Factorial calculator

The factorial of a whole number n, written n!, is the product of all positive whole numbers from 1 to n:

n! = n × (n − 1) × (n − 2) × … × 2 × 1

• 5! = 5 × 4 × 3 × 2 × 1 = 120
• 10! = 3,628,800
• 0! = 1 by definition

Factorials grow extremely fast. This calculator uses exact big-integer arithmetic, so even 5000! (a number with 16,326 digits) is calculated exactly in your browser, with no rounding.

20! is the largest factorial that fits in a standard 64-bit integer, and 70! is the first one larger than a googol (10¹⁰⁰). 52! is the number of ways to shuffle a deck of cards, so a well-shuffled deck is almost certainly in an order no one has seen before.

There is exactly one way to arrange zero objects: do nothing. Defining 0! = 1 also keeps formulas consistent. The rule n! = n × (n − 1)! gives 1! = 1 × 0!, which only works if 0! = 1, and the combination formula C(n, n) = n! / (n! × 0!) correctly gives 1.

Factorials are only defined for non-negative whole numbers in this calculator. (The gamma function extends them to other values, but that is beyond this tool.)

The calculator counts the zeros at the end of n!. Each trailing zero comes from a factor of 10 = 2 × 5, and since there are always more 2s than 5s, you only need to count the 5s:

zeros = ⌊n/5⌋ + ⌊n/25⌋ + ⌊n/125⌋ + …

For 100!: 20 + 4 = 24 trailing zeros. 100! has 158 digits in total.

• Arrangements: 5 books can be lined up on a shelf in 5! = 120 ways.
• Combinations and permutations: C(n, r) = n! / (r! (n − r)!). The probability calculator handles these directly.
• Probability: the chance of a random shuffle putting 10 cards in one particular order is 1 / 10! = 1 in 3,628,800.
• Series in calculus: e = 1/0! + 1/1! + 1/2! + 1/3! + …, and sin, cos and eˣ have similar factorial series.

• The result box scrolls, and the copy button copies the full number without separators.
• For quick small factorials inside other calculations, type n! in the scientific calculator.
• For n up to 12, the calculator also writes out the full product, such as 6 × 5 × 4 × 3 × 2 × 1 = 720.
• Very large factorials take a moment to display; 5000! is a wall of 16,326 digits, so use the digit count and scientific notation for a quick sense of its size.
• To estimate a factorial without computing it, Stirling's approximation n! ≈ √(2πn) × (n/e)ⁿ is accurate to within about 1% for n = 10 and gets better as n grows.
• In spreadsheets, the FACT function returns the same values but switches to rounded floating point above 20!, while this tool stays exact. Everything is calculated locally in your browser, so even the largest results never leave your device.