FACTORIAL

Return the factorial of a non-negative integer.

Category: numericReturns: INTEGERDialect: PostgreSql

Syntax

FACTORIAL(n)

Description

## Overview Returns the factorial of a non-negative integer, defined as n! = n * (n - 1) * ... * 1 with 0! = 1 by convention. FACTORIAL is a closed-form helper for combinatorial calculations in SQL: counting permutations, computing binomial coefficients, and constructing factorial-moment estimators. Because factorials grow extremely fast (21! already exceeds 2^63 - 1), FACTORIAL is defined only up to n = 20. For larger inputs, compute log-factorials via LGAMMA or use arbitrary-precision arithmetic outside SQL. ## Behavior - Accepts a non-negative integer in [0, 20]. - Returns a BIGINT. - Returns NULL if the argument is NULL. - Raises an error for negative inputs and for inputs above 20 (overflow). - FACTORIAL(0) = 1 by convention. ## Numeric precision - All results in the supported range are exactly representable in BIGINT; FACTORIAL is exact. - For inputs above 20, consider computing ln(n!) = LGAMMA(n + 1) and working in log-space. ## Compatibility - Matches the PostgreSQL FACTORIAL scalar function. - The cap at n = 20 reflects the BIGINT representation ceiling shared by most SQL engines that expose a direct factorial function.

Parameters

Name	Type	Description
`n`		Specifies a non-negative integer. Must be in the range 0 to 20 inclusive; values outside this range produce an overflow error because 21! exceeds the BIGINT maximum.

Examples

-- Factorial of 0 is 1 by convention
SELECT FACTORIAL(0);  -- 1

-- Basic literal
SELECT FACTORIAL(5);  -- 120

-- Factorial of 10
SELECT FACTORIAL(10);  -- 3628800

-- Factorial of 1
SELECT FACTORIAL(1);  -- 1

-- Maximum supported value (20! is the largest that fits in BIGINT)
SELECT FACTORIAL(20);  -- 2432902008176640000

-- NULL propagation
SELECT FACTORIAL(NULL);  -- NULL

Pitfalls

FACTORIAL(21) and higher overflow BIGINT and raise an error. For probability formulas that use large factorials, work in log-space with LGAMMA instead.
Negative inputs raise an error. Do not rely on NULL propagation for signed validation; check the sign upstream or clamp with GREATEST.
FACTORIAL is extremely sensitive to small input changes: FACTORIAL(20) is about 2.4e18 while FACTORIAL(10) is 3.6e6. Use it only for small combinatorial ranges.
For binomial coefficients of the form n! / (k! * (n - k)!), computing each factorial separately can overflow when n - k is small. Use a combination-aware function or log-space identity.
FACTORIAL does not accept DECIMAL or DOUBLE input. Cast to INT explicitly if your input has a fractional type even when the value is integer-valued.