Factorial Calculator — Exact n!, Trailing Zeros + Double Factorial

Real-world use cases

• Check a coding interview or homework answer exactly

  You wrote a factorial function and want to confirm it against an exact reference, especially past the point where a 64-bit number breaks. Type the same n here, read the full BigInt result, and diff it against your output. Because 21! already overflows a JavaScript number, this is where naive solutions silently return wrong digits, so checking against the exact 158-digit value of 100! catches overflow bugs your own assertions might wave through.

• Look up one large factorial with every digit intact

  You need 50! or 100! as an exact integer for a proof, a probability problem, or a number-theory note, not a rounded approximation. Enter the index, read the full value, expand the collapsed result if it is enormous, and copy all of it in one click. No spreadsheet rounds it into scientific notation and no online tool quietly truncates the tail.

• Solve probability and combinatorics by hand

  Permutations and combinations are built on factorials: P(n,r) = n!/(n−r)! and C(n,r) = n!/(r!·(n−r)!). Compute the factorials you need here, drop them into the formula, and you have an exact count for a lottery, a seating chart, or a card hand. The digit count and trailing-zero readout also help you sanity-check the magnitude of the final answer.

• Teach why 0! = 1 and how trailing zeros appear

  Showing a class the factorial recurrence or Legendre's formula? Compute 5!, then 10!, then 25! and point at the trailing-zero count climbing from 1 to 2 to 6 exactly as floor(n/5) + floor(n/25) predicts. Share the URL so every student opens the same number, and use the 0! = 1 example to start the conversation about the empty product.

Common pitfalls

• Using a plain number instead of BigInt for large factorials. JavaScript numbers stay exact only to 2^53, and 21! already passes that, so a number-based calculator returns wrong trailing digits from then on. This tool computes the whole product on BigInt, so 100! shows all 158 correct digits rather than a rounded 9.33e157.

• Confusing the double factorial n!! with (n!)!. The double factorial multiplies every second term, so 7!! = 7·5·3·1 = 105, while (7!)! would be the factorial of 5040, an astronomically larger number. Read the !! as one operation on every other integer, not as two factorials stacked.

• Forgetting that factorials are defined only for non-negative integers here. There is no plain factorial of a negative number or a fraction (those need the gamma function instead), so an input like −3 or 2.5 has no value and the tool reports N/A rather than guessing one.

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