Modular Multiplication Calculator

About this calculator

Modular multiplication computes (a × b) mod m — first multiply the two integers normally, then take the remainder after dividing by the modulus m. It behaves like ordinary multiplication but 'wraps around' once the product passes a multiple of m, the same way a 12-hour clock wraps 13 o'clock back to 1.

This operation is a core building block of modern cryptography: RSA encryption and decryption are, at their core, repeated modular multiplications carried out on very large numbers, and Diffie-Hellman key exchange relies on the same operation to make key derivation easy to compute forward but hard to reverse. It also underlies hash functions, pseudorandom number generators, and check-digit schemes like the ISBN or credit card Luhn check, and it is a standard early topic in discrete mathematics and number theory courses because it introduces students to arithmetic that does not behave like ordinary integer arithmetic.

Enter integers a and b and a modulus m, and the calculator computes (a × b) mod m.