Permutation Generator
Generate every ordered arrangement from a list of words, numbers, or labels. Choose the arrangement length, decide whether repetition is allowed, and copy the checked result.
Built and checked by TheToolNet Editorial Team · Last reviewed: September 12, 2026 · How we check math tools
Order matters: A–B and B–A are different permutations.
Generate permutations from a list
Enter up to 10 distinct items. To keep the page responsive, the generator displays at most 10,000 arrangements.
Generated arrangements
No arrangements generatedHow to use the permutation generator
- Enter distinct items, one per line or separated by commas.
- Set r, the number of positions in each output.
- Enable repetition only when an item may be selected again.
- Generate the arrangements and compare the displayed count with the formula check.
For example, three distinct letters arranged two at a time produce 3P2 = 6 results: AB, AC, BA, BC, CA, and CB.
Full and partial permutations
A full permutation uses every item, so n = r and the count is n!. A partial permutation fills only r positions from n available items. Four colors arranged two at a time produce 4P2 = 12 ordered pairs.
Permutations with repetition
When repetition is allowed, every one of r positions has n choices, giving nr results. Binary strings of length three have 2³ = 8 outcomes, including 000 and 111. Without repetition, those outcomes would be invalid.
Why generated output is limited
Permutation lists expand extremely quickly: ten distinct items have 10! = 3,628,800 full arrangements. This tool calculates the expected count first and refuses lists above 10,000 rather than freezing the browser or presenting a partial result as complete.
If you only need the number rather than every row, use the nCr and nPr calculator.
Frequently asked questions
Does order matter in a permutation?
Yes. Swapping positions creates a different permutation.
Can I generate arrangements shorter than the list?
Yes. Set the items-per-arrangement value below the number of available items.
Why are duplicate input labels rejected?
Identical labels make it unclear whether they represent separate objects or a multiset. Enter unique labels, or enable repetition if reuse is intended.