Modulo Calculator (remainder)
Find the remainder and quotient of a division (a mod b).
Result
Remainder (a mod b)
2.0000
Quotient
3
How it works
The modulo operation returns what is left after a division. Euclidean division writes a = quotient × b + remainder, with the remainder between 0 and b−1: for 17 mod 5, since 17 = 3×5 + 2, the quotient is 3 and the remainder 2. Modulo powers anything that cycles. Hours wrap modulo 12 or 24 — 10 o'clock plus 5 hours is (10+5) mod 12 = 3 o'clock. Days of the week cycle modulo 7, and a remainder of 0 is precisely what "divisible" means, which gives instant divisibility tests. In programming it is everywhere: n mod 2 distinguishes even from odd, mod distributes items into a fixed number of buckets (hashing), and mod k makes any counter loop back to 0 after k steps. Note that languages differ on negative numbers — some return −3 mod 5 as 2, others as −3.
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Frequently asked questions
What is 17 mod 5?
2 — because 17 = 3×5 + 2.
What if the divisor is 0?
Division by zero is undefined, so the result is shown as 0.
What are everyday uses of modulo?
Anything cyclic: clock arithmetic (hours mod 12), weekday calculations (mod 7), even/odd checks (mod 2), divisibility tests (remainder 0), and spreading items evenly into groups.
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