Factorial Calculator
Enter any non-negative integer n to calculate n! instantly.
Supports integer values from 0 to 5000. For very large inputs, the result can contain thousands of digits.
What Is a Factorial?
The factorial of a number is written as n! and means “multiply all positive integers from 1 up to n.” For example:
- 5! = 5 × 4 × 3 × 2 × 1 = 120
- 7! = 5040
- 10! = 3,628,800
One special case matters a lot: 0! = 1. This is not a typo—it's a foundational rule used throughout algebra, combinatorics, and probability.
How This Factorial Calculator Works
This tool takes your input and checks that it is a whole number greater than or equal to zero. It then computes factorial using a loop and JavaScript BigInt, which allows exact integer math far beyond normal number limits.
What You Get
- The exact value of n!
- Total number of digits in the result
- Trailing zero count (useful in number theory and exam prep)
Why Factorials Matter
1) Counting Arrangements (Permutations)
If you have n unique items, there are n! ways to order them. That makes factorials central in scheduling, ranking problems, and puzzle design.
2) Combinations and Probability
The common combinations formula uses factorials: nCr = n! / (r!(n-r)!). This appears in statistics, machine learning, and card/game probability problems.
3) Series and Calculus
Factorials appear in Taylor and Maclaurin series (for example, expansions of ex, sin, and cos), making them essential in numerical methods and engineering calculations.
Common Mistakes to Avoid
- Using negative numbers: standard factorial is not defined for negatives.
- Using decimals: factorial calculator expects whole numbers (0, 1, 2, ...).
- Forgetting 0!: by definition, 0! = 1.
- Underestimating growth: factorial values grow extremely fast; even 20! is already huge.
Quick Reference Values
- 0! = 1
- 1! = 1
- 2! = 2
- 3! = 6
- 4! = 24
- 5! = 120
- 10! = 3,628,800
- 15! = 1,307,674,368,000
FAQ
Can I compute very large factorials like 1000!?
Yes. This calculator supports up to 5000!, and displays the exact integer result using BigInt.
Why does my result have so many zeros at the end?
Trailing zeros come from factors of 10, and each 10 is a pair of 2 × 5. In factorials, the count of factor 5s determines the number of trailing zeros.
Is this useful for students?
Absolutely. It’s useful for algebra, probability, permutations/combinations, coding challenges, and competitive exams.
Final Thought
A factorial calculator is simple on the surface, but behind it is one of the most important building blocks in mathematics. Use this page to check homework, verify formulas, or explore how rapidly growth accelerates in discrete math.