3rd October 2019: PostgreSQL 12 Released!
Supported Versions: Current (12) / 11 / 10 / 9.6 / 9.5 / 9.4
Development Versions: devel
Unsupported versions: 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

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 9.4 shows the available mathematical operators.

Table 9.4. 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 9.14.

Table 9.5 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 9.5. 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
log10(dp or numeric) (same as input) base 10 logarithm log10(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
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
scale(numeric) integer scale of the argument (the number of decimal digits in the fractional part) scale(8.41) 2
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(operand dp, b1 dp, b2 dp, count int) int return the bucket number to which operand would be assigned in a histogram having count equal-width buckets spanning the range b1 to b2; returns 0 or count+1 for an input outside the range width_bucket(5.35, 0.024, 10.06, 5) 3
width_bucket(operand numeric, b1 numeric, b2 numeric, count int) int return the bucket number to which operand would be assigned in a histogram having count equal-width buckets spanning the range b1 to b2; returns 0 or count+1 for an input outside the range width_bucket(5.35, 0.024, 10.06, 5) 3
width_bucket(operand anyelement, thresholds anyarray) int return the bucket number to which operand would be assigned given an array listing the lower bounds of the buckets; returns 0 for an input less than the first lower bound; the thresholds array must be sorted, smallest first, or unexpected results will be obtained width_bucket(now(), array['yesterday', 'today', 'tomorrow']::timestamptz[]) 2

Table 9.6 shows functions for generating random numbers.

Table 9.6. 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 random() function uses a simple linear congruential algorithm. It is fast but not suitable for cryptographic applications; see the pgcrypto module for a more secure alternative. If setseed() is called, the results of subsequent random() calls in the current session are repeatable by re-issuing setseed() with the same argument.

Table 9.7 shows the available trigonometric functions. All these functions take arguments and return values of type double precision. Each of the trigonometric functions comes in two variants, one that measures angles in radians and one that measures angles in degrees.

Table 9.7. Trigonometric Functions

Function (radians) Function (degrees) Description
acos(x) acosd(x) inverse cosine
asin(x) asind(x) inverse sine
atan(x) atand(x) inverse tangent
atan2(y, x) atan2d(y, x) inverse tangent of y/x
cos(x) cosd(x) cosine
cot(x) cotd(x) cotangent
sin(x) sind(x) sine
tan(x) tand(x) tangent

Note

Another way to work with angles measured in degrees is to use the unit transformation functions radians() and degrees() shown earlier. However, using the degree-based trigonometric functions is preferred, as that way avoids round-off error for special cases such as sind(30).

Table 9.8 shows the available hyperbolic functions. All these functions take arguments and return values of type double precision.

Table 9.8. Hyperbolic Functions

Function Description Example Result
sinh(x) hyperbolic sine sinh(0) 0
cosh(x) hyperbolic cosine cosh(0) 1
tanh(x) hyperbolic tangent tanh(0) 0
asinh(x) inverse hyperbolic sine asinh(0) 0
acosh(x) inverse hyperbolic cosine acosh(1) 0
atanh(x) inverse hyperbolic tangent atanh(0) 0

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