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How to use
The factorial n! is the product of the positive integers from 1 through n. This calculator uses exact big-integer arithmetic so large results are not rounded.
- Enter a non-negative integer from 0 to 2000.
- Calculate to get the full exact n! value.
- Review its digit count, trailing zeros and scientific summary.
How it is calculated
Example
5! = 5×4×3×2×1 = 120. By convention, 0! = 1.
Important notes
Factorials grow extremely quickly, so the exact result can become very long even though it remains exact up to 2000! here.
Worked examples and interpreting results
Five factorial multiplies the integers from 1 through 5, giving 120. It also counts arrangements of five distinct items in a row when each is used exactly once.
| Case | Calculation | Result |
|---|---|---|
| Five factorial | 5! = 5 × 4 × 3 × 2 × 1 | 120 |
| Zero factorial | 0! = 1 | 1 |
How to check the result
This factorial applies to nonnegative integers. The symbol ! does not mean raising a number to itself: 5! differs from 5⁵. Results grow rapidly, so displaying or copying the full integer can be preferable to rounding it.
Frequently asked questions
Why is 0! equal to 1?
It is the empty-product convention and keeps factorial identities consistent.
Are large factorials rounded?
No. The main n! output is an exact integer.
Can I enter negative or decimal values?
Not for the ordinary factorial definition used here.
Why does factorial grow so quickly?
Because n! multiplies every integer from 1 through n, it eventually grows faster than any fixed power such as n² or n¹⁰. Even moderate n values therefore produce extremely large results.