﻿12.5. Numeric Functions

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## 12.5. Numeric Functions

NameDescription
`ABS()`Return the absolute value
`ACOS()`Return the arc cosine
`ASIN()`Return the arc sine
`ATAN2()`, `ATAN()`Return the arc tangent of the two arguments
`ATAN()`Return the arc tangent
`/`Division operator
`CEILING()`, `CEIL()`Return the smallest integer value not less than the argument
`COS()`Return the cosine
`COT()`Return the cotangent
`CRC32()`(v4.1.0)Compute a cyclic redundancy check value
`DEGREES()`Convert radians to degrees
`DIV`(v4.1.0)Integer division
`EXP()`Raise to the power of
`FLOOR()`Return the largest integer value not greater than the argument
`LN()`Return the natural logarithm of the argument
`LOG10()`Return the base-10 logarithm of the argument
`LOG2()`Return the base-2 logarithm of the argument
`LOG()` Return the natural logarithm of the first argument
`-`Minus operator
`MOD()`Return the remainder
`%`Modulo operator
`PI()`Return the value of pi
`+`Addition operator
`POW()`, `POWER()`Return the argument raised to the specified power
`RADIANS()`Return argument converted to radians
`RAND()`Return a random floating-point value
`ROUND()`Round the argument
`SIGN()`Return the sign of the argument
`SIN()`Return the sine of the argument
`SQRT()`Return the square root of the argument
`TAN()`Return the tangent of the argument
`*`Times operator
`TRUNCATE()`Truncate to specified number of decimal places
`-`Change the sign of the argument

### 12.5.1. Arithmetic Operators

NameDescription
`/`Division operator
`DIV`(v4.1.0)Integer division
`-`Minus operator
`%`Modulo operator
`+`Addition operator
`*`Times operator
`-`Change the sign of the argument

The usual arithmetic operators are available. The precision of the result is determined according to the following rules:

• Note that in the case of `-`, `+`, and `*`, the result is calculated with `BIGINT` (64-bit) precision if both arguments are integers.

• If one of the arguments is an unsigned integer, and the other argument is also an integer, the result is an unsigned integer.

• If any of the operands of a `+`, `-`, `/`, `*`, `%` is a real or string value, then the precision of the result is the precision of the argument with the maximum precision.

• In multiplication and division, the precision of the result when using two exact values is the precision of the first argument + the value of the `div_precision_increment` global variable. For example, the expression `5.05 / 0.0014` would have a precision of six decimal places (`3607.142857`).

These rules are applied for each operation, such that nested calculations imply the precision of each component. Hence, `(14620 / 9432456) / (24250 / 9432456)`, would resolve first to `(0.0014) / (0.0026)`, with the final result having 8 decimal places (`0.57692308`).

Because of these rules and the method they are applied, care should be taken to ensure that components and sub-components of a calculation use the appropriate level of precision. See Section 12.9, “Cast Functions and Operators”.

• `+`

```mysql> `SELECT 3+5;`
-> 8```
• `-`

Subtraction:

```mysql> `SELECT 3-5;`
-> -2```
• `-`

Unary minus. This operator changes the sign of the argument.

```mysql> `SELECT - 2;`
-> -2```

Note: If this operator is used with a `BIGINT`, the return value is also a `BIGINT`. This means that you should avoid using `–` on integers that may have the value of –263.

• `*`

Multiplication:

```mysql> `SELECT 3*5;`
-> 15
mysql> `SELECT 18014398509481984*18014398509481984.0;`
-> 324518553658426726783156020576256.0
mysql> `SELECT 18014398509481984*18014398509481984;`
-> 0```

The result of the last expression is incorrect because the result of the integer multiplication exceeds the 64-bit range of `BIGINT` calculations. (See Section 11.2, “Numeric Types”.)

• `/`

Division:

```mysql> `SELECT 3/5;`
-> 0.60```

Division by zero produces a `NULL` result:

```mysql> `SELECT 102/(1-1);`
-> NULL```

A division is calculated with `BIGINT` arithmetic only if performed in a context where its result is converted to an integer.

• `DIV`

Integer division. Similar to `FLOOR()`, but is safe with `BIGINT` values.

```mysql> `SELECT 5 DIV 2;`
-> 2```
• `N % M`

Modulo operation. Returns the remainder of `N` divided by `M`. For more information, see the description for the `MOD()` function in Section 12.5.2, “Mathematical Functions”.

### 12.5.2. Mathematical Functions

NameDescription
`ABS()`Return the absolute value
`ACOS()`Return the arc cosine
`ASIN()`Return the arc sine
`ATAN2()`, `ATAN()`Return the arc tangent of the two arguments
`ATAN()`Return the arc tangent
`CEILING()`, `CEIL()`Return the smallest integer value not less than the argument
`COS()`Return the cosine
`COT()`Return the cotangent
`CRC32()`(v4.1.0)Compute a cyclic redundancy check value
`DEGREES()`Convert radians to degrees
`EXP()`Raise to the power of
`FLOOR()`Return the largest integer value not greater than the argument
`LN()`Return the natural logarithm of the argument
`LOG10()`Return the base-10 logarithm of the argument
`LOG2()`Return the base-2 logarithm of the argument
`LOG()` Return the natural logarithm of the first argument
`MOD()`Return the remainder
`PI()`Return the value of pi
`POW()`, `POWER()`Return the argument raised to the specified power
`RADIANS()`Return argument converted to radians
`RAND()`Return a random floating-point value
`ROUND()`Round the argument
`SIGN()`Return the sign of the argument
`SIN()`Return the sine of the argument
`SQRT()`Return the square root of the argument
`TAN()`Return the tangent of the argument
`TRUNCATE()`Truncate to specified number of decimal places

All mathematical functions return `NULL` in the event of an error.

• `ABS(X)`

Returns the absolute value of `X`.

```mysql> `SELECT ABS(2);`
-> 2
mysql> `SELECT ABS(-32);`
-> 32```

This function is safe to use with `BIGINT` values.

• `ACOS(X)`

Returns the arc cosine of `X`, that is, the value whose cosine is `X`. Returns `NULL` if `X` is not in the range `-1` to `1`.

```mysql> `SELECT ACOS(1);`
-> 0
mysql> `SELECT ACOS(1.0001);`
-> NULL
mysql> `SELECT ACOS(0);`
-> 1.5707963267949```
• `ASIN(X)`

Returns the arc sine of `X`, that is, the value whose sine is `X`. Returns `NULL` if `X` is not in the range `-1` to `1`.

```mysql> `SELECT ASIN(0.2);`
-> 0.20135792079033
mysql> `SELECT ASIN('foo');`

+-------------+
| ASIN('foo') |
+-------------+
|           0 |
+-------------+
1 row in set, 1 warning (0.00 sec)

mysql> `SHOW WARNINGS;`
+---------+------+-----------------------------------------+
| Level   | Code | Message                                 |
+---------+------+-----------------------------------------+
| Warning | 1292 | Truncated incorrect DOUBLE value: 'foo' |
+---------+------+-----------------------------------------+```
• `ATAN(X)`

Returns the arc tangent of `X`, that is, the value whose tangent is `X`.

```mysql> `SELECT ATAN(2);`
-> 1.1071487177941
mysql> `SELECT ATAN(-2);`
-> -1.1071487177941```
• `ATAN(Y,X)`, `ATAN2(Y,X)`

Returns the arc tangent of the two variables `X` and `Y`. It is similar to calculating the arc tangent of `Y / X`, except that the signs of both arguments are used to determine the quadrant of the result.

```mysql> `SELECT ATAN(-2,2);`
-> -0.78539816339745
mysql> `SELECT ATAN2(PI(),0);`
-> 1.5707963267949```
• `CEILING(X)`, `CEIL(X)`

Returns the smallest integer value not less than `X`. `CEILING()` and `CEIL()` are synonymous.

```mysql> `SELECT CEILING(1.23);`
-> 2
mysql> `SELECT CEIL(-1.23);`
-> -1```

For exact-value numeric arguments, the return value has an exact-value numeric type. For string or floating-point arguments, the return value has a floating-point type.

• `COS(X)`

Returns the cosine of `X`, where `X` is given in radians.

```mysql> `SELECT COS(PI());`
-> -1```
• `COT(X)`

Returns the cotangent of `X`.

```mysql> `SELECT COT(12);`
-> -1.5726734063977
mysql> `SELECT COT(0);`
-> NULL```
• `CRC32(expr)`

Computes a cyclic redundancy check value and returns a 32-bit unsigned value. The result is `NULL` if the argument is `NULL`. The argument is expected to be a string and (if possible) is treated as one if it is not.

```mysql> `SELECT CRC32('MySQL');`
-> 3259397556
mysql> `SELECT CRC32('mysql');`
-> 2501908538```
• `DEGREES(X)`

Returns the argument `X`, converted from radians to degrees.

```mysql> `SELECT DEGREES(PI());`
-> 180
mysql> `SELECT DEGREES(PI() / 2);`
-> 90```
• `EXP(X)`

Returns the value of e (the base of natural logarithms) raised to the power of `X`.

```mysql> `SELECT EXP(2);`
-> 7.3890560989307
mysql> `SELECT EXP(-2);`
-> 0.13533528323661
mysql> `SELECT EXP(0);`
-> 1```
• `FLOOR(X)`

Returns the largest integer value not greater than `X`.

```mysql> `SELECT FLOOR(1.23);`
-> 1
mysql> `SELECT FLOOR(-1.23);`
-> -2```

For exact-value numeric arguments, the return value has an exact-value numeric type. For string or floating-point arguments, the return value has a floating-point type.

• `FORMAT(X,D)`

Formats the number `X` to a format like `'#,###,###.##'`, rounded to `D` decimal places, and returns the result as a string. For details, see Section 12.4, “String Functions”.

• `LN(X)`

Returns the natural logarithm of `X`; that is, the base-e logarithm of `X`.

```mysql> `SELECT LN(2);`
-> 0.69314718055995
mysql> `SELECT LN(-2);`
-> NULL```

This function is synonymous with `LOG(X)`.

• `LOG(X)`, `LOG(B,X)`

If called with one parameter, this function returns the natural logarithm of `X`.

```mysql> `SELECT LOG(2);`
-> 0.69314718055995
mysql> `SELECT LOG(-2);`
-> NULL```

If called with two parameters, this function returns the logarithm of `X` for an arbitrary base `B`.

```mysql> `SELECT LOG(2,65536);`
-> 16
mysql> `SELECT LOG(10,100);`
-> 2```

`LOG(B,X)` is equivalent to `LOG(X) / LOG(B)`.

• `LOG2(X)`

Returns the base-2 logarithm of `X`.

```mysql> `SELECT LOG2(65536);`
-> 16
mysql> `SELECT LOG2(-100);`
-> NULL```

`LOG2()` is useful for finding out how many bits a number requires for storage. This function is equivalent to the expression `LOG(X) / LOG(2)`.

• `LOG10(X)`

Returns the base-10 logarithm of `X`.

```mysql> `SELECT LOG10(2);`
-> 0.30102999566398
mysql> `SELECT LOG10(100);`
-> 2
mysql> `SELECT LOG10(-100);`
-> NULL```

`LOG10(X)` is equivalent to `LOG(10,X)`.

• `MOD(N,M)`, `N % M`, `N MOD M`

Modulo operation. Returns the remainder of `N` divided by `M`.

```mysql> `SELECT MOD(234, 10);`
-> 4
mysql> `SELECT 253 % 7;`
-> 1
mysql> `SELECT MOD(29,9);`
-> 2
mysql> `SELECT 29 MOD 9;`
-> 2```

This function is safe to use with `BIGINT` values.

`MOD()` also works on values that have a fractional part and returns the exact remainder after division:

```mysql> `SELECT MOD(34.5,3);`
-> 1.5```

`MOD(N,0)` returns `NULL`.

• `PI()`

Returns the value of π (pi). The default number of decimal places displayed is seven, but MySQL uses the full double-precision value internally.

```mysql> `SELECT PI();`
-> 3.141593
mysql> `SELECT PI()+0.000000000000000000;`
-> 3.141592653589793116```
• `POW(X,Y)`, `POWER(X,Y)`

Returns the value of `X` raised to the power of `Y`.

```mysql> `SELECT POW(2,2);`
-> 4
mysql> `SELECT POW(2,-2);`
-> 0.25```
• `RADIANS(X)`

Returns the argument `X`, converted from degrees to radians. (Note that π radians equals 180 degrees.)

```mysql> `SELECT RADIANS(90);`
-> 1.5707963267949```
• `RAND()`, `RAND(N)`

Returns a random floating-point value `v` in the range `0` <= `v` < `1.0`. If a constant integer argument `N` is specified, it is used as the seed value, which produces a repeatable sequence of column values.

```mysql> `SELECT RAND();`
-> 0.9233482386203
mysql> `SELECT RAND(20);`
-> 0.15888261251047
mysql> `SELECT RAND(20);`
-> 0.15888261251047
mysql> `SELECT RAND();`
-> 0.63553050033332
mysql> `SELECT RAND();`
-> 0.70100469486881
mysql> `SELECT RAND(20);`
-> 0.15888261251047```

The effect of using a non-constant argument is undefined. As of MySQL 5.0.13, non-constant arguments are disallowed.

To obtain a random integer `R` in the range `i` <= `R` < `j`, use the expression `FLOOR(i + RAND() * (j – i))`. For example, to obtain a random integer in the range the range `7` <= `R` < `12`, you could use the following statement:

`SELECT FLOOR(7 + (RAND() * 5));`

You cannot use a column with `RAND()` values in an `ORDER BY` clause, because `ORDER BY` would evaluate the column multiple times. However, you can retrieve rows in random order like this:

`mysql> `SELECT * FROM tbl_name ORDER BY RAND();``

`ORDER BY RAND()` combined with `LIMIT` is useful for selecting a random sample from a set of rows:

`mysql> `SELECT * FROM table1, table2 WHERE a=b AND c<d` -> `ORDER BY RAND() LIMIT 1000;``

Note that `RAND()` in a `WHERE` clause is re-evaluated every time the `WHERE` is executed.

`RAND()` is not meant to be a perfect random generator, but instead is a fast way to generate ad hoc random numbers which is portable between platforms for the same MySQL version.

• `ROUND(X)`, `ROUND(X,D)`

Rounds the argument `X` to `D` decimal places. The rounding algorithm depends on the data type of `X`. `D` defaults to 0 if not specified. `D` can be negative to cause `D` digits left of the decimal point of the value `X` to become zero.

```mysql> `SELECT ROUND(-1.23);`
-> -1
mysql> `SELECT ROUND(-1.58);`
-> -2
mysql> `SELECT ROUND(1.58);`
-> 2
mysql> `SELECT ROUND(1.298, 1);`
-> 1.3
mysql> `SELECT ROUND(1.298, 0);`
-> 1
mysql> `SELECT ROUND(23.298, -1);`
-> 20```

The return type is the same type as that of the first argument (assuming that it is integer, double, or decimal). This means that for an integer argument, the result is an integer (no decimal places):

```mysql> `SELECT ROUND(150.000,2), ROUND(150,2);`
+------------------+--------------+
| ROUND(150.000,2) | ROUND(150,2) |
+------------------+--------------+
|           150.00 |          150 |
+------------------+--------------+```

Before MySQL 5.0.3, the behavior of `ROUND()` when the argument is halfway between two integers depends on the C library implementation. Different implementations round to the nearest even number, always up, always down, or always toward zero. If you need one kind of rounding, you should use a well-defined function such as `TRUNCATE()` or `FLOOR()` instead.

As of MySQL 5.0.3, `ROUND()` uses the precision math library for exact-value arguments when the first argument is a decimal value:

• For exact-value numbers, `ROUND()` uses the “round half up” or “round toward nearest” rule: A value with a fractional part of .5 or greater is rounded up to the next integer if positive or down to the next integer if negative. (In other words, it is rounded away from zero.) A value with a fractional part less than .5 is rounded down to the next integer if positive or up to the next integer if negative.

• For approximate-value numbers, the result depends on the C library. On many systems, this means that `ROUND()` uses the "round to nearest even" rule: A value with any fractional part is rounded to the nearest even integer.

The following example shows how rounding differs for exact and approximate values:

```mysql> `SELECT ROUND(2.5), ROUND(25E-1);`
+------------+--------------+
| ROUND(2.5) | ROUND(25E-1) |
+------------+--------------+
| 3          |            2 |
+------------+--------------+```

• `SIGN(X)`

Returns the sign of the argument as `-1`, `0`, or `1`, depending on whether `X` is negative, zero, or positive.

```mysql> `SELECT SIGN(-32);`
-> -1
mysql> `SELECT SIGN(0);`
-> 0
mysql> `SELECT SIGN(234);`
-> 1```
• `SIN(X)`

Returns the sine of `X`, where `X` is given in radians.

```mysql> `SELECT SIN(PI());`
-> 1.2246063538224e-16
mysql> `SELECT ROUND(SIN(PI()));`
-> 0```
• `SQRT(X)`

Returns the square root of a non-negative number `X`.

```mysql> `SELECT SQRT(4);`
-> 2
mysql> `SELECT SQRT(20);`
-> 4.4721359549996
mysql> `SELECT SQRT(-16);`
-> NULL```
• `TAN(X)`

Returns the tangent of `X`, where `X` is given in radians.

```mysql> `SELECT TAN(PI());`
-> -1.2246063538224e-16
mysql> `SELECT TAN(PI()+1);`
-> 1.5574077246549```
• `TRUNCATE(X,D)`

Returns the number `X`, truncated to `D` decimal places. If `D` is `0`, the result has no decimal point or fractional part. `D` can be negative to cause `D` digits left of the decimal point of the value `X` to become zero.

```mysql> `SELECT TRUNCATE(1.223,1);`
-> 1.2
mysql> `SELECT TRUNCATE(1.999,1);`
-> 1.9
mysql> `SELECT TRUNCATE(1.999,0);`
-> 1
mysql> `SELECT TRUNCATE(-1.999,1);`
-> -1.9
mysql> `SELECT TRUNCATE(122,-2);`
-> 100
mysql> `SELECT TRUNCATE(10.28*100,0);`
-> 1028```

All numbers are rounded toward zero.