Calculator Uni

Modulo Calculator

Find remainders with correct handling of negative numbers.

a mod n

-17 mod 5

3

JavaScript % operator gives

-2

Quotient (floored)

-4

Clock arithmetic

Modulo keeps the remainder after division — 17 mod 5 is 2, and clocks are mod 12: 9 + 5 o'clock wraps to 2. The mathematical convention keeps results in 0…n−1 even for negatives: −17 mod 5 is 3, since −17 = −4×5 + 3.

The negative-number trap

Most programming languages' % operator returns −2 for −17 % 5, following the dividend's sign — a classic off-by-wrap bug in calendars and array indexing. The fix shown here, ((a % n) + n) % n, is a rite of passage.

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