Calculate Factorial (n!)
Enter a non-negative integer (0-170):
Calculation Result
Step-by-Step Calculation
Factorial Calculator Solver: Quickly Calculate Factorials Online
Our free factorial calculator tool helps you instantly compute factorials of any non-negative integer. Whether you're a student learning combinatorics, a programmer debugging code, or a math enthusiast exploring number properties, this factorial solver provides accurate results with detailed explanations.
Our free factorial calculator tool helps you instantly compute factorials of any non-negative integer. Whether you're a student learning combinatorics, a programmer debugging code, or a math enthusiast exploring number properties, this factorial solver provides accurate results with detailed explanations.
What is a Factorial in Mathematics?
The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. Factorials play a crucial role in combinatorics, probability theory, algebra, and many other mathematical disciplines.
Factorial Formula
The factorial formula is defined as:
n! = n × (n-1) × (n-2) × ... × 3 × 2 × 1
By definition, the factorial of 0 is 1 (0! = 1).
Practical Applications of Factorials
Factorials are essential in various mathematical and real-world applications:
- Combinatorics: Calculating permutations and combinations
- Probability: Determining possible outcomes in complex events
- Algebra: Used in binomial theorem and series expansions
- Calculus: Appearing in Taylor series and other expansions
- Computer Science: Algorithm analysis, particularly recursive functions
How to Use Our Factorial Calculator
Our factorial calculator solver is designed for simplicity and educational value:
- Enter any non-negative integer (from 0 to 170) in the input field
- Click the "Calculate Factorial" button
- View the result with a detailed explanation
- Examine the step-by-step calculation process
- Use the reset button to perform new calculations
Frequently Asked Questions About Factorials
Why is 0! equal to 1?
The value of 0! is defined as 1 based on these mathematical reasons:
- It maintains consistency with the combinatorial interpretation where there's exactly one way to arrange zero objects.
- It preserves the multiplicative identity in various mathematical formulas.
- It aligns with the gamma function where Γ(1) = 1, and n! = Γ(n+1).
What is the largest factorial this calculator can compute?
Our factorial calculator can compute factorials up to 170! (170 factorial). Beyond this value, numbers exceed JavaScript's maximum floating point precision, resulting in Infinity. 170! is approximately 7.26 × 10306, an astronomically large number with 309 digits.
How are factorials used in real-world applications?
Factorials have practical applications in:
- Statistics: Calculating binomial coefficients and probabilities
- Computer Algorithms: Analyzing complexity of recursive functions
- Physics: Quantum mechanics and statistical mechanics calculations
- Operations Research: Solving optimization and scheduling problems
What is the difference between permutations and combinations?
Permutations and combinations both deal with selecting items from a collection:
- Permutations consider the order of selection (nPr = n!/(n-r)!)
- Combinations do not consider order (nCr = n!/[r!(n-r)!])
Both rely heavily on factorial calculations.
