Permutation Calculator

Simplicity at Its Best

Use this permutation calculator to list and count orders where item order matters.

It handles full sets and subsets using nPr and n factorial.

Enter items with commas, set the subset size if needed, then run the calculation.

The tool shows the formula, the working, and a numbered list of permutations.

The page now supports subset permutations, and it explains permutations clearly.

How It Works

Permutations count ordered arrangements of items.

Combinations treat different orders as the same, permutations treat them as different.

For n items, full permutations equal n factorial.

For a subset of size r, nPr equals n factorial divided by n minus r factorial.

Factorial means multiply whole numbers from 1 up to the number.

How to use this tool

1. Type your items in the box. Separate each item with a comma.
2. Set the subset size r if you need partial permutations.
3. Leave r blank to use all items in the list.
4. Click Calculate Permutations to see the count and the list.
5. Read the formula line to see nPr and the numbers used.
6. Scroll the results to view each ordered arrangement.

Input fields explained

• Items box: Enter any labels, one after another, and separate them with commas.
• The calculator trims spaces around items for clean input.
• Repeated labels count as separate items in the count and the list.
• Subset size r: Enter a positive whole number to pick a subset.
• Leave r blank to use the full list with n factorial.
• Set r at most n, which equals the number of items you entered.

What the results show

• The formula line shows n factorial or n factorial over n minus r factorial.
• The calculation line expands factorial values and shows the final count.
• The results area lists each permutation as a numbered list.
• For counts above 10000, the tool shows the first 100 permutations.
• For counts above 1000, the tool asks before listing all permutations.

Notes and limits

• Large lists grow fast since factorial values increase quickly.
• Use simple item names without commas inside a single label.
• Use digits for r only, and start at one.
• Set r no greater than the number of items to get a valid result.
• The list order follows the generator steps used by the tool.
• Repeated labels act like different tokens, which raises the count.

Examples

• Full permutations: Items A B C with r blank produce six orders.
• These include ABC, ACB, BAC, BCA, CAB, and CBA.
• Partial permutations: Items A B C D with r set to two produce twelve orders.
• Examples include AB, AC, AD, BA, BC, BD, CA, CB, CD, DA, DB, and DC.
• Mixed labels: Items apple, banana, cherry with r set to two produce six orders.

Why Use Our Permutation Calculator?

This tool saves time on any task where order matters.

• Plan seating orders for events or meetings.
• Arrange tasks in different orders to test workflows.
• Create sample passwords from a set of symbols without repeats.
• Study math homework or teach counting rules with clear lists.
• Explore schedule orders for small teams or class groups.

A quick recap helps lock it in.

• Use commas for items, and use r for subset size.
• Leave r blank for all items and n factorial.
• Read the formula line to learn how the count was built.
• Scan the list to see each order in plain text.

Try a short list first and grow from there.

This permutation calculator keeps math clear and your work fast.