# 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

OperatorDescriptionExampleResult
- subtraction2 - 3-1
* multiplication2 * 36
/ division (integer division truncates the result)4 / 22
% modulo (remainder)5 % 41
^ exponentiation2.0 ^ 3.08
|/ square root|/ 25.05
||/ cube root||/ 27.03
! factorial5 !120
!! factorial (prefix operator)!! 5120
@ absolute value@ -5.05
& bitwise AND91 & 1511
| bitwise OR32 | 335
# bitwise XOR17 # 520
~ bitwise NOT~1-2
<< bitwise shift left1 << 416
>> bitwise shift right8 >> 22

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 9-10.

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

FunctionReturn TypeDescriptionExampleResult
`abs(x)`(same as input)absolute valueabs(-17.4)17.4
`cbrt(dp)`dpcube rootcbrt(27.0)3
`ceil(dp or numeric)`(same as input)smallest integer not less than argumentceil(-42.8)-42
`ceiling(dp or numeric)`(same as input)smallest integer not less than argument (alias for `ceil`)ceiling(-95.3)-95
`degrees(dp)`dpradians to degreesdegrees(0.5)28.6478897565412
```div(y numeric, x numeric)```numericinteger quotient of y/xdiv(9,4)2
`exp(dp or numeric)`(same as input)exponentialexp(1.0)2.71828182845905
`floor(dp or numeric)`(same as input)largest integer not greater than argumentfloor(-42.8)-43
`ln(dp or numeric)`(same as input)natural logarithmln(2.0)0.693147180559945
`log(dp or numeric)`(same as input)base 10 logarithmlog(100.0)2
```log(b numeric, x numeric)```numericlogarithm to base blog(2.0, 64.0)6.0000000000
```mod(y, x)```(same as argument types)remainder of y/xmod(9,4)1
`pi()`dp"π" constantpi()3.14159265358979
```power(a dp, b dp)```dpa raised to the power of bpower(9.0, 3.0)729
```power(a numeric, b numeric)```numerica raised to the power of bpower(9.0, 3.0)729
`radians(dp)`dpdegrees to radiansradians(45.0)0.785398163397448
`random()`dprandom value in the range 0.0 <= x < 1.0random()
`round(dp or numeric)`(same as input)round to nearest integerround(42.4)42
`round(v numeric, s int)`numericround to s decimal placesround(42.4382, 2)42.44
`setseed(dp)`voidset seed for subsequent random() calls (value between -1.0 and 1.0, inclusive)setseed(0.54823)
`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 rootsqrt(2.0)1.4142135623731
`trunc(dp or numeric)`(same as input)truncate toward zerotrunc(42.8)42
`trunc(v numeric, s int)`numerictruncate to s decimal placestrunc(42.4382, 2)42.43
`width_bucket(op numeric, b1 numeric, b2 numeric, count int)`intreturn the bucket to which operand would be assigned in an equidepth histogram with count buckets, in the range b1 to b2width_bucket(5.35, 0.024, 10.06, 5)3
`width_bucket(op dp, b1 dp, b2 dp, count int)`intreturn the bucket to which operand would be assigned in an equidepth histogram with count buckets, in the range b1 to b2width_bucket(5.35, 0.024, 10.06, 5)3

Finally, Table 9-4 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 9-4. Trigonometric Functions

FunctionDescription
`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