This calculator computes the modulo operation, the remainder left after dividing one number by another, along with the quotient. Written as a mod n, the modulo is one of the most useful operations in mathematics and programming, yet it is easy to get wrong by hand, especially with negative numbers. It answers the question: after dividing a by n as many whole times as possible, what is left over? Modulo is the engine behind a huge range of everyday computing and maths: telling whether a number is even or odd, wrapping a value around a clock or a calendar, distributing items into groups, generating cycles and patterns, hashing, and checking divisibility. You enter the dividend, a, and the divisor, n, and the calculator returns the remainder and the quotient. It uses the standard mathematical convention where the remainder has the same sign as the divisor, giving a non-negative result for a positive divisor even when a is negative, which is how mathematicians define modulo and how many programming languages behave, though some differ. The results update as you type. Use it to check programming logic, to work out divisibility and cycles, to solve number-theory problems, or simply to find a remainder quickly without long division. A common use is testing for even or odd: a number is even if a mod 2 is zero. Remember the divisor cannot be zero, since dividing by zero is undefined. The calculation is exact for whole-number inputs.
Uses the mathematical convention: the remainder takes the sign of the divisor (non-negative for a positive n). Divisor cannot be zero.
The quotient is the largest whole number of times the divisor fits into the dividend, rounded toward negative infinity. The remainder is the dividend minus the quotient times the divisor, which leaves a value with the same sign as the divisor. For positive divisors this gives a non-negative remainder between zero and the divisor.
For 17 mod 5, the divisor 5 fits into 17 three whole times (3 times 5 is 15), leaving a remainder of 2. So 17 mod 5 equals 2, with a quotient of 3. For a negative dividend like minus 17 mod 5, the convention gives a remainder of 3 and a quotient of minus 4.
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