Factorial Calculator
Enter a non-negative integer and instantly compute its factorial (n!). This tool uses high-precision arithmetic for large values.
What does “calcula factorial” mean?
“Calcula factorial” means “calculate factorial.” In mathematics, the factorial of a number is one of the most common operations used in combinatorics, probability, and computer science. It is written with an exclamation mark: n!.
The definition is simple:
- 0! = 1 (by definition)
- 1! = 1
- n! = n × (n-1) × (n-2) × ... × 2 × 1 for n ≥ 2
Quick examples
Small values
- 3! = 3 × 2 × 1 = 6
- 5! = 5 × 4 × 3 × 2 × 1 = 120
- 7! = 5040
Reference table
| n | n! |
|---|---|
| 0 | 1 |
| 1 | 1 |
| 2 | 2 |
| 3 | 6 |
| 4 | 24 |
| 5 | 120 |
| 6 | 720 |
| 10 | 3,628,800 |
Why factorials matter
Factorials appear anywhere we count arrangements, orders, or combinations. If you have 5 distinct books and want to know how many ways they can be arranged on a shelf, the answer is 5! = 120.
In probability, factorials are essential for formulas like permutations and combinations:
- Permutations: P(n, r) = n! / (n-r)!
- Combinations: C(n, r) = n! / (r!(n-r)!)
How this factorial calculator works
Input rules
- You must enter a whole number (integer).
- The value must be non-negative (0 or greater).
- Very large values are capped to keep the calculator fast and usable.
High-precision output
Factorials grow very quickly. For example, 20! is already 2,432,902,008,176,640,000. Standard floating-point math can lose precision for large numbers, so this calculator uses exact big-integer arithmetic.
Common mistakes when calculating factorial
- Forgetting 0! = 1: this is one of the most frequent errors.
- Using decimals: factorial in this basic form is defined for whole numbers.
- Mixing up formulas: combinations and permutations both use factorials, but in different arrangements.
Practical study tips
If you are learning algebra, statistics, or discrete math, try these steps:
- Memorize factorial values from 0! through 10!.
- Practice reducing expressions like 9!/7! before multiplying everything.
- Check units in probability problems to ensure the formula matches the question.
Final thoughts
A reliable “calcula factorial” tool saves time, reduces arithmetic mistakes, and helps you focus on understanding concepts. Use the calculator above whenever you need fast, exact factorial results for homework, coding, analytics, or exam prep.