Modular inverse calculator

Client

Find x such that a·x ≡ 1 (mod m) when gcd(a,m)=1. Common in RSA key math, competitive programming, and cryptography homework.

How to use

Enter integer a and modulus m. The result is x with a·x ≡ 1 (mod m) when coprime.

About Modular inverse calculator

Compute the modular multiplicative inverse with the extended Euclidean algorithm—in your browser. The interactive transform on this page runs in your browser tab—Toolcore does not need your paste for the core operation described above.

How to use this page

Paste or type in the main workspace, run the primary action from the toolbar, then copy or download the result. Use Load example when the page offers it, or URL prefill (?q= / ?qb=) so agents and tickets open the same input.

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Nearby workflows on Toolcore

  • Modulo calculator — Integer remainder and truncated quotient (a mod b)—BigInt math in your browser. when units or numeric output should be checked on a related calculator.
  • GCD & LCM calculator — Greatest common divisor and least common multiple for two non-negative integers—BigInt, local only. when units or numeric output should be checked on a related calculator.
  • Modular exponentiation — Fast modular power a^b mod m for large exponents—binary exponentiation in the browser. when units or numeric output should be checked on a related calculator.
  • Math expression evaluator — Evaluate basic + − × ÷ arithmetic with parentheses in your browser—no variables. when units or numeric output should be checked on a related calculator.

Common use cases

  • Verify hand calculations for modular inverse in discrete math.
  • Check whether two numbers are coprime before running RSA-style exercises.

Common mistakes to avoid

  • Modulus 1

    Every residue mod 1 is 0—there is no useful inverse.

FAQ

What if no inverse exists?

When gcd(a,m)≠1 the tool reports that no inverse exists.

Is data uploaded?

No—all arithmetic runs locally.

More tools

Related utilities you can open in another tab—mostly client-side.