Modular Inverse Calculator

About this calculator

This calculator finds the modular multiplicative inverse of a number a modulo m — the value x such that a·x ≡ 1 (mod m) — using the extended Euclidean algorithm. An inverse exists only when gcd(a, m) = 1, i.e. a and m are coprime.

Cryptography engineers and computer science students use modular inverses constantly in RSA key generation (finding the private exponent d from the public exponent e), Diffie–Hellman variants, and other modular-arithmetic algorithms; they're also a standard topic in number theory courses. Enter a and m to get the inverse, or a note that none exists.