```kusto
bin(25.73, 4) == 24
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B'sample-http-logs'%5D%5Cn%7C%20project%20round_value%20%3D%20bin%2825.73%2C%204%29%22%7D)

## bin\_auto()

Rounds values down to a fixed-size "bin", the `bin_auto()` function can only be used with the [summarize operator](/apl/tabular-operators/summarize-operator) by statement with the `_time` column.

### Arguments

* Expression: A scalar expression of a numeric type indicating the value to round.

### Returns

The nearest multiple of `query_bin_auto_at` below Expression, shifted so that `query_bin_auto_at` will be translated into itself.

### Example

```kusto
summarize count() by bin_auto(_time)
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B'sample-http-logs'%5D%5Cn%7C%20summarize%20count%28%29%20by%20bin_auto%28_time%29%22%7D)

## floor()

Calculates the largest integer less than, or equal to, the specified numeric expression.

### Arguments

* number: A real number.

### Returns

* The largest integer greater than, or equal to, the specified numeric expression.

### Examples

```kusto
floor(number)
```

```kusto
floor(25.73) == 25
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B'sample-http-logs'%5D%5Cn%7C%20project%20largest_integer_number%20%3D%20floor%2825.73%29%22%7D)