Factorial Calculator
Calculate the factorial of any non-negative integer. The factorial of a number n (denoted as n!) is the product of all positive integers less than or equal to n. This calculator supports large numbers, displays step-by-step multiplication, and includes a factorial reference table.
What Is a Factorial?
The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n.
n! = n × (n − 1) × (n − 2) × ... × 2 × 1
For example: 5! = 5 × 4 × 3 × 2 × 1 = 120
By definition, 0! = 1 (the empty product).
Factorial Values for Common Numbers
- 0! = 1
- 1! = 1
- 2! = 2
- 3! = 6
- 4! = 24
- 5! = 120
- 6! = 720
- 7! = 5,040
- 8! = 40,320
- 9! = 362,880
- 10! = 3,628,800
- 20! = 2.43 × 10¹⁸
- 50! = 3.04 × 10⁶⁴
- 100! = 9.33 × 10¹⁵⁷
Applications of Factorials
- Permutations: The number of ways to arrange n items is n!.
- Combinations: The number of ways to choose k items from n is n! / (k! × (n−k)!).
- Probability: Factorials are used in many probability formulas.
- Statistics: Factorials appear in distributions like the Poisson distribution.
- Computer Science: Factorials are used in algorithm analysis and recursive functions.
Why Use This Factorial Calculator?
- Large Numbers: Calculate factorials up to 1,000! with full precision.
- Step-by-Step: See the multiplication process for any number.
- Factorial Table: Quickly reference factorial values up to your input number.
- Visual Growth: Understand how fast factorial grows with a logarithmic chart.
- Free & Private: No registration, no data storage.
❓ Factorial Calculator FAQ
What is a factorial?
A factorial (n!) is the product of all positive integers from 1 to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.
What is 0! (zero factorial)?
By definition, 0! = 1. This is the empty product and is used in many mathematical formulas.
How large can factorial values get?
Factorials grow extremely fast. 10! = 3.6 million, 20! = 2.4 × 10¹⁸, 50! = 3.0 × 10⁶⁴, and 100! = 9.3 × 10¹⁵⁷.
What is the largest factorial this calculator can compute?
This calculator can compute factorials up to 1,000! using JavaScript's BigInt for exact integer arithmetic.
What are trailing zeros in a factorial?
Trailing zeros are the number of zeros at the end of a factorial. For example, 10! = 3,628,800 has 2 trailing zeros. The number of trailing zeros in n! is the number of times 10 divides n!, which is determined by the number of factors of 5.
What is the difference between factorial and double factorial?
A double factorial (n!!) is the product of every other integer. For example, 7!! = 7 × 5 × 3 × 1 = 105. This calculator computes the regular factorial (n!).
Can factorial be defined for negative numbers?
The factorial function is not defined for negative integers in the traditional sense. However, the gamma function extends the factorial to all real numbers except negative integers.
How are factorials used in probability?
Factorials are used in permutations (n!) and combinations (n! / (k! × (n−k)!)), which are fundamental to probability theory.
Is this calculator free?
Yes, this calculator is completely free to use. No registration or personal data storage is required. All calculations are performed in your browser.