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Factorial Calculator

Calculate n! exactly for any whole number from 0 to 5,000, with every digit. You also get the digit count, trailing zeros, the double factorial n!! and a nearby-factorials table.

Number n

Whole number from 0 to 5,000

Enter your values to see the result.

How to use the Factorial Calculator

Enter a whole number n from 0 to 5,000, or tap an example.
Press Calculate factorial (results also update as you type).
Read n!, its digit count, trailing zeros and n!!.
Scroll the exact value box for every digit, or press Copy results to copy them all.

Factorial formulas

Factorial: n! = n × (n − 1) × (n − 2) × … × 2 × 1, with 0! = 1
Recursive rule: n! = n × (n − 1)!
Double factorial: n!! = n × (n − 2) × (n − 4) × … ending at 1 (odd n) or 2 (even n)
Trailing zeros (Legendre): Z(n) = ⌊n/5⌋ + ⌊n/25⌋ + ⌊n/125⌋ + …
Number of digits: ⌊log₁₀ 1 + log₁₀ 2 + … + log₁₀ n⌋ + 1
Stirling's approximation: n! ≈ √(2πn) · (n / e)ⁿ

Factorial table 0! to 20!

n	n!	n	n!
0	1	11	39,916,800
1	1	12	479,001,600
2	2	13	6,227,020,800
3	6	14	87,178,291,200
4	24	15	1,307,674,368,000
5	120	16	20,922,789,888,000
6	720	17	355,687,428,096,000
7	5,040	18	6,402,373,705,728,000
8	40,320	19	121,645,100,408,832,000
9	362,880	20	2,432,902,008,176,640,000
10	3,628,800	21	51,090,942,171,709,440,000

21! is the first factorial that no longer fits in a 64-bit integer, and 171! overflows ordinary double-precision floating point. That is why this calculator uses exact big-integer arithmetic.

Frequently asked questions

What is a factorial?

n! (n factorial) is the product of all whole numbers from 1 to n. For example 5! = 5 × 4 × 3 × 2 × 1 = 120. It counts the number of ways to arrange n different items in a row.

Why is 0! equal to 1?

There is exactly one way to arrange zero items (do nothing), and the rule n! = n × (n − 1)! only works for n = 1 if 0! = 1. It also keeps formulas such as nCr = n! ÷ (r!(n − r)!) correct.

How many trailing zeros does 100! have?

24. Each trailing zero comes from a factor 10 = 2 × 5, and there are fewer 5s than 2s, so count the 5s: ⌊100/5⌋ + ⌊100/25⌋ = 20 + 4 = 24 (Legendre's formula).

How many digits does 100! have?

100! has 158 digits. In general the digit count is ⌊log₁₀(n!)⌋ + 1, which you can find by adding log₁₀ of every number from 1 to n.

What is a double factorial?

n!! multiplies every second number down from n: 7!! = 7 × 5 × 3 × 1 = 105 and 8!! = 8 × 6 × 4 × 2 = 384. It is not the same as (n!)!.

Can you take the factorial of a negative number or a decimal?

Not with the ordinary definition, which only covers whole numbers 0, 1, 2 and so on. The gamma function extends it to decimals (Γ(n + 1) = n!), but it is undefined at negative integers.

What is 52 factorial?

52! ≈ 8.0658 × 10^67, a 68-digit number. It is the number of ways to shuffle a standard deck of 52 cards, so a well-shuffled deck is almost certainly in an order that has never existed before.

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