Factorial Calculator

A factorial is the product of all positive integers from 1 up to a given number n, written as n!. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials are used in permutations, combinations, and many areas of mathematics.

The factorial formula is: n! = n × (n − 1) × (n − 2) × ... × 2 × 1. This means you multiply n by every positive integer less than it down to 1. For example, 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720.

By mathematical convention, 0! = 1. This is defined so that formulas for permutations and combinations work correctly when no elements are selected. It is not an error — it is an accepted definition in mathematics.

This calculator computes exact integer factorials up to 170!. Beyond 170!, the result exceeds the maximum value representable by standard floating-point numbers (it becomes Infinity). Scientific notation is shown for large values to give an approximate magnitude.

Scientific notation expresses very large numbers in the form a × 10^b, where 1 ≤ a < 10. For example, 10! = 3,628,800 ≈ 3.628800 × 10^6. This is useful when the full integer result is too long to display or interpret easily.

Factorials appear in probability, statistics, and combinatorics. They are used to count the number of ways to arrange n distinct objects (n! permutations), to compute combinations in the binomial theorem, and in Taylor series expansions in calculus.

Standard factorials are only defined for non-negative integers (0, 1, 2, 3, …). The factorial of a decimal or negative number is not defined in the classical sense, though the Gamma function extends the concept to real numbers. This calculator accepts non-negative integers only.

The number of digits in n! grows rapidly. For example, 10! has 7 digits, 50! has 65 digits, and 100! has 158 digits. This calculator shows the digit count alongside the result so you can appreciate the scale of large factorials.