Factorial Calculator: Instantly Find the Factorial of a Number

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Searching for a fast, accurate n factorial calculator? Use this free tool to compute n! in seconds. It shows the working (multiplication steps) and formats results neatly for easy reading. Perfect for students, competitive exams, programming, and data science.

Factorial Calculator
Compute n! and show working

What is the Factorial of a Number?

Factorial is the product of all positive integers from 1 to n.

  • Definition: n! = n × (n−1) × (n−2) × … × 3 × 2 × 1
  • Special case: 0! = 1 by definition.
  • Examples:
    • 4! = 4 × 3 × 2 × 1 = 24
    • 6! = 720
    • 7! = 5,040
    • 8! = 40,320

Use the n factorial calculator above to verify these and compute any n!.

Formula for Factorial

Factorial of n (written as n!) is the result of multiplying all whole numbers from n down to 1.

  • Basic rule:
    • n! = n × (n−1) × (n−2) × … × 3 × 2 × 1
    • Example: 5! = 5 × 4 × 3 × 2 × 1 = 120
  • Special case:
    • 0! = 1 (by definition, so formulas work nicely)

That’s it multiply all the numbers from 1 to n, and that product is n!.

How to Use the factorial calculator online

  1. Enter a non‑negative integer n.
  2. Press Calculate.
  3. See:
    • The exact value of n!
    • The working: n × (n−1) × … × 1
    • Digits count, useful for very large results

Tip: For learning, enable “Working” to see step‑by‑step multiplication up to a sensible limit so the page stays fast.

  • What is the factorial of 100?
    • 100! is a 158‑digit number. It’s far too large to write here, but the calculator returns the exact value instantly and shows the digits count.
  • 10 factorial value:
    • 10! = 3,628,800
  • 8 factorial:
    • 8! = 40,320
  • 7 factorial:
    • 7! = 5,040
  • 6 factorial:
    • 6! = 720
  • 4 factorial:
    • 4! = 24
  • 3 factorial:
    • 3! = 6
  • 2 factorial:
    • 2! = 2
  • 1 factorial:
    • 1! = 1

These examples are quickly verifiable using the calculator for factorial on this page.

Where Are Factorials Used?

  • Combinatorics: permutations and combinations (e.g., nPr, nCr)
  • Probability and statistics: binomial/Poisson distributions, likelihoods
  • Algorithms: counting problems, dynamic programming, recursion practice
  • Mathematics education: series expansions, limits, and growth comparisons

FAQs: n Factorial Calculator

What does n factorial mean?

It’s the product of the first n natural numbers. Example: 5! = 120.

Is 0! really 1?

Yes. By definition and to make formulas (like combinations) consistent, 0! is 1.

How big can factorials get?

Extremely large very quickly. Even 20! is 2,432,902,008,176,640,000. That’s why a dedicated n factorial calculator is ideal.

Can I see the steps?

Yes. The tool shows the multiplication chain n × (n−1) × … × 1, and progressive steps for manageable n to keep performance smooth.

    Tips for Learning Factorials

    • Start small: verify 1!, 2!, 3!, … on the calculator to build intuition.
    • Use the working view to connect the definition with the final value.
    • For permutations (nPr) and combinations (nCr), recall:
      • nPr = n!/(n−r)!
      • nCr = n!/[r!(n−r)!]

    Use the n factorial calculator now to find the factorial of a number, check homework, or prepare for exams with confidence.