Modular Multiplicative Inverse
Modular Multiplicative Inverse with stated conventions, validation and a worked example.
Formula
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- Exact integer arithmetic uses BigInt. Enter signed decimal integers of at most 200 digits unless a different limit is stated. Decimal approximations are explicitly labelled.
Example Calculation
- Integer a: 3
- Modulus m: 11
3×4=12≡1 (mod 11), so the inverse is 4.
Frequently asked questions
How do I use this calculator?
Enter integer a, modulus m. The result updates automatically. Use Reset to restore the example values.
What method does it use?
Find x with ax≡1 (mod m) using the extended Euclidean algorithm.. Exact integer arithmetic uses BigInt. Enter signed decimal integers of at most 200 digits unless a different limit is stated. Decimal approximations are explicitly labelled.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.