Modular Arithmetic Calculator
Calculate exact modular powers or inverses for bounded whole numbers.
Loading tool…
How to use Modular Arithmetic Calculator
Binary square-and-multiply computes powers efficiently; extended Euclid finds an inverse only for coprime operands.
- Enter integer value, modulus, nonnegative exponent.
- Check the model, units, and supported limits before calculating.
- Run the tool, inspect the result, then copy or download it.
Good to know
- Integer magnitudes at most 1e12, modulus at least two, exponent 0–1e12. Exact BigInt arithmetic; no cryptographic key-generation service.
- Runs locally. Numeric inputs are bounded; floating-point output is approximate and rounded to 12 significant digits. Unsupported or non-finite calculations produce an error.
Common questions
How does Modular Arithmetic Calculator calculate its result?
Binary square-and-multiply computes powers efficiently; extended Euclid finds an inverse only for coprime operands.
What assumptions and boundaries apply?
Integer magnitudes at most 1e12, modulus at least two, exponent 0–1e12. Exact BigInt arithmetic; no cryptographic key-generation service.
Keep going with related tools
All math →Integer Factorization Calculator
Factor a bounded positive integer into exact prime powers and verify reconstruction.
MathChinese Remainder Theorem Calculator
Solve compatible residue and modulus pairs, including noncoprime moduli.
MathPrime Number Checker
Determine primality for whole numbers up to 4,294,967,295 using bounded deterministic testing.
MathPrime-field Linear System Workbench
Solve a rectangular modular system and preserve inconsistent, unique and affine-family outcomes with exact solution witnesses.