Factorial Calculator
Calculate n! — the product of every whole number from 1 to n. Results up to 30 digits are shown in full; larger ones, up to 5,000!, are worked out exactly and displayed in scientific notation with the digit count and the number of trailing zeros.
- Scientific notation
- 3.6288 × 10⁶
- Number of digits
- 7
- Trailing zeros
- 2
Saved setups
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Your recent calculations
Results you calculate here are kept on this device so you can come back to them.
Formula
How to use it
- Enter a whole number from 0 to 5,000.
- Read n!. If it is too long to show in full, use the scientific notation and digit count.
Worked examples
10 factorial
- n!
- 3,628,800
- Scientific notation
- 3.6288 × 10⁶
- Number of digits
- 7
- Trailing zeros
- 2
20 factorial
- n!
- 2,432,902,008,176,640,000
- Number of digits
- 19
- Trailing zeros
- 4
52 factorial — the number of ways to order a deck of cards
- n!
- 8.06581752 × 10⁶⁷
- Number of digits
- 68
- Trailing zeros
- 12
How fast factorials grow
10! is 3,628,800. 20! is about 2.43 × 10¹⁸. 52!, the number of ways to order a deck of cards, is about 8.07 × 10⁶⁷. 70! is the first factorial above 10¹⁰⁰, and 170! (about 7.26 × 10³⁰⁶) is the largest that fits in ordinary double-precision arithmetic, which is why many calculators give an error beyond that.
This calculator multiplies whole numbers exactly rather than using floating point, so it keeps going: 5,000! has 16,326 digits.
What factorials count
n! is the number of ways to arrange n different things in a row: 3 books can be ordered 3! = 6 ways. Factorials are the building blocks of permutations (n! ÷ (n − r)!) and combinations (n! ÷ (r! × (n − r)!)).
0! is defined as 1 because there is exactly one way to arrange nothing, and because it makes those formulas work when r = n.
Questions people ask
What is 5 factorial?
120. 5 × 4 × 3 × 2 × 1 = 120.
What is 10 factorial?
3,628,800.
Why is 0! equal to 1?
There is exactly one way to arrange zero objects — do nothing — and the pattern n! = (n + 1)! ÷ (n + 1) gives 1! ÷ 1 = 1 for n = 0.
How many zeros are at the end of 100!?
24. Count the factors of 5: 100 ÷ 5 = 20, plus 100 ÷ 25 = 4.