Chinese Remainder Calculator
Chinese Remainder 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. Non-coprime moduli are supported when the congruences are compatible.
Example Calculation
- Residue a: 2
- Modulus m: 3
- Residue b: 3
- Modulus n: 5
x≡2 mod3 and x≡3 mod5 give x=8+15k, for any integer k.
Frequently asked questions
How do I use this calculator?
Enter residue a, modulus m, residue b, modulus n. The result updates automatically. Use Reset to restore the example values.
What method does it use?
Solve x≡a (mod m), x≡b (mod n); consistency requires gcd(m,n) to divide b−a.. 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. Non-coprime moduli are supported when the congruences are compatible.
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.