Modular Addition Calculator

About this calculator

Modular addition computes (a + b) mod m — the remainder left after dividing the ordinary sum a + b by the modulus m — and always returns a normalized result in the range 0 to m−1, no matter how large or negative a and b are. It follows the familiar rule of "wrapping around" once the sum reaches m, exactly like a clock face wraps from 12 back to 1.

This operation is the basis of modular arithmetic, taught alongside congruences in number theory, and it underlies practical systems from clock and calendar arithmetic to cyclic redundancy checks, hash table indexing, and cryptographic algorithms such as RSA and elliptic-curve schemes, where all arithmetic is deliberately confined to a fixed modulus.

Enter any two integers and a positive modulus m to get the normalized sum (a + b) mod m, computed directly from the definition.