Factorial Calculator
The exact factorial n! of any whole number up to 1,000, every digit shown, with its double factorial n!!, digit count and trailing zeros.
Result
n!: 3628800
Exact: every digit is computed, nothing is rounded except the scientific form.
- n! in scientific notation
- 3.6288 × 10^6
- Digits in n!
- 7
- Trailing zeros in n!
- 2
- Double factorial, n!!
- 3840
https://calcgallery.com/algebra-numbers/factorial-calculator/
Results follow the mathematical operation and values shown. Check that you selected the intended operation, convention and dataset type before relying on the result. Read the full disclaimer
How to use the Factorial Calculator
- Enter a whole number n from 0 to 1,000.
- Read n! exactly. Past 50 digits the headline switches to scientific notation and every digit is listed below it.
- Use the digit count, the trailing zeros and the double factorial n!! if you need them.
The definition
n! = n × (n − 1) × (n − 2) × … × 2 × 1, 0! = 1n!! = n × (n − 2) × (n − 4) × …, ending at 2 or 1, 0!! = 1Factorials grow faster than any power: 10! is a little over 3.6 million, 20! is about 2.4 × 10¹⁸, and 171! is too large for the floating-point numbers most calculators and spreadsheets use, which is why they stop at 170. This page multiplies whole numbers exactly, with no size limit short of 1,000!, a number of 2,568 digits.
Reading a long answer
A result longer than 50 digits is headlined in scientific notation, rounded to ten significant figures from its own digits, and the full number is given underneath. The digit count tells you its size at a glance; the trailing zeros come from Legendre’s formula, ⌊n/5⌋ + ⌊n/25⌋ + ⌊n/125⌋ + …, which counts how many times 5 divides n!.
Where factorials are used
Arrangements and selections: the number of ways to choose r things from n is n! ÷ (r! (n − r)!), which the permutation and combination calculator works out directly. Factorials of fractions, such as (1/2)!, belong to the gamma function and are not covered here.
With your numbers
- 10! = 10 × 9 × … × 2 × 1
- Trailing zeros: one for each factor of 5 among 1 to 10, counting 25 twice, 125 three times
Quick reference
Exact: every digit is computed, nothing is rounded except the scientific form.
| Example | n! |
|---|---|
| 0! | 1 |
| 5! | 120 |
| 10! | 3628800 |
| 20! | 2432902008176640000 |
| 25! | 15511210043330985984000000 |
| 52!, a deck of cards | 8.065817517 × 10^67 |
| 100! | 9.332621544 × 10^157 |
| 1000! | 4.023872601 × 10^2567 |
Common questions about the Factorial Calculator
- What does n! mean?
- The product of every whole number from n down to 1. 5! = 5 × 4 × 3 × 2 × 1 = 120. It counts the ways to put n different things in order: 5 books can stand on a shelf in 120 orders.
- Why is 0! equal to 1?
- Because there is exactly one way to arrange nothing, and because it keeps the rule n! = n × (n − 1)! working at n = 1: 1! = 1 × 0!, so 0! must be 1. It is the empty product, which is 1 in the same way an empty sum is 0.
- How big is 52!?
- About 8.07 × 10⁶⁷, a 68-digit number. That is the number of orders a standard deck of 52 cards can be shuffled into, which is why a well-shuffled deck is almost certainly in an order no deck has been in before.
- How many zeros does 100! end in?
- Twenty-four. Each trailing zero needs a factor of 10, that is a 2 and a 5, and 2s are plentiful, so count the 5s: 100 ÷ 5 = 20 multiples of 5, plus 100 ÷ 25 = 4 that give a second 5. The page counts them the same way, and it matches the digits.
- What is a double factorial?
- n!! multiplies every second number: n × (n − 2) × (n − 4) and so on, down to 2 or 1. So 7!! = 7 × 5 × 3 × 1 = 105 and 8!! = 8 × 6 × 4 × 2 = 384. It is not (n!)!, the factorial of a factorial, which would be astronomically larger. 0!! is 1.