How this calculation works
Factorials count arrangements of distinct objects. This tool accepts integers from 0 to 170 to stay within finite numeric range. Large results use scientific notation and are approximate.
n! = 1 × 2 × … × n; 0! = 1A worked example
5! = 5 × 4 × 3 × 2 × 1 = 120.
Good to know
Uses the stated formula and assumptions. Displayed decimal values are rounded; use consistent units for all inputs.
A small group can create many arrangements
Five distinct books can be ordered in 5 × 4 × 3 × 2 × 1 = 120 ways: five choices for the first position, then four remaining choices, and so on. Ten distinct books already have 3,628,800 possible orders.
This rapid growth is why brute-force arrangement problems become difficult even when the number of objects looks modest. Adding an eleventh object multiplies the count by 11 rather than simply adding 11.
Large results are approximate browser numbers
The tool uses ordinary numerical multiplication and accepts up to 170, beyond which the result overflows the finite numeric range. Values beyond the safe-integer range are not guaranteed to retain every integer digit. Scientific notation is a compact display, not a promise of exact arbitrary-precision counting.
The conventional value 0! = 1 is useful because there is one empty arrangement. Negative integers and fractional factorial extensions require different mathematics and are not accepted here.
A few questions, answered
Why is 0! equal to 1?
There is one way to arrange zero objects: the empty arrangement. It also keeps standard factorial identities consistent.
Does this handle repeated identical objects?
No. Distinct-object arrangements use n!. Identical repeated objects require dividing by the appropriate repetition factorials.