Big Number Calculator

Frequently Asked Questions

How does arbitrary-precision arithmetic work?

It uses JavaScript BigInt, which represents integers of unlimited size exactly (no floating-point rounding), so 100! or 2^1000 is computed digit-perfect.

Why can't a normal calculator do this?

Standard numbers are 64-bit doubles with ~15–17 significant digits; beyond 2^53 integers lose precision. BigInt has no such limit (bounded only by memory).

What operations are supported?

Addition, subtraction, multiplication, integer division and modulo, exponentiation, and factorial - all exact, with the result's digit count shown.

What are the limits?

BigInt is integer-only (no fractions/decimals). Extremely large powers/factorials can be slow or memory-heavy, but thousands of digits compute instantly.

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Estimates for informational purposes only.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

JavaScript is required to use the interactive calculator above. The questions and answers below remain readable without JavaScript.

How This Calculator Works

Ordinary JavaScript numbers are IEEE-754 doubles and lose exactness above 2⁵³ − 1 ≈ 9 × 10¹⁵ - 9007199254740993 prints as 9007199254740992. This calculator uses BigInt, an arbitrary-precision integer type limited only by memory, so every digit is exact no matter how large. Each operand is validated as a pure integer string and converted with BigInt(). Addition, subtraction, and multiplication use schoolbook/Karatsuba-style algorithms internally; division and modulo are integer (truncated) operations satisfying a = b·q + r; exponentiation uses fast binary (square-and-multiply) so a^b needs about log₂(b) multiplications; factorial multiplies 1×2×…×n in a loop. Because results can balloon - 10000! has 35660 digits - the tool reports the exact digit count and shows a head…tail preview for enormous outputs so the page stays responsive.

Worked Example: 2¹⁰⁰ and 20!

2¹⁰⁰ = 1267650600228229401496703205376 - 31 digits, far beyond a double's 15–16 reliable digits, yet BigInt returns every digit exactly. 20! = 2432902008176640000 (19 digits), which already overflows a 32-bit and even barely fits a 64-bit integer; 21! = 51090942171709440000 (20 digits) overflows signed 64-bit entirely, but here it is exact. Multiplying two 30-digit numbers such as 123456789012345678901234567890 × 987654321 yields a precise ≈ 39-digit product with no rounding - impossible with floating point, where the low-order digits would silently become zeros. Integer division 100 ÷ 7 returns quotient 14 with 100 mod 7 = 2, satisfying 7×14 + 2 = 100.

Where Big-Integer Math Is Used

Cryptography: RSA keys are 2048–4096-bit integers (600+ digits); every encryption is modular exponentiation on numbers this large.

Combinatorics: permutations and combinations use factorials that explode - 100! has 158 digits.

Number theory: primality testing, factoring, and perfect/Mersenne numbers require exact giant integers.

Finance & ledgers: exact integer cents avoid the rounding drift floating point introduces over millions of transactions.

Common Mistakes & Edge Cases

Entering a decimal point - BigInt is integer-only; this tool rejects non-integer input rather than truncating silently.

Expecting a remainder from the divide operation: use the dedicated modulo operation; integer divide returns only the quotient.

Negative or fractional exponents are undefined for integers - rejected here.

Factorial of a negative number is undefined (the Gamma function extends it, but not as an integer).

Astronomically large powers or factorials can exhaust memory; sane limits (exponent ≤ 100,000, factorial ≤ 50,000) are enforced.

Related Concepts & Limits

BigInt gives exact integers, not arbitrary-precision decimals - for fractional precision you need a decimal/rational library, and for huge factorials Stirling's approximation n! ≈ √(2πn)(n÷e)ⁿ estimates the magnitude when only the digit count matters. Modular exponentiation (the heart of RSA) keeps numbers small by reducing mod n at every step - see the Modulo Calculator. The number of digits of N in base 10 is ⌊log₁₀ N⌋ + 1, which is why factorial digit counts grow roughly like n·log n. This tool is bounded only by browser memory and the printable-size guards above; within those limits every result is mathematically exact, with zero rounding error.

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