Supported Versions: Current (16) / 15 / 14 / 13 / 12
Development Versions: devel
Unsupported versions: 11 / 10 / 9.6 / 9.5 / 9.4 / 9.3 / 9.2 / 9.1 / 9.0 / 8.4 / 8.3 / 8.2 / 8.1 / 8.0 / 7.4 / 7.3 / 7.2 / 7.1
This documentation is for an unsupported version of PostgreSQL.
You may want to view the same page for the current version, or one of the other supported versions listed above instead.

9.3. Mathematical Functions and Operators

Mathematical operators are provided for many PostgreSQL types. For types without common mathematical conventions for all possible permutations (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 results) 4 / 2 2
% modulo (remainder) 5 % 4 1
^ exponentiation 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 are also available for the bit string types bit and bit varying, as shown in Table 9-3. Bit string operands of &, |, and # must be of equal length. When bit shifting, the original length of the string is preserved, as shown in the table.

Table 9-3. Bit String Bitwise Operators

Example Result
B'10001' & B'01101' 00001
B'10001' | B'01101' 11101
B'10001' # B'01101' 11100
~ B'10001' 01110
B'10001' << 3 01000
B'10001' >> 2 00100

Table 9-4 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 may therefore vary depending on the host system.

Table 9-4. Mathematical Functions

Function Return Type Description Example Result
abs(x) (same as x) absolute value abs(-17.4) 17.4
cbrt(dp) dp cube root cbrt(27.0) 3
ceil(dp or numeric) (same as input) smallest integer not less than argument ceil(-42.8) -42
degrees(dp) dp radians to degrees degrees(0.5) 28.6478897565412
exp(dp or numeric) (same as input) exponential exp(1.0) 2.71828182845905
floor(dp or numeric) (same as input) largest integer not greater than 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
pow(a dp, b dp) dp a raised to the power of b pow(9.0, 3.0) 729
pow(a numeric, b numeric) numeric a raised to the power of b pow(9.0, 3.0) 729
radians(dp) dp degrees to radians radians(45.0) 0.785398163397448
random() dp random value between 0.0 and 1.0 random()  
round(dp or numeric) (same as input) round to nearest integer round(42.4) 42
round(v numeric, s integer) numeric round to s decimal places round(42.4382, 2) 42.44
setseed(dp) int32 set seed for subsequent random() calls setseed(0.54823) 1177314959
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 integer) numeric truncate to s decimal places trunc(42.4382, 2) 42.43

Finally, Table 9-5 shows the available trigonometric functions. All trigonometric functions take arguments and return values of type double precision.

Table 9-5. Trigonometric Functions

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