Modulo Calculator

a mod n is the amount left over after dividing a by n as many whole times as possible: 17 mod 5 = 2, because 5 fits into 17 three times (15) with 2 left over. Modulo powers clock arithmetic (23:00 + 5 hours is 4:00, i.e. (23+5) mod 24), hashing, and divisibility tests.

Languages disagree. Truncated division (C, Java, JavaScript %) gives −7 mod 3 = −1 — the remainder takes the dividend's sign. Floored or Euclidean division (Python, mathematics) gives 2, always non-negative. Both are shown so you can match whichever convention your context uses.

Deciding if a number is even (n mod 2 = 0), rotating schedules (day-of-week math is mod 7), checking divisibility, wrapping array indices, converting units (total inches mod 12 = remaining inches), and cryptography — RSA is built almost entirely on modular exponentiation.