Factorial Calculator

Calculate factorials (n!), permutations (nPr), and combinations (nCr). Supports ...

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5! = 5 × 4 × 3 × 2 × 1
= 120
Result
120
Digits: 3

Factorial Reference (n!)

When to Use Each

Factorial (n!)

Total ways to arrange ALL n items. Example: 5 people in a line = 5! = 120 arrangements.

Permutation (nPr)

Arrangements where ORDER MATTERS. Example: Gold/Silver/Bronze from 10 athletes = P(10,3) = 720.

Combination (nCr)

Selections where ORDER DOESN'T MATTER. Example: Choose 3 from 10 for a team = C(10,3) = 120.

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Calculator Features

Factorial (n!) - Product of 1 to n
Permutation - Ordered arrangements
Combination - Unordered selections
BigInt - Unlimited precision
Step View - See calculation steps
Reference Table - Quick factorial lookup

Why Use Factorial Calculator?

Three Calculations in One

Calculate factorials (n!), permutations (nPr), and combinations (nCr) in one tool.

BigInt Support

Calculate factorials up to 10,000 using JavaScript BigInt for unlimited precision.

Step-by-Step Breakdown

See the multiplication steps for small factorials to understand the calculation.

Formula Display

View the mathematical formula being used for each calculation type.

Copy Large Results

Copy results with thousands of digits to clipboard for use elsewhere.

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All calculations happen in your browser. No data sent to servers.

Common Uses

Probability

Calculate the number of ways events can occur in probability problems.

Combinatorics

Count arrangements and selections in discrete mathematics.

Statistics

Used in binomial distributions, permutation tests, and sampling.

Computer Science

Algorithm analysis, sorting complexity, and graph theory.

How It Works

1

Choose Calculation Type

Select Factorial (n!), Permutation (nPr), or Combination (nCr) based on your needs.

2

Enter Your Values

Input n (and r if using permutations or combinations). Max n is 10,000.

3

View the Formula

See the mathematical formula being applied to your values.

4

Get Your Result

See the result with digit count. Copy large numbers to clipboard if needed.

Math Tips

Factorials Grow Fast

10! = 3.6 million, 20! = 2.4 quintillion. Factorials grow extremely fast - that's why BigInt is needed.

nCr vs nPr

Use nPr when order matters (podium positions). Use nCr when order doesn't matter (team selection).

Copy Large Results

Results with 50+ digits are truncated for display. Use the Copy button to get the full number.

Frequently Asked Questions

A factorial (written as n!) is the product of all positive integers from 1 to n. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120. By definition, 0! = 1.
This calculator can handle very large factorials thanks to BigInt support. You can calculate factorials up to about 10,000 without issues. However, the result may have thousands of digits!
Permutations (nPr) count arrangements where order matters: how many ways to arrange r items from n items. Combinations (nCr) count selections where order doesn't matter: how many ways to choose r items from n items.
Factorials are used in probability, statistics, combinatorics, and calculus. They help calculate permutations, combinations, Taylor series, and appear in many mathematical formulas.
nPr (permutation) counts ordered arrangements - selecting r items from n where order matters (like race positions). nCr (combination) counts unordered selections - selecting r items from n where order doesn't matter (like lottery numbers).
By convention, 0! = 1. This makes many mathematical formulas work correctly, including the formula for combinations: nC0 = n!/0!(n-0)! = 1, which correctly states there's exactly one way to choose nothing from n items.

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