Quadratic Equation Solver (ax² + bx + c = 0)
About Factorial Calculator
The Arbitrary-Precision Factorial ($n!$) & Permutations Calculator computes exact integer factorials ($n! = n \times (n-1) \dots 1$), Double Factorials ($n!!$), Multifactorials, Log Factorials ($\ln(n!)$), and Stirling Approximation for huge integers ($n > 10,000$) using JavaScript BigInt.
How to Use Factorial Calculator
Step 1
Enter an integer $n$ (e.g. 100).
Step 2
Select calculation type (Standard $n!$, Double $n!!$, or Derangement $!n$).
Step 3
Review computed exact integer result, digit count, and trailing zero breakdown.
Step 4
Click "Copy Result".
Practical Use Cases for Factorial Calculator
Combinatorics, Probability & Lottery Odds Calculation
Compute total permutations and combinations for probability distributions ($nPr = n! / (n-r)!$, $nCr = n! / (r!(n-r)!)$) without floating-point overflow.
Statistical Mechanics & Quantum Thermodynamic States
Calculate large log factorials using Ramanujan and Stirling formulas for entropy and microstate statistical counting ($S = k_B \ln \Omega$).
Input & Output Examples
Calculating Factorial of 50 (50!)
Number: `n = 50`
Result: `30414093201713378043612608166064768844377641568960512000000000000` (65 Digits, 12 Trailing Zeros)
Key Features & Performance
- ✓Exact BigInt Precision: calculates exact factorials up to $n = 5,000$ without scientific notation truncation.
- ✓Computes: Exact Value, Total Digit Count, Trailing Zero Count (Legendre Formula), $\ln(n!)$, and Stirling Approximation.
- ✓Multi-factorial modes: Standard ($n!$), Double Factorial ($n!!$), and Subfactorial / Derangements ($!n$).
- ✓100% Client-Side arbitrary-precision arithmetic.
- ✓1-Click Copy full number string.
Key Terminology & Definitions
Factorial ($n!$)
The product of all positive integers less than or equal to $n$, with $0! = 1$ by mathematical definition.
Legendre Formula for Trailing Zeros
A formula calculating the exact number of trailing zeros in $n!$: $Z(n!) = \sum_{k=1}^\infty \lfloor n / 5^k \rfloor$.