When does the difference matter?

Only with negative dividends. -7 mod 5: math = 3 (clock-wraps), JS % = -2.

Modular arithmetic use?

Hashing, cryptography (RSA, ECC), random number generators, cyclic schedules ("every 7th day").

Undefined — division by zero. Calc returns "undefined".

Exists if gcd(a, n) = 1. Computed via extended Euclidean algorithm.

Modulo Calculator (a mod n)

a mod n: remainder of a divided by n. Always non-negative for positive n.

Result

a mod n

17 = 3 × 5 + 2.

a17
n5
a mod n (math)always 0 to n−12
a % n (JS)sign follows a2
Quotient (trunc)3
Quotient (floor)3
Verify3 × 5 + 2 = 17

Step-by-step

a / n = 17 / 5 = 3.4 → floor = 3.
Math mod = a − floor(a/n) × n = 17 − 15 = 2.
JS and math agree (a ≥ 0).

How to use this calculator

Enter a and n.
Read mathematical mod (always 0..n−1) and JS-style mod (signed).

About this calculator

Modulo (a mod n) returns the remainder when a is divided by n. For positive operands: 17 mod 5 = 2 (since 17 = 3 × 5 + 2). For negative dividends, conventions differ: math mod is always non-negative (−7 mod 5 = 3); programmer's remainder follows sign of dividend (-7 % 5 = -2 in JS/C/Java). Used in cryptography, hashing, cyclic structures (clocks, calendars), and array indexing.