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Calculate the factorial of any non-negative integer — with the full digit count for large factorials and scientific notation for display.
Factorial Calculator · exact calculation using BigInt · 100% private client-side
Type any non-negative integer. For n ≤ 20, the exact full result is shown. For larger n, the result is shown in scientific notation with the exact digit count.
n! is calculated and displayed with the number of digits.
For small n, the full multiplication expression is shown (e.g., 5! = 5 × 4 × 3 × 2 × 1 = 120).
The factorial of a non-negative integer n (written n!) is the product of all positive integers from 1 to n. 5! = 5 × 4 × 3 × 2 × 1 = 120. 0! is defined as 1 by convention. Factorials grow extremely rapidly — 20! is already over 2.4 quintillion.
Factorials appear in combinatorics (the number of ways to arrange n objects is n!), probability calculations, Taylor series expansions, the Poisson distribution, permutations and combinations (nPr, nCr formulas), and many areas of mathematics and statistics.
Factorials grow faster than exponential functions. 100! has 158 digits. 1000! has 2,568 digits. For reference: 70! exceeds the number of atoms in the observable universe. The calculator handles large n using big-integer arithmetic for exact results up to several hundred digits, and scientific notation for very large values.
0! = 1 by mathematical convention. The most intuitive justification: there is exactly one way to arrange zero objects (doing nothing), and this definition makes combinatorial formulas (like nCr = n! / (r!(n−r)!)) work correctly when r = 0 or r = n.
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Factorials are a cornerstone of combinatorics, probability, and mathematical analysis — they appear in permutation and combination formulas, Taylor and Maclaurin series, Poisson distributions, and the gamma function. The challenge with factorials in standard calculators is that they overflow quickly — a basic calculator can’t handle anything beyond 69! without producing an error or Infinity. This calculator uses arbitrary-precision arithmetic to compute exact results for moderate n and displays large factorials in both scientific notation and with the precise digit count, making it useful for students, mathematicians, and developers working with combinatorial problems.
All calculations run in your browser. No data is transmitted to any server.
