What is n factorial in plain language?
n! means multiply every whole number from 1 up to n. Example: 4! = 4×3×2×1 = 24. Special case: 0! = 1.
10! = 3628800
Evaluate n! = n × (n−1) × … × 1 for non-negative integers—including 0! = 1—using exact browser math. Nothing is uploaded.
10! = 3628800
A factorial calculator computes n! = n × (n−1) × … × 1 for non-negative integers, with 0! = 1 by definition. Results use exact big integers in your browser—no upload.
The factorial of a non-negative integer n, written n!, is the product of all positive integers from 1 through n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. By convention, 0! = 1.
Factorials grow extremely fast: 20! has 19 digits; 100! has 158 digits. They are the building block for permutations nPr = n!/(n−r)! and combinations nCr = n!/(r!(n−r)!) in combinatorics, probability, and computer science.
EverydayTools evaluates n! with JavaScript BigInt for n from 0 through 500—exact integers, no rounding. Your input stays in the browser tab and is not sent to a server.
Enter n → get exact n! locally. Use combination or permutation calculators when you need nCr or nPr directly.
Concise answers for common searches — definitions, steps, and comparisons.
n! means multiply every whole number from 1 up to n. Example: 4! = 4×3×2×1 = 24. Special case: 0! = 1.
Permutations nPr = n!/(n−r)! count ordered picks; combinations nCr = n!/(r!(n−r)!) count unordered picks. Both need factorials in the denominator and numerator.
No. n! is calculated locally in your browser with BigInt—n is not sent to EverydayTools servers.
Factorials beyond n ≈ 500 can exceed practical browser memory for exact integers. Use smaller n for homework; specialized math software for research-scale values.
Type a non-negative whole number (0 ≤ n ≤ 500). Decimals and negative values show an error.
The tool multiplies 1 × 2 × … × n using arbitrary-precision integers and displays the full value (for example 10! = 3628800).
Remember 0! = 1 by definition—useful in empty-product and combinatorics edge cases.
For ordered or unordered selections, open the permutation or combination calculator instead of hand-multiplying factorials.
Input
n = 6Output
6! = 7206 × 5 × 4 × 3 × 2 × 1 = 720—common intro combinatorics exercise.
Input
n = 0Output
0! = 1By definition, the empty product is 1; required for consistent nCr formulas.
Input
n = 10 (then use combination tool for r = 3)Output
10! = 362880010C3 = 10!/(3!×7!) = 120; factorial tool verifies 10! before you divide in other tools.
Common real-world scenarios where this tool saves time.
Verify n! by hand or spot-check steps before submitting permutation and combination problems.
See exact factorial sizes for complexity examples (n! growth) without scientific notation rounding.
Understand how counting formulas use factorials before using nPr, nCr, or the probability calculator.
Confirm 8!, 12!, or similar values while studying—faster than multiplying by hand.
| Tool | Formula | What it answers | Example |
|---|---|---|---|
| Factorial (n!) | n × (n−1) × … × 1 | Product of first n integers | 5! = 120 |
| Permutation (nPr) | n!/(n−r)! | Ordered arrangements | 10P3 = 720 |
| Combination (nCr) | n!/(r!(n−r)!) | Unordered selections | 10C3 = 120 |
| Tool | Output type | When to use |
|---|---|---|
| Factorial calculator | Exact integer n! | Counting products; formula building blocks |
| Probability calculator | Decimal P(A) between 0 and 1 | Chance of independent events |
Use n = 0 in the tool to see 0! = 1—required for empty sets and consistent nCr edge cases.
This tool caps at n = 500 for browser safety. Split problems or use computer algebra for larger n.
Open the combination or permutation calculator—they apply the full formula so you do not divide factorials by hand.
Results are exact integers (BigInt). Very large n! displays many digits—that is correct, not an error.
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n! = n × (n−1) × … × 1 for n ≥ 1. By definition, 0! = 1. Example: 5! = 120.
Enter a non-negative integer n (0–500) and the tool instantly shows n! using exact integer math in your browser.
0! = 1 by convention. The calculator returns 1 when n = 0.
nPr = n!/(n−r)! and nCr = n!/(r!(n−r)!). Use the permutation or combination calculator when you need those results directly.
Factorials grow faster than exponential; n > 500 can exceed practical browser memory for exact BigInt results.
Factorial returns a counting product (integer). The probability calculator returns event likelihoods between 0 and 1.
Factorial is defined only for non-negative integers. Negative or fractional n show an error—not a factorial value.
No. n is processed locally in your browser—it is not sent to EverydayTools servers.
Values of n are processed in your browser—they are not uploaded to EverydayTools servers.
Uses JavaScript BigInt for exact n! when 0 ≤ n ≤ 500.
Educational combinatorics aid—not a substitute for formal coursework grading policies.
More free tools for the same workflow.
Calculate combinations nCr = n!/(r!(n−r)!) for unordered selections. No upload: runs locally in your browser. Free, instant nCr results.
Calculate permutations nPr = n!/(n−r)! when order matters—5P2, 10P3, 26P3 & more. Runs locally in your browser, no upload. Exact results up to n=500.
Calculate P(A), complements, P(A and B), and P(A or B) for independent events. No upload—runs locally in your browser. Free, instant.
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Reviewed by EverydayTools Editorial Team on 2026-05-20.