18th October 2018: PostgreSQL 11 Released!
Supported Versions: Current (11) / 10 / 9.6 / 9.5 / 9.4 / 9.3
Development Versions: devel
Unsupported versions: 9.2 / 9.1 / 9.0 / 8.4 / 8.3 / 8.2 / 8.1 / 8.0 / 7.4 / 7.3 / 7.2 / 7.1

# 9.3. Mathematical Functions and Operators

Mathematical operators are provided for many PostgreSQL types. For types without standard mathematical conventions (e.g., date/time types) we describe the actual behavior in subsequent sections.

Table 9-2 shows the available mathematical operators.

Table 9-2. Mathematical Operators

Operator Description Example Result
+ addition 2 + 3 5
- subtraction 2 - 3 -1
* multiplication 2 * 3 6
/ division (integer division truncates the result) 4 / 2 2
% modulo (remainder) 5 % 4 1
^ exponentiation (associates left to right) 2.0 ^ 3.0 8
|/ square root |/ 25.0 5
||/ cube root ||/ 27.0 3
! factorial 5 ! 120
!! factorial (prefix operator) !! 5 120
@ absolute value @ -5.0 5
& bitwise AND 91 & 15 11
| bitwise OR 32 | 3 35
# bitwise XOR 17 # 5 20
~ bitwise NOT ~1 -2
<< bitwise shift left 1 << 4 16
>> bitwise shift right 8 >> 2 2

The bitwise operators work only on integral data types, whereas the others are available for all numeric data types. The bitwise operators are also available for the bit string types bit and bit varying, as shown in Table 9-11.

Table 9-3 shows the available mathematical functions. In the table, dp indicates double precision. Many of these functions are provided in multiple forms with different argument types. Except where noted, any given form of a function returns the same data type as its argument. The functions working with double precision data are mostly implemented on top of the host system's C library; accuracy and behavior in boundary cases can therefore vary depending on the host system.

Table 9-3. Mathematical Functions

Function Return Type Description Example Result
`abs(x)` (same as input) absolute value abs(-17.4) 17.4
`cbrt(dp)` dp cube root cbrt(27.0) 3
`ceil(dp or numeric)` (same as input) nearest integer greater than or equal to argument ceil(-42.8) -42
`ceiling(dp or numeric)` (same as input) nearest integer greater than or equal to argument (same as `ceil`) ceiling(-95.3) -95
`degrees(dp)` dp radians to degrees degrees(0.5) 28.6478897565412
```div(y numeric, x numeric)``` numeric integer quotient of y/x div(9,4) 2
`exp(dp or numeric)` (same as input) exponential exp(1.0) 2.71828182845905
`floor(dp or numeric)` (same as input) nearest integer less than or equal to argument floor(-42.8) -43
`ln(dp or numeric)` (same as input) natural logarithm ln(2.0) 0.693147180559945
`log(dp or numeric)` (same as input) base 10 logarithm log(100.0) 2
```log(b numeric, x numeric)``` numeric logarithm to base b log(2.0, 64.0) 6.0000000000
`mod(y, x)` (same as argument types) remainder of y/x mod(9,4) 1
`pi()` dp "π" constant pi() 3.14159265358979
`power(a dp, b dp)` dp a raised to the power of b power(9.0, 3.0) 729
```power(a numeric, b numeric)``` numeric a raised to the power of b power(9.0, 3.0) 729
`radians(dp)` dp degrees to radians radians(45.0) 0.785398163397448
`round(dp or numeric)` (same as input) round to nearest integer round(42.4) 42
```round(v numeric, s int)``` numeric round to s decimal places round(42.4382, 2) 42.44
`sign(dp or numeric)` (same as input) sign of the argument (-1, 0, +1) sign(-8.4) -1
`sqrt(dp or numeric)` (same as input) square root sqrt(2.0) 1.4142135623731
`trunc(dp or numeric)` (same as input) truncate toward zero trunc(42.8) 42
```trunc(v numeric, s int)``` numeric truncate to s decimal places trunc(42.4382, 2) 42.43
```width_bucket(op numeric, b1 numeric, b2 numeric, count int)``` int return the bucket to which operand would be assigned in an equidepth histogram with count buckets, in the range b1 to b2 width_bucket(5.35, 0.024, 10.06, 5) 3
```width_bucket(op dp, b1 dp, b2 dp, count int)``` int return the bucket to which operand would be assigned in an equidepth histogram with count buckets, in the range b1 to b2 width_bucket(5.35, 0.024, 10.06, 5) 3

Table 9-4 shows functions for generating random numbers.

Table 9-4. Random Functions

Function Return Type Description
`random()` dp random value in the range 0.0 <= x < 1.0
`setseed(dp)` void set seed for subsequent random() calls (value between -1.0 and 1.0, inclusive)

The characteristics of the values returned by `random()` depend on the system implementation. It is not suitable for cryptographic applications; see pgcrypto module for an alternative.

Finally, Table 9-5 shows the available trigonometric functions. All trigonometric functions take arguments and return values of type double precision. Trigonometric functions arguments are expressed in radians. Inverse functions return values are expressed in radians. See unit transformation functions `radians()` and `degrees()` above.

Table 9-5. Trigonometric Functions

Function Description
`acos(x)` inverse cosine
`asin(x)` inverse sine
`atan(x)` inverse tangent
```atan2(y, x)``` inverse tangent of y/x
`cos(x)` cosine
`cot(x)` cotangent
`sin(x)` sine
`tan(x)` tangent