Advanced Factorial Calculator with Steps, Insights and Exports

Example: Calculate 7! using this calculator.

1. Select Factorial n! from the operation dropdown.
2. Enter 7 into the n field.
3. Click Calculate to compute the result.
4. The results section displays 7! = 5040 with steps and statistics.
5. Review digits count, trailing zeros, logs and scientific notation values.
6. Use Download CSV or Download PDF to export your output.

This simple walkthrough shows how to confirm factorial values and capture structured data for learning, research or documentation.

Factorial: For any integer n ≥ 0, n! = n × (n − 1) × ... × 2 × 1, with 0! = 1.

Trailing Zeros in n!: ⌊n/5⌋ + ⌊n/25⌋ + ⌊n/125⌋ + ...

Double Factorial: n!! = n × (n − 2) × (n − 4) × ... down to 1 or 2.

Permutation (nPr): P(n, r) = n! / (n − r)!.

Combination (nCr): C(n, r) = n! / (r!(n − r)!).

Falling Factorial: (n)_k = n × (n − 1) × ... × (n − k + 1).

Rising Factorial: (n)^k = n × (n + 1) × ... × (n + k − 1).

Logs & Scientific Notation: Approximated using leading digits and digit count for stable insight into magnitude of very large results.

1. Choose the operation: factorial, double factorial, permutations, combinations, falling or rising factorial.
2. Enter n (and r or k when required by the selected operation).
3. Click Calculate to generate the exact value and key statistics.
4. Review digits, trailing zeros, logs and scientific notation for magnitude analysis.
5. For n!, inspect multiplication steps and optional prime factorization breakdown.
6. Use Download CSV to export the current results and example table.
7. Use Download PDF to open a printable report (then save as PDF).

Ideal for students, data scientists, engineers and developers needing transparent, exportable combinatorial calculations with clear structure and documentation.

• Supports exact large integer arithmetic for n up to 1000.
• Multiple modes: n!, n!!, nPr, nCr, falling and rising factorials.
• Shows digits count, trailing zeros, logarithms and scientific notation.
• Displays readable step-by-step expansion for reasonable n values.
• Exports results and tables directly as CSV or printable PDF.

• Counting arrangements and selections in combinatorics and probability.
• Evaluating permutations, combinations and binomial coefficients in statistics.
• Supporting recursive definitions and series expansions in calculus.
• Modeling discrete processes in computer science and algorithm analysis.
• Teaching growth rates, asymptotics and Stirling-style approximations.

Factorials grow super-exponentially: even modest n produce extremely large values. Digits, logs and scientific notation help interpret magnitude safely and clearly.

Use these indicators when comparing models, validating formulas, or avoiding overflow in software, spreadsheets and numerical experiments involving combinatorial terms.

Q1. What input range does this factorial calculator support?

You can enter any non-negative integer n from 0 to 1000. This keeps calculations precise, prevents browser slowdown, and still covers typical school, university, research, and engineering combinatorics use-cases effectively.

Q2. Why does the calculator show digits, zeros and scientific notation?

Factorials grow extremely fast, so full numbers become unreadable. Digits, trailing zeros, logarithms, and scientific notation summarize size safely, help compare magnitudes, and prevent overflow or misinterpretation in spreadsheets, code, or documentation.

Q3. Can I use this tool for permutations and combinations?

Yes. Select permutation or combination mode, provide n and r, and the calculator returns exact nPr or nCr along with digit count, trailing zeros, and magnitude statistics for deeper probabilistic or statistical analysis.

Q4. What is the difference between falling and rising factorials?

Falling factorial multiplies decreasing terms from n, used in combinatorics and discrete calculus. Rising factorial multiplies increasing terms from n, often used in series expansions, special functions, and advanced probability modeling.

Q5. Why do large factorials matter in real-world problems?

Large factorials appear in permutations, combinations, binomial distributions, reliability models, algorithm complexity, Monte Carlo setups, and counting configurations. This tool helps evaluate such expressions accurately for teaching, research proofs, or engineering calculations.

Q6. Can I export my factorial results for reports or homework?

Yes. Use the CSV button to download structured numeric data, or use the PDF button to open a print-ready view and save it as PDF through your browser’s print dialog.