Factorial Calculator
Result
| Factorial |
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Factorial Calculator — Exact n!, However Big
Factorials outgrow ordinary calculators almost immediately: 13! overflows a 32-bit integer, 21! overflows 64 bits, and most calculators surrender to approximation by 70!. This free calculator computes exact factorials with big-integer arithmetic — every digit of 500! if you want it — plus digit counts, trailing zeros, and scientific notation for scale. In-browser, no signup.
How Fast Factorials Explode
| n | n! | Scale |
|---|---|---|
| 5 | 120 | arrangements of 5 books |
| 10 | 3,628,800 | ~population of a large city |
| 13 | 6,227,020,800 | overflows 32-bit integers |
| 52 | 8.07 × 10⁶⁷ | shufflings of a card deck — more than atoms in Earth |
| 100 | 9.33 × 10¹⁵⁷ | 158 digits, 24 trailing zeros |
The card-deck fact deserves a pause: every fair shuffle you've ever performed almost certainly produced an ordering no human has ever seen before.
Where Factorials Do Real Work
- Permutations — arrangements of r items from n: n!/(n−r)!. Race podiums from 10 runners: 10!/7! = 720.
- Combinations — selections ignoring order: n!/(r!(n−r)!). Lottery odds, team choices, poker hands all reduce to this.
- Probability — the birthday paradox and matching problems are factorial ratios.
- Calculus — e^x = Σ xⁿ/n!; factorials in denominators are why Taylor series converge.
The Trailing-Zeros Puzzle
A favorite interview question: how many zeros end 100!? Count the factors of 5: ⌊100/5⌋ + ⌊100/25⌋ = 20 + 4 = 24. (2s are plentiful; 5s are the bottleneck.) The calculator reports this count for any n — and shows the formula.
Free and Instant
Exact big-integer results computed locally — for students, combinatorics work, and settling arguments about card decks.