MOD

Return the remainder of dividing one number by another (truncated division, sign follows dividend).

Syntax

MOD(dividend, divisor)

Description

## Overview Returns the remainder of dividing the dividend by the divisor using truncated division: the quotient is truncated toward zero, and the remainder takes the sign of the dividend. This is the convention used by the C / and % operators and by most SQL engines that expose MOD directly. When the non-negative remainder is required (for example, when the output is used as an array or partition index), use PMOD or ((x % d) + d) % d instead. ## Behavior - Accepts any numeric type for both arguments. - Returns a value of the promoted common type. - Returns NULL if either argument is NULL. - Returns NULL (or raises an error, depending on engine) when the divisor is zero. - The sign of the result matches the sign of the dividend: MOD(-10, 3) = -1, MOD(10, -3) = 1. ## Numeric precision - For integer types, MOD is exact. - For DOUBLE, MOD uses fmod semantics: the result is the remainder of the floating-point division truncated toward zero. Results can have surprising rounding for values that are not exactly representable in binary. - For DECIMAL, MOD preserves scale. ## Compatibility - Conforms to the SQL standard scalar function MOD with the truncated-division convention. - Matches the C % operator and typical mathematical library implementations.

Parameters

Name	Type	Description
dividend		Specifies the value to be divided. Accepts any numeric type.
divisor		Specifies the value to divide by. Must be non-zero; a zero divisor returns NULL (some engines raise an error instead).

Examples

-- Basic modulo
SELECT MOD(10, 3);
-- Result: 1

-- Negative dividend: result takes the sign of the dividend
SELECT MOD(-10, 3);
-- Result: -1

-- Negative divisor: result takes the sign of the dividend
SELECT MOD(10, -3);
-- Result: 1

-- Division by zero
SELECT MOD(10, 0);
-- Result: NULL

-- Evenly divisible
SELECT MOD(12, 4);
-- Result: 0

-- NULL propagation
SELECT MOD(NULL, 3);
-- Result: NULL

Pitfalls

• MOD follows the sign of the dividend, not the divisor. MOD(-10, 3) = -1, which is a common source of off-by-one bugs in array-index code. Use PMOD when you need a guaranteed non-negative result.
• Division by zero returns NULL silently in some engines and raises an error in others. Check your engine's behavior if your data can legitimately contain zero divisors.
• MOD on DOUBLE inputs uses fmod semantics and can produce unexpected rounding for non-exactly-representable fractions. Prefer integer or DECIMAL types for exact remainder math.
• MOD does not preserve the sign-of-the-divisor convention used in some mathematics textbooks. If you are porting from a system that follows Knuth's convention, rewrite with ((a % b) + b) % b or PMOD.
• MOD(x, 1) is always 0 for integer x. Use FLOOR(x) or the fractional part x - FLOOR(x) depending on what you really want.

See Also

• pmod
• div
• round
• floor
• ceil