Student learning the factorial definition
See the finite product and the special value 0!=1.
Enter a small nonnegative whole number.
Gets an exact integer and a compact auditable product.
Factorial Calculator
Calculate an exact factorial from 0! through 500! with arbitrary-precision integer arithmetic, a digit count, and clear domain limits.
Use this result well
- Inputs that matter
- One nonnegative whole number n from 0 through 500
- Output to expect
- Exact arbitrary-precision n!, its digit count, and a compact product description
- How it works
- Defines 0! as 1 and multiplies the integers from 2 through n using BigInt, avoiding Number precision loss
- Factorial grows rapidly and this tool intentionally stops at 500; fractions, negatives, and gamma-function extensions are outside scope.
- Arrangement interpretations require distinct items and order sensitivity; use a combinations model when order does not matter.
Choose your path
Built around the job you need to finish
Calculate an exact factorial for a nonnegative whole number through 500 using arbitrary-precision integer arithmetic.
Probability student checking a large count
Avoid floating-point rounding above 18!.
Enter a larger n and inspect the unrounded exact integer and digit count.
Can copy the exact BigInt result rather than exponential notation.
Developer validating a boundary
Reject fractional, negative, or impractically large input clearly.
Enter the boundary case and read the validation alert.
Does not receive a rounded or misleading factorial.
Authoritative checks for this tool
Outputs and checklists are planning aids. Review the linked current authorities and the records, terms, instructions, and requirements that apply to your exact situation before a consequential decision.
- DLMF §5.4 — Special Values and ExtremaNational Institute of Standards and Technology · Authoritative identity n! = Γ(n+1), including Γ(1)=1 and therefore 0!=1.
- Contemporary Mathematics — Counting PrinciplesOpenStax, Rice University · Educational finite-product and arrangement-count context for factorials of nonnegative integers.
- ECMAScript — BigInt ObjectsEcma International · Normative arbitrary-precision integer type used to avoid binary floating-point precision loss in exact factorial results.
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Reference & details
How it works
Updated August 2026
How it works
Updated August 2026Finite-product definition
For a positive whole number n, factorial multiplies every whole number from n down through 1; 0! is defined as 1.
0! = 1; n! = n × (n−1) × … × 2 × 1Exact BigInt arithmetic
The engine multiplies integers using BigInt, so factorials above the Number safe-integer boundary are neither rounded nor converted to exponential notation.
Bounded output
Only whole numbers from 0 through 500 are accepted. Small results show the factors; large results use a concise product description and exact digit count.
Updated: August 2026
Example Scenarios
A student enters 6 and checks the exact result 720 against the compact product 6×5×4×3×2×1.
A probability student copies the complete exact value of 20! instead of a rounded floating-point result.
A developer tests 0, a fraction, and 501 to confirm the definition and the explicit whole-number range.
Common Mistakes to Avoid
Common Mistakes to Avoid
Using floating-point factorials as exact
Ordinary Number arithmetic loses integer precision for sufficiently large factorials; this tool uses BigInt for every accepted result.
Applying n! to the wrong counting model
Plain n! assumes n distinct items and order matters; combinations or repeated-item arrangements need different formulas.
FAQ
Yes. Every accepted result from 0! through 500! is computed with arbitrary-precision integer arithmetic and displayed as the complete exact integer.
Defining 0!=1 preserves factorial identities such as n!=Γ(n+1) and matches the empty-product convention used in counting.
This tool implements factorial only for nonnegative whole numbers. Gamma-function extensions and other generalized factorials are outside its scope.
Factorials grow extremely quickly. The documented limit keeps output and browser work bounded while still producing a 1,135-digit exact value at 500!.
n! counts orderings of n distinct items. Repetition, indistinguishable items, or unordered selections require a different counting model.
About Factorial Calculator
Enter a nonnegative whole number from 0 through 500. The result uses BigInt for an exact integer rather than a rounded JavaScript Number, and small inputs include a compact product form.