Factorial Calculator: Calculate n! & Double Factorial
Calculate exact factorials (n!) and double factorials with BigInt.
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How to Use the Factorial Calculator: Calculate n! & Double Factorial
- 1Enter a non-negative integer (e.g. 5, 20, 100).
- 2View the exact calculated factorial immediately.
- 3Review the total digit length and double factorial (n!!).
- 4Copy the complete digits or scientific notation.
Formula & How It Works
Factorial Definition
n! = Product of all positive integers from 1 up to n. 0! = 1 by mathematical definition.
Worked Examples
Small Factorial
Input: 5!
Explanation: 5 * 4 * 3 * 2 * 1 = 120.
Ten Factorial
Input: 10!
Explanation: 10 * 9 * ... * 1 = 3,628,800.
Double Factorial
Input: 7!!
Explanation: 7 * 5 * 3 * 1 = 105.
Frequently Asked Questions
What is a factorial?▼
The factorial of a non-negative integer n is the product of all positive integers less than or equal to n.
Why is 0 factorial equal to 1?▼
0! = 1 represents the empty product (the number of ways to arrange zero items is exactly 1).
What is a double factorial (n!!)?▼
A double factorial multiplies only integers with the same parity (e.g. 7!! = 7*5*3*1; 8!! = 8*6*4*2).
What is 52! in card shuffling?▼
52! is approximately 8.0658 × 10⁶⁷, meaning every fair shuffle of a 52-card deck produces a sequence that has likely never existed before.
Can I calculate 100!?▼
Yes, our calculator uses JavaScript BigInt to compute 100! (a 158-digit number) instantly without rounding.
Is this tool free?▼
Yes, Toolzy math tools are 100% free and run client-side.
Quick Reference & Conversion Table
| n | Factorial (n!) | Double Factorial (n!!) | Total Digits |
|---|---|---|---|
| 1 | 1 | 1 | 1 digit |
| 5 | 120 | 15 | 3 digits |
| 10 | 3,628,800 | 3,840 | 7 digits |
| 15 | 1,307,674,368,000 | 2,027,025 | 13 digits |
| 20 | 2,432,902,008,176,640,000 | 3,715,891,200 | 19 digits |
⚠️ Common Pitfalls to Avoid
- •Assuming 0! is 0 (by mathematical definition, 0! = 1).
- •Using standard 64-bit floats that overflow to Infinity above 170! (our BigInt handles exact values).
💡 Practical Real-World Uses
- •Calculating permutations and combinations in statistics and probability.
- •Determining deck of cards shuffle possibilities (52! ≈ 8.0658 × 10⁶⁷).
- •Taylor series polynomial expansion in calculus.
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