Factorial Calculator
Calculate n! exactly for n up to 5000, with digit count, scientific notation and trailing zeros.
Your inputs
Results
25!
15511210043330985984000000
- Scientific notation
- 1.551121004333 × 10^25
- Number of digits
- 26
- Trailing zeros
- 6
✓Exact calculation — rounded only for display
What this calculator does
The factorial n! is the product of all integers from 1 to n. It grows extremely fast, so exact results need big-integer arithmetic.
Formula and method
n! = 1 × 2 × … × n, with 0! = 1. Trailing zeros = Σ floor(n ÷ 5^k).
Worked example
Calculated by this tool with its default inputs:
Inputs
- n: 25
Results
- 25!: 15511210043330985984000000
- Scientific notation: 1.551121004333 × 10^25
- Number of digits: 26
- Trailing zeros: 6
How to read the results
n! counts the ways to arrange n distinct items in order.
Assumptions and limitations
- Defined here for non-negative integers.
Questions
Why is 0! equal to 1?
There is exactly one way to arrange zero items, and it keeps formulas consistent.
Methodology and verification
- Result type
- Exact mathematical calculation (rounded only for display)
- Formula version
- 1.0
- Automated verification
- 5 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
- Editorial review
- Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.
Privacy
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