Factorial Calculator

Type a whole number, get its factorial back with every digit intact. That sounds basic until you try it on your phone. Ask a phone, a browser, or a spreadsheet for 20! and it says 2.43290200817664e18, which looks authoritative but is wrong, it rounded off the tail and the real answer keeps going a few digits past what it bothered to show. Here you get every one of those digits, so 20! comes back as the full 2,432,902,008,176,640,000, and 100! comes back with all 158 of its digits instead of a scientific-notation stand-in. It multiplies your number by every whole number below it down to 1 and hands you the complete integer, grouped in threes so a giant result is still readable. Everything runs in your browser, nothing you type leaves your machine, and after the first load it keeps working with no connection.

1. Type any whole number into the box, zero or anything above it. The result updates live as you type, so a valid number shows its factorial the moment it lands. Type a decimal or a negative and you get a plain note back, not a bogus answer.
2. Read the full result underneath, every digit, grouped in threes so a long number stays legible. For an ordinary-sized answer that is the whole thing spelled out.
3. Once a result runs past a thousand digits the tool switches to a summary: how many digits it has, a short scientific-notation reading, and the first twenty digits, because dumping forty thousand digits on the page helps nobody. 100! still prints all 158 in full.
4. On small numbers, from 2 up to 12, a dashed box writes out the chain, 5! = 5 · 4 · 3 · 2 · 1 = 120, so you can see exactly where the answer came from instead of taking it on faith.
5. Tap a preset in the Try row to watch it run, 0! through 20!, plus 52! and 100!. The 52! one is the good one, it is how many distinct ways a single deck of cards can be shuffled, a 68-digit number.

The input caps at 10,000, and that is a courtesy to your browser rather than a math limit. 10000! already runs past 35,000 digits, and letting someone paste a million would lock the tab building a number no one could read. Ten thousand covers anything you would realistically hit.

Factorials get huge fast, and that speed is exactly what breaks an ordinary calculator. 13! is already past six billion, 21! runs to twenty digits. The trouble is that the floating-point math inside almost every calculator, phone, browser, or spreadsheet only holds about 15 or 16 significant digits before it starts rounding. So the instant a factorial crosses that line, and it crosses early, the tool stops giving you the true value and starts handing back a rounded approximation shown in scientific notation. 21! shows up as roughly 5.109094217e19, close enough to look right and wrong in every digit past the tenth.

For a lot of what people actually use factorials for, those dropped digits are the whole answer. If you are checking a combinatorics count against a textbook, or a grader wants the exact integer on a homework problem, an answer that has the right first few digits and rounds off the rest is still wrong. And because it looks right, you might not catch that it isn't.

This tool keeps every digit because it does the multiplication with big-integer arithmetic, the kind with no size ceiling. It grows the number to whatever length the answer needs, and it never rounds along the way. 100! comes back as the complete 158-digit integer with every digit correct, and 52! gives you all 68 digits of the deck-shuffle number rather than a rounded stand-in. The free calculators stop being exact the moment a factorial gets interesting, and this one just keeps handing you the real thing.

Type 0 and the tool answers 1, and a fair number of people stop and squint at that. You multiplied nothing and got one instead of zero? It looks like a mistake, but it isn't one.

The clearest way to see it is to count the factorials downward. Stepping from any n! down to (n-1)! just means dividing by n. So 4! = 24, then 3! = 24 / 4 = 6, then 2! = 6 / 3 = 2, then 1! = 2 / 2 = 1. Run the same rule one more notch and 0! = 1! / 1 = 1. Nobody bolted a special case onto zero to keep things tidy, one is simply the value that stops the pattern from breaking.

There is a second reason, and it is the practical one. Combinations and permutations are built by dividing factorials by other factorials, and plenty of those formulas end up dividing by 0!. If 0! were zero you would be dividing by zero all over combinatorics, and those formulas would simply stop working. Defining it as one is what keeps everything downstream working, which is a decent sign the answer is real and not just convenient.