Large Number Modulo Calculator

Handle huge inputs across bases two through thirty‑six. Choose Euclidean or truncated remainder for negative values. Paste numbers or upload CSV for high‑volume batch jobs. Accurate streaming arithmetic avoids overflow and preserves exactness. Export results, detailed audit trails, and logs as CSV or PDF anytime easily. Built for accuracy, speed, and dependable workflows everywhere.

Enter Values

Separators allowed: spaces, commas, underscores. Case-insensitive for bases > 10.

Formula Used

The remainder r of dividing an integer N by a nonzero M is:

r = N − M ⌊N / M⌋.

We compute N mod |M| by streaming digits in the selected base: rem = (rem × base + digit) mod |M|. This avoids overflow and matches exact arithmetic.

Conventions:

  • Euclidean: remainder in [0, |M|−1], independent of sign of N.
  • Truncated: remainder has the sign of N, magnitude < |M|.

How to Use

  1. Enter N and choose its base.
  2. Enter M and choose its base.
  3. Select Remainder Convention as needed.
  4. Click Compute Remainder to calculate precisely.
  5. Use CSV importer for batch jobs, then export results.

CSV Import (Streaming)

Columns: N,M,[baseN],[baseM],[convention]. Convention is euclid or trunc. Up to 10,000 rows processed line‑by‑line.

Results History

# Time Digits N (truncated) baseN M baseM Convention Remainder Method
No results yet. Compute something to populate history.

Example Data

Try these to verify correctness and base handling:

NbaseNMbaseMConventionExpected Remainder
123456789123456789123456789109710euclid83
FFFFFFFFFFFFFFFFFFFF16100000316euclid1048061
1011011101110001112101012euclid9
314159265358979323846264338327950288419716939937510103B9ACA0716euclid266635010
-12345678901234567890101110trunc-1
-12345678901234567890101110euclid10

FAQs

N can contain thousands of digits. Streaming arithmetic processes digits without overflow in any base.

Yes with BCMath or GMP. Without them, the fallback requires |M| within native integer range after base conversion.

Yes. Choose Euclidean to get nonnegative remainders, or Truncated to match C‑style sign rules.

Digits and A–Z for bases above 10, plus an optional leading sign. Separators are stripped automatically.

The table previews N for readability. The CSV and PDF exports include full values for N and more columns.

It demonstrates exact arithmetic for large values and bases. For production cryptography, use vetted, constant‑time libraries.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.