What is Factorial Calculator?

A factorial calculator computes n! (n factorial) — the product of all positive integers up to n. Factorials appear in combinatorics, probability, and statistics. This tool handles large numbers instantly and shows step-by-step multiplication.

The tool accepts any whole number from 0 up to 10,000, displays the result along with the full expansion (n × (n-1) × … × 1), and gives a plain-language interpretation: 12! is the number of ways to arrange 12 distinct items in a row. Because it computes with BigInt, even a value like 10,000! comes back exact rather than rounded. You can also generate a table of factorials across a range for quick reference, and copy the result or download the table as needed.

How to use

1. Enter a non-negative integer from 0 to 10,000 — every result is exact, with no rounding.
2. View the factorial result and the expanded multiplication expression.
3. Copy the result or download a table of factorials for a range of values.

When to use

• Counting how many ways a set of distinct items (cards, players, files) can be ordered.
• Computing the denominator of a binomial coefficient when solving probability homework.
• Estimating the search space of a brute-force permutation algorithm.

Result

Enter 12 to get 479,001,600. The tool shows 12 × 11 × 10 × … × 1 = 479,001,600, useful for calculating permutations of 12 items.

FAQ

How large a number can the calculator handle?

Up to 10,000. The tool uses BigInt arithmetic, so every result is exact no matter how many digits it runs to — 10,000! is a 35,660-digit number and still computes instantly. The 10,000 cap exists only because a result with tens of thousands of digits gets unwieldy to render and read, not because of any precision limit.

Is 0! really equal to 1, or is that a bug?

It's correct. The empty product convention defines 0! as 1, which keeps formulas like nCr = n! / (r!·(n-r)!) working when r equals 0 or n. Without this, half of combinatorics would need special-case code.

Can I compute factorials of fractions or negative numbers?

Not with this tool. Factorials are only defined for non-negative integers. The continuous extension is the gamma function — Γ(n+1) equals n! for whole numbers and is finite for most non-integer inputs, but that's a different calculator.

What is the 9.33 × 10^157 line shown next to a big result?

That is a quick scientific-notation summary, not the answer itself. The calculator always prints the complete digit string first (100! is all 158 digits, every one shown). For results of 16 digits or more it adds a compact 9.33 × 10^157 read plus the digit count so you can grasp the scale at a glance. Nothing is rounded or replaced, and Copy puts the full exact number on your clipboard.

What's the practical use of computing 100!?

100! pops up when counting permutations of a standard 52-card deck times two, in probability estimates of unlikely events, and in numerical methods like Taylor series where you divide by factorials to ensure terms shrink rapidly.

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