Big Number Calculator
Add, subtract, multiply, divide or take the modulo of integers of any length. Every digit is kept exactly — nothing is rounded to floating point.
Why Ordinary Calculators Fail on Large Integers
Most calculators, spreadsheets and programming languages store a number in a fixed-width slot. A signed 64-bit integer — the widest common type — stops at 9,223,372,036,854,775,807. Past that, one of two things happens, and both are silent.
Overflow: the value wraps around. Add 1 to the maximum and you get the most negative number instead of a larger one. Precision loss: the value is converted to floating point, which keeps about 15–17 significant digits and discards the rest. This is why a spreadsheet shows 1.23456789012346E+19 — that is not your number rounded for display, it is your number rounded in storage. The lost digits are gone.
Arbitrary-precision arithmetic sidesteps both problems by storing every digit explicitly and carrying between them the way you would on paper. It is slower, but it is exact at any size.
Integer Limits by Type
| Type | Maximum value | Digits |
|---|---|---|
| 32-bit signed (int) | 2,147,483,647 | 10 |
| 32-bit unsigned (uint) | 4,294,967,295 | 10 |
| JavaScript safe integer | 9,007,199,254,740,991 | 16 |
| 64-bit signed (long) | 9,223,372,036,854,775,807 | 19 |
| 64-bit unsigned (ulong) | 18,446,744,073,709,551,615 | 20 |
| Arbitrary precision | limited only by memory | any |
Where Big Integers Actually Come Up
Factorials
Factorials outgrow hardware types almost immediately. 20! is 2,432,902,008,176,640,000, which still fits in a signed 64-bit integer. 21! is 51,090,942,171,709,440,000 and does not — it overflows. Any combinatorics work past 20 items needs arbitrary precision.
Public-key cryptography
RSA operates on integers the size of the key. A 2048-bit modulus is roughly 617 decimal digits, and every encryption step is a modular exponentiation on numbers that large. Rounding even one digit breaks the maths entirely, so exact arithmetic is not optional.
Money and identifiers
Accounting systems that store amounts in minor units (cents, satoshi) reach large integers quickly at scale, and account numbers, IMEIs and checksums must never be rounded. A single lost digit changes the value, so these are held as exact integers or strings, never as floating point.
Related Calculators
Integer Division and Modulo
Divide here returns the integer quotient with the remainder discarded: 100 ÷ 7 gives 14, not 14.2857. Modulo returns the remainder that divide threw away: 100 mod 7 gives 2. Together they reconstruct the original value, since 14 × 7 + 2 = 100.
That pairing is why modulo appears throughout computing. Hash tables use it to map any key into a fixed number of buckets. Check-digit schemes such as the Luhn algorithm on card numbers and ISBN validation use it to catch typos. Cyclic scheduling uses it to wrap a counter back to zero. In every case the input may be arbitrarily large while the output stays in a small, predictable range — and the result must be exact, which rules out floating point.
| Expression | Result | Note |
|---|---|---|
| 100 ÷ 7 | 14 | remainder discarded |
| 100 mod 7 | 2 | the discarded remainder |
| 264 | 18,446,744,073,709,551,616 | one past the unsigned 64-bit maximum |
| 21! | 51,090,942,171,709,440,000 | overflows a signed 64-bit integer |
