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Math · Live

Big Number Calculator — arbitrary-precision arithmetic.

Perform exact arithmetic on integers with up to 1,000 digits. Add, subtract, multiply, divide, raise to a power, and compute GCD or LCM, all powered by JavaScript's native BigInt, with no rounding error.

How it worksReal-time

Inputs

Big integers

A × B

Limits

Max digits per input1,000
Max result digits50,000
Max exponent (^ op)9,999

Multiply

40 digits · positive

40 digits

999999999999999…000000000001

Digits
40
Sign
Positive
Parity
Odd
Trailing 0s
0

Full result

40 digits, grouped by 10 for readability.

9999999999 9999999998 0000000000 0000000001

Digit sum

180

Sum of all decimal digits

Trailing zeros

0

Consecutive zeros at the end

JS Number safe?

No

Requires BigInt for exact arithmetic

Field guide

Why regular calculators fail on large numbers.

JavaScript (and most programming languages) represents numbers using the IEEE 754 double-precision floating-point standard. That standard can store at most 53 bits of integer precision, which corresponds to values up to:

Number.MAX_SAFE_INTEGER = 2⁵³ − 1 = 9,007,199,254,740,991

Any integer larger than this cannot be represented exactly in a standard JavaScript Number. The arithmetic appears to work, but the results silently round to the nearest representable value — introducing errors that can be catastrophic in financial, cryptographic, or scientific applications.

What is BigInt?

BigInt is a native JavaScript type, introduced in ES2020, that supports arbitrarily large integers with exact precision. It stores integers as variable-length data (like a library such as GNU MP, but built into the engine) and performs all arithmetic exactly, regardless of size.

This calculator uses BigInt exclusively. The result of multiplying two 1,000-digit numbers is always exact — there is no floating-point rounding, no overflow, no silent approximation.

Supported operations

  • Addition (A + B): exact, always. The result can have at most one more digit than the longer operand.
  • Subtraction (A − B): exact. Works for positive and negative integers.
  • Multiplication (A × B): exact. The result can have up to sum of digits digits (e.g., a 500-digit × 500-digit multiplication can produce up to 1000 digits).
  • Integer division (A ÷ B): truncates toward zero, like C and Java's integer division. The remainder is also shown.
  • Modulo (A mod B): the remainder of integer division; carries the same sign as A.
  • Exponentiation (A ^ B): A raised to a non-negative integer power B. B is capped at 9,999 and the result is capped at 50,000 digits to prevent browser freezing.
  • GCD: greatest common divisor, computed via the Euclidean algorithm. Fast even for 1,000-digit inputs.
  • LCM: least common multiple, computed as LCM(A, B) = |A × B| / GCD(A, B).

Where big-integer arithmetic matters

  • Cryptography: RSA encryption uses numbers with hundreds of digits. The key generation and encryption/ decryption operations require exact modular arithmetic on numbers far beyond IEEE 754 range.
  • Factorials and combinatorics: 100! has 158 digits; 1000! has 2,568 digits. Exact computation of large factorials is only possible with arbitrary precision.
  • Number theory: primality tests, GCD computations, and modular exponentiation all require integer precision.
  • Financial computing: transactions in some systems are stored as integers (e.g., satoshis in Bitcoin, basis points in bond pricing) to avoid floating-point errors.
  • Competitive programming: many algorithm contests require computing large Fibonacci numbers, power series coefficients, or combinations exactly.

Digits and the growth of large numbers

The number of decimal digits in a number n is:

digits(n) = ⌊log₁₀(n)⌋ + 1

This means the number of digits grows slowly relative to the value:

  • 10 has 2 digits
  • 1,000 has 4 digits
  • 10^100 (a googol) has 101 digits
  • 2^1000 ≈ 10^301 has 302 digits
  • 1000! has 2,568 digits

But exponential growth is fast — 2^9999 has 3,010 digits, and 999^9999 has approximately 30,000 digits.

Performance and limits

Modern JavaScript engines (V8, SpiderMonkey) implement BigInt using efficient algorithms:

  • Addition and subtraction are O(n), linear in the number of digits. Always instant.
  • Multiplication uses Karatsuba or Toom-Cook algorithms, running in roughly O(n^1.6) — very fast for up to a few thousand digits.
  • Exponentiation uses repeated squaring (binary exponentiation), so A^B requires about log₂(B) multiplications. The bottleneck is the size of the result, not B itself. This calculator estimates the result size before computing and cancels if it would exceed 50,000 digits.
  • GCD uses the Euclidean algorithm, which converges very quickly (in O(n) iterations where n = digits).

Tips for using this calculator

  • Paste numbers directly from other applications — the calculator strips spaces, commas, and underscores automatically.
  • Use the Copy button to copy the raw result (no formatting spaces) for use in code or other tools.
  • For the power operation, keep the result size in mind: computing 10^9999 takes milliseconds (it's a 1 followed by 9999 zeros), but computing 999^5000 produces a ~15,000-digit number and takes a bit longer.
  • Negative numbers are supported — type a minus sign at the beginning of either field.