Factorial Calculator – Factorial Calculations and Combinatorial Operations

Professional factorial calculator for factorial calculations, permutations, combinations, and combinatorial operations. Perfect choice for students, mathematicians, and statisticians.

Factorial Calculator – Professional Factorial Calculations

The factorial calculator is a professional online tool that allows you to perform factorial calculations quickly and accurately. It is a perfect choice for students, teachers, mathematicians, statisticians, and anyone who needs to perform factorial calculations.

What factorial calculations can you perform?

Basic factorial calculations

• Factorial: Calculating the factorial of a number
• Permutation: Determining the k-th class permutation of n elements
• Combination: Calculating the k-th class combination of n elements
• Subfactorial: Determining the subfactorial of a number
• Multifactorial: Calculating the multifactorial of a number

Special factorial calculations

• Double factorial: n!! calculations
• Triple factorial: n!!! calculations
• Factorial properties: Applying factorial identities
• Exact factorial calculations: High-precision calculations
• Factorial graphs: Visualizing factorial functions

Why choose the factorial calculator?

The factorial calculator has several advantages over traditional calculators:

• Precision: Performs calculations with high precision
• Speed: Instant results
• Features: Five different calculation types
• History: Save calculation history
• Responsive: Works perfectly on all devices
• Free: Completely free to use
• User-friendly: Simple and intuitive interface

Usage guide

Using the factorial calculator is extremely simple:

1. Select the calculation type
2. Enter the number
3. Enter the second number (if needed)
4. Set the desired precision
5. Click the „Calculate” button
6. The result appears immediately

Mathematical formulas and explanations

Factorial

Formula: n! = n × (n-1) × (n-2) × … × 1

Example: 5! = 5 × 4 × 3 × 2 × 1 = 120

Properties: 0! = 1, 1! = 1, n! = n × (n-1)!

Application: Permutations, combinations, probability theory

Permutation

Formula: P(n,k) = n!/(n-k)!

Example: P(5,3) = 5!/(5-3)! = 120/2 = 60

Properties: P(n,0) = 1, P(n,n) = n!, P(n,1) = n

Application: Order calculation, arrangement problems

Combination

Formula: C(n,k) = n!/(k!(n-k)!)

Example: C(5,3) = 5!/(3!×2!) = 120/(6×2) = 10

Properties: C(n,0) = 1, C(n,n) = 1, C(n,k) = C(n,n-k)

Application: Probability theory, statistics

Subfactorial

Formula: !n = n! × Σ(-1)^k/k!

Example: !4 = 9

Application: Derangement problems

Multifactorial

Formula: n!! = n × (n-2) × (n-4) × …

Example: 6!! = 6 × 4 × 2 = 48

Application: Special mathematical problems

Frequently asked questions

What is the difference between permutation and combination?

Permutation takes order into account, while combination does not. For example: P(3,2) = 6 (AB, BA, AC, CA, BC, CB), C(3,2) = 3 (AB, AC, BC).

How do I calculate the factorial of negative numbers?

The factorial is only defined for non-negative integers. The factorial of negative numbers is not defined.

What is the relationship between the factorial and the gamma function?

The gamma function is a generalization of the factorial: Γ(n+1) = n! for all non-negative integers n.

How accurate is the calculator?

The calculator performs calculations with high precision, up to 8 decimal places. The precision can be adjusted in the interface.

Practical application areas

Probability theory

• Combinatorial probability
• Binomial distribution
• Hypergeometric distribution
• Poisson distribution
• Normal distribution

Statistics

• Sampling
• Hypothesis testing
• Confidence intervals
• Regression analysis
• Correlation calculations

IT applications

• Algorithm complexity
• Recursive functions
• Dynamic programming
• Machine learning
• Data structures

Mathematical background

The factorial is one of the fundamental operations in mathematics:

• Factorial: n! = n × (n-1) × (n-2) × … × 1
• Permutation: Permutation of n elements taken k at a time
• Combination: Combination of n elements taken k at a time
• Subfactorial: Derangement numbers
• Multifactorial: Generalization of the factorial

Related calculators

If the factorial calculator is not enough, try our additional math calculators:

• Scientific calculator – Complex mathematical operations
• Percentage calculator – Percentage calculations
• Power Calculator – Exponentiation operations
• Root Calculator – Root extraction operations
• Logarithm Calculator – Logarithm Calculations

Technical Information

The factorial calculator is built with modern web technologies and offers the following features:

• JavaScript-based calculations
• Responsive design
• Accessibility support
• SEO optimized
• Fast loading time
• Cross-browser compatibility

The factorial calculator is under continuous development to always provide the best user experience. If you have any suggestions or comments, please contact us.