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Arithmetic & Numbers

Factorial Calculator

Enter a whole number n and get n! computed with exact integer arithmetic, plus how many digits it has and why it ends in so many zeros.

Updated October 3, 2026Written and reviewed by Mateuss M.Method: how we calculate

Try an example:

Answer5! = 120

3 digits
1 trailing zero

Step-by-step working 3 steps

1
Definition
```
n! = n × (n − 1) × … × 2 × 1,  and 0! = 1
```
The factorial counts the ways to arrange n different items in a row.
2
Multiply it out
```
5! = 5 × 4 × 3 × 2 × 1 = 120
```
3
Trailing zeros
```
Count the factors of 5: ⌊5/5⌋ = 1
```
Each factor of 5 pairs with a factor of 2 to make a trailing zero.

How to use the factorial calculator

Enter a whole number from 0 to 1000.
Read n! (shown in scientific form if very long).
Check the digit count.
See the trailing-zero count worked out.

Factorial

n! = n × (n − 1) × … × 2 × 1
0! = 1
Trailing zeros = ⌊n/5⌋ + ⌊n/25⌋ + ⌊n/125⌋ + …

n! counts the ways to arrange n distinct objects in a row.

Worked examples

Each example below is generated by the same calculator you used above, so the working always matches the answer.

5!

Answer5! = 120

3 digits
1 trailing zero

Step-by-step working 3 steps

1
Definition
```
n! = n × (n − 1) × … × 2 × 1,  and 0! = 1
```
The factorial counts the ways to arrange n different items in a row.
2
Multiply it out
```
5! = 5 × 4 × 3 × 2 × 1 = 120
```
3
Trailing zeros
```
Count the factors of 5: ⌊5/5⌋ = 1
```
Each factor of 5 pairs with a factor of 2 to make a trailing zero.

10!

Answer10! = 3,628,800

7 digits
2 trailing zeros

Step-by-step working 3 steps

1
Definition
```
n! = n × (n − 1) × … × 2 × 1,  and 0! = 1
```
The factorial counts the ways to arrange n different items in a row.

2

Multiply it out

10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800

3
Trailing zeros
```
Count the factors of 5: ⌊10/5⌋ = 2
```
Each factor of 5 pairs with a factor of 2 to make a trailing zero.

25!

Answer25! = 15,511,210,043,330,985,984,000,000

26 digits
6 trailing zeros

Step-by-step working 3 steps

1
Definition
```
n! = n × (n − 1) × … × 2 × 1,  and 0! = 1
```
The factorial counts the ways to arrange n different items in a row.
2
Multiply it out
```
25! has 26 digits
```
The product is computed with exact whole-number arithmetic, so no digits are rounded.
3
Trailing zeros
```
Count the factors of 5: ⌊25/5⌋ + ⌊25/25⌋ = 6
```
Each factor of 5 pairs with a factor of 2 to make a trailing zero.

100!

Answer100! = 9.3326215 × 10^157

158 digits
24 trailing zeros

Step-by-step working 3 steps

1
Definition
```
n! = n × (n − 1) × … × 2 × 1,  and 0! = 1
```
The factorial counts the ways to arrange n different items in a row.
2
Multiply it out
```
100! has 158 digits
```
The product is computed with exact whole-number arithmetic, so no digits are rounded.
3
Trailing zeros
```
Count the factors of 5: ⌊100/5⌋ + ⌊100/25⌋ = 24
```
Each factor of 5 pairs with a factor of 2 to make a trailing zero.

Common mistakes to avoid

Thinking 0! is 0

0! is 1, which keeps combination formulas consistent.

Using factorials of negatives or fractions

Ordinary factorials are only defined for whole numbers 0 and up.

Underestimating growth

20! is already over two quintillion; 100! has 158 digits.

Frequently asked questions

Why does 0! equal 1?

There is exactly one way to arrange zero objects: do nothing.

Where are factorials used?

In permutations, combinations, probability and series expansions.