High-Precision Combinatorics Engine
Factorial Calculator
Calculate exact arbitrary-precision factorials, permutations (nPr), combinations (nCr), and double factorials (n!!) with zero rounding errors.
Input Values
Quick Presets:
Active Mathematical Formula:
n! = n × (n - 1) × (n - 2) × ... × 1 (0! = 1)
Exact Computed Result
7 digits
10! =
3628800
Total Digits
7
Trailing Zeros
2
Expanded Multiplication:
1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10
Runs locally with Native JavaScript BigInt. Uncapped integer precision.
Factorial Combinatorics Reference
Why is 0! = 1?
There is exactly 1 way to arrange zero objects (the empty set). Mathematically, from n! = (n+1)! / (n+1), 0! = 1! / 1 = 1.
Permutations vs Combinations
Permutations care about order (race finishes, passwords). Combinations ignore order (card hands, team rosters).
Stirling's Formula
For astronomical numbers, Stirling's approximation n! ≈ √(2πn) × (n/e)ⁿ gives accurate estimates of magnitude and digits.