Modular Arithmetic Calculator (mod, Inverse & More)

Use this free modular arithmetic calculator to compute a mod m, modular addition, subtraction, multiplication, fast modular exponentiation, and the modular inverse. Each result comes with clear step-by-step working.

What it does

Pick an operation, enter your integers and a modulus m, and the tool reduces the result into the range 0 to m−1. The modular inverse uses the extended Euclidean algorithm and exists only when gcd(a, m) = 1.

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How to use it

1. Choose the operation (mod, +, −, ×, ^, or inverse).
2. Enter the whole numbers and the modulus.
3. Press Solve for the result and the steps.

More tools: free math calculators.

Frequently asked questions

What is a modular inverse?

The modular inverse of a (mod m) is the value x with a·x ≡ 1 (mod m). It exists only when gcd(a, m) = 1.

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How is modular exponentiation computed?

By fast square-and-multiply, which keeps the numbers small even for large exponents.

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Does it handle negative numbers?

Yes — the result is always reduced to the standard range 0 to m−1.

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