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Updated 2026-03-07 UTC
Factorial Calculator — n! with Worked Examples
Compute factorials (n!) for non‑negative integers. Includes examples, verification tips, and common mistakes — powered by GetCalcMaster Scientific Calculator.
Factorials show up everywhere: permutations, combinations, probability, series expansions, and algorithm analysis. This page explains factorial notation (n!), shows examples, and gives quick ways to verify results.
Important: This content and tool are for educational purposes only. Outputs are estimates; always cross‑verify with official sources and/or a qualified professional.
What this calculator is
The Scientific Calculator is an interactive tool inside GetCalcMaster. It’s designed to help you explore scenarios, understand formulas, and document assumptions.
Key features
- Immediate results as you change inputs
- Transparent assumptions and explainable outputs
- Works well with the built‑in Notebook for saving scenarios
Formula
n! = n × (n−1) × (n−2) × … × 2 × 1
0! = 1Quick examples
factorial(0) # 1factorial(5) # 120factorial(10) # 3628800# Growth check factorial(8) / factorial(7) # should be 8
Verification tips
- Sanity check: factorial(0) = 1 and factorial(1) = 1.
- Recursive check: factorial(n) = n × factorial(n−1) for integer n≥1.
- Factorials grow extremely fast; use scientific notation or logs for large n.
Common mistakes
- Using negative n. Factorials are typically defined for non‑negative integers in basic combinatorics.
- Accidentally using a non‑integer. If you need non‑integer factorials, that’s the Gamma function (not the same thing as n!).
- Overflow/precision issues for huge n — use logs if you only need magnitude.
How to use it (quick steps)
- Choose a non‑negative integer n.
- Open the Scientific Calculator.
- Enter factorial(n) or n! (depending on your preferred syntax).
- Verify with quick identities (see tips below).
- For very large n, consider using log10(factorial(n)) for magnitude/number of digits.
Related tools and guides
Featured guides
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Scientific calculator guide
Scientific workflows and key functions.
Trigonometry workflow
sin/cos/tan with unit checks.
Logarithms workflow
ln, log10, and change-of-base.
Math hub
Tools + explainers across math topics.
FAQ
What is 0 factorial (0!)?
0! is defined as 1. This makes many combinatorics identities work cleanly (and matches the Gamma function relationship Γ(1)=1).
How fast does n! grow?
Very fast — faster than any exponential a^n. Even 20! is already ~2.43×10^18.
Is factorial defined for non‑integers?
A common extension is the Gamma function Γ(n+1), but that’s a different function than the integer factorial definition.
Tip: For reproducible work, save your inputs and reasoning in Notebook.