**Instructions:**

- Enter a non-negative integer in the input field.
- Click "Calculate Factorial" to calculate the factorial.
- View the result, detailed calculation, and formula.
- Your calculation history will be displayed below.
- Click "Clear Results" to reset the results and history.
- Click "Copy Results" to copy the result and explanation to the clipboard.

**Calculation History:**

## What is Factorial?

In mathematics, the factorial of a non-negative integer “n,” denoted as “n!”, is the product of all positive integers from 1 to “n.” It is a fundamental mathematical operation used in various mathematical and combinatorial calculations. The factorial of 0 is defined to be 1 by convention.

## All Formulae Related to Factorial

**Factorial Formula**:- The factorial of a non-negative integer “n” is calculated as follows:
`n! = n × (n - 1) × (n - 2) × ... × 3 × 2 × 1`

- The factorial of a non-negative integer “n” is calculated as follows:
**Factorial of 0**:- By convention, the factorial of 0 is defined to be 1:Copy code
`0! = 1`

- By convention, the factorial of 0 is defined to be 1:Copy code
**Factorial of 1**:- The factorial of 1 is also 1:
`1! = 1`

- The factorial of 1 is also 1:
**Factorial of a Negative Integer**:- Factorials are not defined for negative integers. The factorial function is only defined for non-negative integers (including zero).

**Factorial Recursion**:- Factorials can be expressed recursively as follows:
`n! = n × (n - 1)!`

- Factorials can be expressed recursively as follows:
**Factorial Properties**:- Factorials have several properties, including:
- Multiplying a factorial by a positive integer “k” results in a new factorial:
`(k × n)! = k! × n!`

- Dividing a factorial by a positive integer “k” results in a new factorial:
`(n / k)! = n! / (n - k)!`

- Factorials grow rapidly with increasing “n.” For large values of “n,” the approximation
`n! ≈ √(2πn) * (n/e)^n`

is used.

- Multiplying a factorial by a positive integer “k” results in a new factorial:

- Factorials have several properties, including:

## Applications of Factorial Calculator in Various Fields

A Factorial Calculator, which computes the factorial of a non-negative integer, has various applications in different fields of mathematics, science, engineering, and computer science. Here are some of the key applications of a Factorial Calculator in various fields:

**Combinatorics**:- Factorials are fundamental in combinatorial mathematics, where they are used to calculate permutations and combinations. They help determine the number of ways to arrange or choose elements from a set.

**Probability and Statistics**:- In statistics, factorials are used in calculating probabilities, especially in problems involving permutations and combinations. They play a crucial role in probability distributions like the binomial and Poisson distributions.

**Mathematical Analysis**:- Factorials appear in series expansions and power series, such as Taylor series and Maclaurin series, used for mathematical analysis and approximation of functions.

**Calculus**:- Factorials are encountered in calculus, particularly in the derivatives and integrals of functions involving factorials.

**Engineering**:- Engineers use factorials in problems related to reliability analysis, quality control, and system design. They help calculate the probability of success or failure in complex systems.

## Benefits of Using the Factorial Calculator

Here are the key advantages of using such a calculator:

**Accuracy**: Factorial calculations can become complex for large values of “n.” A calculator ensures accurate results without the risk of manual calculation errors.**Time-Saving**: Factorial calculations can be time-consuming, especially for large numbers. A calculator provides quick results, saving valuable time.**Efficiency**: It streamlines the process of calculating factorials, making it more efficient, especially when dealing with multiple calculations.**Reduced Risk of Errors**: Manual calculations of factorials can lead to mistakes, but a calculator minimizes the potential for errors, ensuring reliability.**Versatility**: Factorial calculators are versatile tools that can handle a wide range of values for “n,” from small integers to very large numbers.

## References

**“Beyond Repeated Multiplication: Factorials in Combinatorics and Probability”**by Discrete Mathematics**“From Stirling’s Approximation to Asymptotic Analysis: Unveiling the Hidden Depths of Factorials”**by Journal of Mathematical Analysis and Applications

Last Updated : 31 July, 2024

Sandeep Bhandari holds a Bachelor of Engineering in Computers from Thapar University (2006). He has 20 years of experience in the technology field. He has a keen interest in various technical fields, including database systems, computer networks, and programming. You can read more about him on his bio page.

James FoxThe in-depth explanation provided about factorials and their significance in various fields is truly enlightening. I appreciate the clarity and precision of this article.

Craig37I found this article to be immensely informative and instructive. The clarification on factorial functions and their real-world implications is exceptional.

Becky GreenAbsolutely. The thoroughness and accuracy of the factorial related concepts presented in this post are top-notch.

Maria91I share the same sentiment, Craig37. The insights into factorials and their practical applications are very beneficial for anyone interested in mathematics and related fields.

LmorrisWhat an interesting and detailed explanation about the concept of Factorial and its applications. I will definitely use this knowledge in my daily work!

IwalkerI completely agree with you, Lmorris! This article is a great resource for understanding factorials and their practical uses.

Jayden38This is an exemplary explanation of the factorial concept, leaving no room for ambiguity. Great work!

WmartinIt’s amazing how factorials are so widely applicable. I’m glad to have learned about this.

Heather JohnsonI couldn’t agree more, James Fox. The level of detail in this article is commendable, especially when describing the factorial properties and applications.