Factorial Calculator
The Factorial Calculator computes n! - the product of every whole number from 1 up to n - with exact BigInt precision for values from 0 all the way to 170.
What a factorial is
The factorial of n (written n!) multiplies together all positive integers up to n: 5! = 5 × 4 × 3 × 2 × 1 = 120. By definition 0! = 1. Factorials count the number of ways to arrange things, which is why they appear throughout probability, permutations, and combinations.
Exact big numbers
Factorials grow astonishingly fast - 20! already exceeds two quintillion. This calculator uses arbitrary-precision (BigInt) arithmetic so the digits are exact rather than rounded into scientific notation, and it shows the full step-by-step expansion for smaller values.
Frequently Asked Questions
Why is 0! equal to 1?
There is exactly one way to arrange zero items (the empty arrangement), and defining 0! = 1 keeps the formulas for permutations and combinations consistent.
How large a factorial can it calculate?
It handles n from 0 to 170 with exact digits. Beyond 170 the numbers exceed standard double-precision limits, which is why the range is capped.
Are the results exact or rounded?
Exact. The calculator uses BigInt arithmetic, so even very large factorials are shown with every digit rather than in rounded scientific notation.
What are factorials used for?
They count arrangements and are the basis of permutations, combinations, and many probability formulas.
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