Factorial Calculator
This free factorial calculator allows you to compute the factorial of any non-negative integer n, denoted by n!. Factorials are commonly used in combinatorics, probability, and algebra.
Understanding Factorials
The factorial of a non-negative integer n is the product of all positive integers less than or equal to n.
Formula: n! = n × (n-1) × (n-2) × ... × 3 × 2 × 1
Example: 5! = 5 × 4 × 3 × 2 × 1 = 120
How the Calculator Works
The calculator automatically:
Step 1: Checks if the input is a valid non-negative integer
Step 2: Computes factorial using a JavaScript loop
Step 3: Handles the special case 0! = 1
Step 4: Displays the result instantly
Examples
1. 0! = 1
2. 1! = 1
3. 3! = 6
4. 5! = 120
Why Factorials Matter
Factorials are fundamental in mathematics, especially in combinatorics (permutations and combinations), probability, algebra, and sequences.
Common Mistakes to Avoid
- Entering negative numbers (factorials are undefined for negatives)
- Entering decimals (factorials are defined only for integers in this basic calculator)
- Confusing factorial with exponentiation
Important: Factorials grow extremely fast. For n > 20, results may be very large numbers.
Correct: 0! is defined as 1, not 0.
Frequently Asked Questions
What is 0!?
By definition, 0! = 1.
Can I enter negative numbers?
No. Factorials are only defined for non-negative integers in this calculator.
Can I calculate factorials of large numbers?
Yes, but results may become extremely large and exceed standard display limits for very large n.
Conclusion
Calculating factorials is a key skill in math and science. This calculator provides quick, accurate factorial values for any non-negative integer.