Swift Remainder Operator: Why -9 % 4 Returns -1

Swift’s % operator behaves differently with negative numbers than you might expect.

The Question

9 % 4    // What does this return?
-9 % 4   // What about this?

The Answer

9 % 4    // = 1
-9 % 4   // = -1

Why It Works This Way

The formula: a = (b × multiplier) + remainder

For 9 % 4:

9 = (4 × 2) + 1

For -9 % 4:

-9 = (4 × -2) + -1

The remainder keeps the sign of the dividend (left side).

Remainder vs Modulo

Swift calls % the remainder operator, not modulo. They differ with negative numbers:

Expression	Swift Remainder	Mathematical Modulo
9 % 4	1	1
-9 % 4	-1	3

The Divisor Sign Is Ignored

-9 % 4    // = -1
-9 % -4   // = -1 (same result)

The sign of the right operand has no effect on the result.

Getting True Modulo Behavior

If you need mathematical modulo (always positive result):

func mod(_ a: Int, _ n: Int) -> Int {
    let r = a % n
    return r >= 0 ? r : r + abs(n)
}

mod(-9, 4)  // = 3