Factorial Calculator 2026
Instantly calculate the factorial (n!) of any number up to 10,000. Perfect for students, mathematicians, and programmers needing exact BigInt precision.
Factorial Properties
Enter a non-negative integer to calculate its factorial
Enter a whole number between 0 and 10,000. Larger numbers may take a moment to compute.
Factorial Results
Exact value, digit count, and mathematical properties
Enter a number above and click Calculate Factorial to see the exact result and properties.
Common Factorials
The factorial values for small integers, along with their total digit count. Notice how rapidly the numbers grow!
| n | n! (Factorial) | Digits |
|---|---|---|
| 0 | 1 | 1 |
| 1 | 1 | 1 |
| 2 | 2 | 1 |
| 3 | 6 | 1 |
| 4 | 24 | 2 |
| 5 | 120 | 3 |
| 6 | 720 | 3 |
| 7 | 5,040 | 4 |
| 8 | 40,320 | 5 |
| 9 | 362,880 | 6 |
| 10 | 3,628,800 | 7 |
| 20 | 2.43 × 1018 | 19 |
| 50 | 3.04 × 1064 | 65 |
| 100 | 9.33 × 10157 | 158 |
Factorial FAQ
Everything you need to understand factorials, from basic definitions to advanced mathematical properties.
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. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials are widely used in combinatorics, probability, and calculus to determine permutations and combinations.
To calculate a factorial, you multiply the number by every positive integer less than it. The formula is n! = n × (n-1) × (n-2) × … × 1. For example, to calculate 4!, you multiply 4 × 3 × 2 × 1, which equals 24.
The factorial of 0 is defined as 1 (0! = 1). This is known as the ’empty product’ convention in mathematics, meaning the product of no factors at all is the multiplicative identity, 1. This definition is crucial for the consistency of combinatorial formulas like binomial coefficients.
No, the standard factorial function is not defined for negative integers. The factorial formula only applies to non-negative whole numbers. For negative numbers or non-integers, mathematicians use the Gamma function, which extends the factorial concept to complex numbers.
Large factorials end in multiple zeros because of the factors of 10 in their multiplication. Since 10 = 2 × 5, and there are always more factors of 2 than 5 in a factorial sequence, the number of trailing zeros is determined by the number of times 5 is a factor in the numbers being multiplied.