The remainder after division
The modulo operation gives what is left over after dividing one whole number by another. Seventeen divided by five is three with two to spare, so 17 mod 5 is 2. This calculator returns that remainder, the floored quotient, and tells you whether the division comes out even.
Modulo and the quotient
Every division satisfies a = n times q plus r, where q is the quotient and r the remainder. The calculator reports the least non-negative remainder — the clock-style answer between 0 and n minus 1 — and also the programming-style result that takes the sign of the dividend, since the two differ for negatives.
Where modulo shows up
It is the math of anything that cycles: clock times, days of the week, wrapping around an array, and checking divisibility. A number is even exactly when it mod 2 is 0, and divisible by 9 when its digit sum mod 9 is 0.
Related tools
For converting between number systems, use the base converter; for common divisors, the GCD and LCM calculator.
Worked example
17 mod 5: five goes into seventeen three times (15), leaving 2. So the remainder is 2 and the quotient is 3, since 17 = 5 times 3 + 2.
FAQ
How is a negative dividend handled?
The headline uses the least non-negative remainder, so -17 mod 5 is 3. The programming-style row shows -2 instead, matching how most languages compute the percent operator.
What if the divisor is zero?
Division by zero is undefined, so the calculator asks for a non-zero divisor.