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ClickHouse/docs/en/sql-reference/functions/rounding-functions.md
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---
slug: /en/sql-reference/functions/rounding-functions
sidebar_position: 155
sidebar_label: Rounding
---
# Rounding Functions
## floor(x\[, N\])
Returns the largest round number that is less than or equal to `x`. A round number is a multiple of 1/10N, or the nearest number of the appropriate data type if 1 / 10N isn’t exact.
‘N’ is an integer constant, optional parameter. By default it is zero, which means to round to an integer.
‘N’ may be negative.
Examples: `floor(123.45, 1) = 123.4, floor(123.45, -1) = 120.`
`x` is any numeric type. The result is a number of the same type.
For integer arguments, it makes sense to round with a negative `N` value (for non-negative `N`, the function does not do anything).
If rounding causes overflow (for example, floor(-128, -1)), an implementation-specific result is returned.
## ceil(x\[, N\]), ceiling(x\[, N\])
Returns the smallest round number that is greater than or equal to `x`. In every other way, it is the same as the `floor` function (see above).
## trunc(x\[, N\]), truncate(x\[, N\])
Returns the round number with largest absolute value that has an absolute value less than or equal to `x`‘s. In every other way, it is the same as the ’floor’ function (see above).
**Syntax**
```sql
trunc(input, precision)
```
Alias: `truncate`.
**Parameters**
- `input`: A numeric type ([Float](/docs/en/sql-reference/data-types/float.md), [Decimal](/docs/en/sql-reference/data-types/decimal.md) or [Integer](/docs/en/sql-reference/data-types/int-uint.md)).
- `precision`: An [Integer](/docs/en/sql-reference/data-types/int-uint.md) type.
**Returned value**
- A data type of `input`.
**Example**
Query:
```sql
SELECT trunc(123.499, 1) as res;
```
```response
┌───res─┐
│ 123.4 │
└───────┘
```
## round(x\[, N\])
Rounds a value to a specified number of decimal places.
The function returns the nearest number of the specified order. In case when given number has equal distance to surrounding numbers, the function uses banker’s rounding for float number types and rounds away from zero for the other number types (Decimal).
``` sql
round(expression [, decimal_places])
```
**Arguments**
- `expression` — A number to be rounded. Can be any [expression](../../sql-reference/syntax.md#syntax-expressions) returning the numeric [data type](../../sql-reference/data-types/index.md#data_types).
- `decimal-places` — An integer value.
- If `decimal-places > 0` then the function rounds the value to the right of the decimal point.
- If `decimal-places < 0` then the function rounds the value to the left of the decimal point.
- If `decimal-places = 0` then the function rounds the value to integer. In this case the argument can be omitted.
**Returned value:**
The rounded number of the same type as the input number.
**Examples**
Example of usage with Float:
``` sql
SELECT number / 2 AS x, round(x) FROM system.numbers LIMIT 3;
```
``` text
┌───x─┬─round(divide(number, 2))─┐
│ 0 │ 0 │
│ 0.5 │ 0 │
│ 1 │ 1 │
└─────┴──────────────────────────┘
```
Example of usage with Decimal:
``` sql
SELECT cast(number / 2 AS Decimal(10,4)) AS x, round(x) FROM system.numbers LIMIT 3;
```
``` text
┌───x─┬─round(CAST(divide(number, 2), 'Decimal(10, 4)'))─┐
│ 0 │ 0 │
│ 0.5 │ 1 │
│ 1 │ 1 │
└─────┴──────────────────────────────────────────────────┘
```
If you want to keep the trailing zeros, you need to enable `output_format_decimal_trailing_zeros`
``` sql
SELECT cast(number / 2 AS Decimal(10,4)) AS x, round(x) FROM system.numbers LIMIT 3 settings output_format_decimal_trailing_zeros=1;
```
``` text
┌──────x─┬─round(CAST(divide(number, 2), 'Decimal(10, 4)'))─┐
│ 0.0000 │ 0.0000 │
│ 0.5000 │ 1.0000 │
│ 1.0000 │ 1.0000 │
└────────┴──────────────────────────────────────────────────┘
```
Examples of rounding to the nearest number:
``` text
round(3.2, 0) = 3
round(4.1267, 2) = 4.13
round(22,-1) = 20
round(467,-2) = 500
round(-467,-2) = -500
```
Banker’s rounding.
``` text
round(3.5) = 4
round(4.5) = 4
round(3.55, 1) = 3.6
round(3.65, 1) = 3.6
```
**See Also**
- [roundBankers](#roundbankers)
## roundBankers
Rounds a number to a specified decimal position.
- If the rounding number is halfway between two numbers, the function uses banker’s rounding. Banker's rounding is a method of rounding fractional numbers. When the rounding number is halfway between two numbers, it's rounded to the nearest even digit at the specified decimal position. For example: 3.5 rounds up to 4, 2.5 rounds down to 2. It's the default rounding method for floating point numbers defined in [IEEE 754](https://en.wikipedia.org/wiki/IEEE_754#Roundings_to_nearest). The [round](#rounding_functions-round) function performs the same rounding for floating point numbers. The `roundBankers` function also rounds integers the same way, for example, `roundBankers(45, -1) = 40`.
- In other cases, the function rounds numbers to the nearest integer.
Using banker’s rounding, you can reduce the effect that rounding numbers has on the results of summing or subtracting these numbers.
For example, sum numbers 1.5, 2.5, 3.5, 4.5 with different rounding:
- No rounding: 1.5 + 2.5 + 3.5 + 4.5 = 12.
- Banker’s rounding: 2 + 2 + 4 + 4 = 12.
- Rounding to the nearest integer: 2 + 3 + 4 + 5 = 14.
**Syntax**
``` sql
roundBankers(expression [, decimal_places])
```
**Arguments**
- `expression` — A number to be rounded. Can be any [expression](../../sql-reference/syntax.md#syntax-expressions) returning the numeric [data type](../../sql-reference/data-types/index.md#data_types).
- `decimal-places` — Decimal places. An integer number.
- `decimal-places > 0` — The function rounds the number to the given position right of the decimal point. Example: `roundBankers(3.55, 1) = 3.6`.
- `decimal-places < 0` — The function rounds the number to the given position left of the decimal point. Example: `roundBankers(24.55, -1) = 20`.
- `decimal-places = 0` — The function rounds the number to an integer. In this case the argument can be omitted. Example: `roundBankers(2.5) = 2`.
**Returned value**
A value rounded by the banker’s rounding method.
**Examples**
Query:
``` sql
SELECT number / 2 AS x, roundBankers(x, 0) AS b fROM system.numbers limit 10
```
Result:
``` text
┌───x─┬─b─┐
│ 0 │ 0 │
│ 0.5 │ 0 │
│ 1 │ 1 │
│ 1.5 │ 2 │
│ 2 │ 2 │
│ 2.5 │ 2 │
│ 3 │ 3 │
│ 3.5 │ 4 │
│ 4 │ 4 │
│ 4.5 │ 4 │
└─────┴───┘
```
Examples of Banker’s rounding:
``` text
roundBankers(0.4) = 0
roundBankers(-3.5) = -4
roundBankers(4.5) = 4
roundBankers(3.55, 1) = 3.6
roundBankers(3.65, 1) = 3.6
roundBankers(10.35, 1) = 10.4
roundBankers(10.755, 2) = 10.76
```
**See Also**
- [round](#rounding_functions-round)
## roundToExp2
Accepts a number. If the number is less than one, it returns `0`. Otherwise, it rounds the number down to the nearest (whole non-negative) degree of two.
**Syntax**
```sql
roundToExp2(num)
```
**Parameters**
- `num`: A number representing an age in years. [UInt](../data-types/int-uint.md)/[Float](../data-types/float.md).
**Returned value**
- `0`, for `num` $\lt 1$. [UInt8](../data-types/int-uint.md).
- `num` rounded down to the nearest (whole non-negative) degree of two. [UInt](../data-types/int-uint.md)/[Float](../data-types/float.md) equivalent to the input type.
**Example**
Query:
```sql
SELECT *, roundToExp2(*) FROM system.numbers WHERE number IN (0, 2, 5, 10, 19, 50)
```
Result:
```response
┌─number─┬─roundToExp2(number)─┐
│ 0 │ 0 │
│ 2 │ 2 │
│ 5 │ 4 │
│ 10 │ 8 │
│ 19 │ 16 │
│ 50 │ 32 │
└────────┴─────────────────────┘
```
## roundDuration
Accepts a number. If the number is less than one, it returns `0`. Otherwise, it rounds the number down to numbers from the set of commonly used durations: `1, 10, 30, 60, 120, 180, 240, 300, 600, 1200, 1800, 3600, 7200, 18000, 36000`.
**Syntax**
```sql
roundDuration(num)
```
**Parameters**
- `num`: A number to round to one of the numbers in the set of common durations. [UInt](../data-types/int-uint.md)/[Float](../data-types/float.md).
**Returned value**
- `0`, for `num` $\lt 1$.
- Otherwise, one of: `1, 10, 30, 60, 120, 180, 240, 300, 600, 1200, 1800, 3600, 7200, 18000, 36000`. [UInt16](../data-types/int-uint.md).
**Example**
Query:
```sql
SELECT *, roundDuration(*) FROM system.numbers WHERE number IN (0, 9, 19, 47, 101, 149, 205, 271, 421, 789, 1423, 2345, 4567, 9876, 24680, 42573)
```
Result:
```response
┌─number─┬─roundDuration(number)─┐
│ 0 │ 0 │
│ 9 │ 1 │
│ 19 │ 10 │
│ 47 │ 30 │
│ 101 │ 60 │
│ 149 │ 120 │
│ 205 │ 180 │
│ 271 │ 240 │
│ 421 │ 300 │
│ 789 │ 600 │
│ 1423 │ 1200 │
│ 2345 │ 1800 │
│ 4567 │ 3600 │
│ 9876 │ 7200 │
│ 24680 │ 18000 │
│ 42573 │ 36000 │
└────────┴───────────────────────┘
```
## roundAge
Accepts a number within various commonly used ranges of human age and returns either a maximum or a minimum within that range.
**Syntax**
```sql
roundAge(num)
```
**Parameters**
- `age`: A number representing an age in years. [UInt](../data-types/int-uint.md)/[Float](../data-types/float.md).
**Returned value**
- Returns `0`, for $age \lt 1$.
- Returns `17`, for $1 \leq age \leq 17$.
- Returns `18`, for $18 \leq age \leq 24$.
- Returns `25`, for $25 \leq age \leq 34$.
- Returns `35`, for $35 \leq age \leq 44$.
- Returns `45`, for $45 \leq age \leq 54$.
- Returns `55`, for $age \geq 55$.
Type: [UInt8](../data-types/int-uint.md).
**Example**
Query:
```sql
SELECT *, roundAge(*) FROM system.numbers WHERE number IN (0, 5, 20, 31, 37, 54, 72);
```
Result:
```response
┌─number─┬─roundAge(number)─┐
│ 0 │ 0 │
│ 5 │ 17 │
│ 20 │ 18 │
│ 31 │ 25 │
│ 37 │ 35 │
│ 54 │ 45 │
│ 72 │ 55 │
└────────┴──────────────────┘
```
## roundDown
Accepts a number and rounds it down to an element in the specified array. If the value is less than the lowest bound, the lowest bound is returned.
**Syntax**
```sql
roundDown(num, arr)
```
**Parameters**
- `num`: A number to round down. [Numeric](../data-types/int-uint.md).
- `arr`: Array of elements to round `age` down to. [Array](../data-types/array.md) of [UInt](../data-types/int-uint.md)/[Float](../data-types/float.md) type.
**Returned value**
- Number rounded down to an element in `arr`. If the value is less than the lowest bound, the lowest bound is returned. [UInt](../data-types/int-uint.md)/[Float](../data-types/float.md) type deduced from the type of `arr`.
**Example**
Query:
```sql
SELECT *, roundDown(*, [3, 4, 5]) FROM system.numbers WHERE number IN (0, 1, 2, 3, 4, 5)
```
Result:
```response
┌─number─┬─roundDown(number, [3, 4, 5])─┐
│ 0 │ 3 │
│ 1 │ 3 │
│ 2 │ 3 │
│ 3 │ 3 │
│ 4 │ 4 │
│ 5 │ 5 │
└────────┴──────────────────────────────┘
```
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