Modular Arithmetic Calculator

Run modulo operations, find inverses, compute powers mod n, and solve systems with the Chinese Remainder Theorem. Results include step-by-step working so you see how each answer is derived.

Result

Pick an operation and enter values, then tap Calculate.

Step-by-step

Steps appear here after a calculation.

Properties

Properties appear here after a calculation.

What this tool does

Modular arithmetic works with remainders after division by a fixed modulus. You get congruences (e.g. 17 ≡ 5 (mod 12)), basic operations mod m, modular inverse when it exists, fast exponentiation mod m, and the Extended Euclidean algorithm for GCD and Bézout coefficients. The Chinese Remainder Theorem solves systems of congruences with pairwise coprime moduli.

Use it for number theory, crypto basics, or checking remainders without hand work.