Arbitrary Precision Math
Big Number
Calculator
Exact arithmetic on integers with hundreds of digits. Add, subtract, multiply, divide, factorial, power, GCD, LCM, and primality testing — no rounding, ever.
—
Result Digits
—
Operation
Big Integer Arithmetic
Operation
Factorial (n!)
⚡ n! = n × (n−1) × … × 2 × 1. Values above 1000 may take a moment.
Power (base^exp)
Analyze a Number
Result
Result
🌌 Famous Big Numbers — Click to Load
What Is Arbitrary-Precision Arithmetic?
Regular computer arithmetic uses 64-bit floating-point numbers (IEEE 754), which give about 15–16 significant decimal digits. Beyond that, precision is lost. Arbitrary-precision (bignum) arithmetic stores numbers as sequences of digits with no fixed size limit, giving exact results regardless of magnitude.
Key Facts About Big Numbers
100! = 9.3 × 10^157 (158 digits)
1000! = 4.0 × 10^2567 (2,568 digits)
2^100 = 1,267,650,600,228,229,401,496,703,205,376 (31 digits)
2^1000 has 302 digits
Googol = 10^100 (101 digits: 1 followed by 100 zeros)
Googolplex = 10^(10^100) — more digits than atoms in universe
Why do regular calculators get big numbers wrong?
Standard IEEE 754 double-precision floating-point uses 53 bits for the significand, giving about 15–16 decimal digits of precision. Numbers larger than 2⁵³ (≈ 9 × 10¹⁵) lose integer precision — JavaScript's Number type shows 9007199254740993 and 9007199254740992 as the same value. JavaScript's BigInt type (used here) stores integers exactly with no size limit.
How fast do factorials grow?
Factorials grow faster than exponential functions. By Stirling's approximation: log₁₀(n!) ≈ n·log₁₀(n) − n·log₁₀(e) + ½·log₁₀(2πn). So n! has approximately n·log₁₀(n/e) digits. Notable milestones: 10! = 3.6 million (7 digits), 100! has 158 digits, 1,000! has 2,568 digits, 10,000! has 35,660 digits, 1,000,000! has over 5 million digits.
What is a googol and googolplex?
A googol is 10¹⁰⁰ — a 1 followed by 100 zeros. It was coined by 9-year-old Milton Sirotta in 1920, nephew of mathematician Edward Kasner. A googolplex is 10^(googol) = 10^(10¹⁰⁰). It cannot be written in decimal even if every atom in the observable universe (≈ 10⁸⁰) were a digit — the universe isn't big enough. Google's name is a misspelling of googol.
Where are big numbers used in computing?
Cryptography is the biggest use — RSA encryption uses prime numbers with 2048+ bits (about 617 decimal digits). The security relies on the difficulty of factoring a product of two large primes. Hash functions output 256-bit numbers. Blockchain addresses are derived from 256-bit keys. Scientific computing uses arbitrary precision for problems requiring exact results — computing π to trillions of digits, verifying mathematical conjectures, etc.