Permutation Calculator

Calculate permutations where order matters (e.g., ABC is different from BAC)



Leave empty for all items

How It Works

This tool calculates permutations where the order of items matters:

  • Full permutations (n!): All possible arrangements of all items
  • Partial permutations (nPr): All possible arrangements of r items selected from n items
  • Formula: nPr = n! / (n-r)! where n is total items and r is subset size

Note: Permutations differ from combinations - in permutations, ABC and BAC are counted as different arrangements.

Worked example

Items: A, B, C, D (n = 4). Subset size r = 2.

₄P₂ = 4! / (4−2)! = 24 / 2 = 12

All 12 ordered pairs: AB, AC, AD, BA, BC, BD, CA, CB, CD, DA, DB, DC. Notice AB and BA both appear as separate entries — that's the defining feature of a permutation. A combination calculator, by contrast, would count AB and BA as the same outcome and report only 6 pairs.

Why the count can explode fast

Leave the subset size blank and the tool arranges all n items, giving n! total orders. With just 8 items that's 8! = 40,320 permutations, and with 10 items it's 3,628,800 — past 10,000 the tool caps the on-screen list at the first 100 results (still reporting the true total count) so the browser tab doesn't freeze trying to render millions of list entries. Between 1,000 and 10,000 results it asks for confirmation before rendering the full list.

Duplicate items

If you type the same item twice (e.g., "A, A, B"), the tool warns you but still treats the two A's as distinct positions when generating orders, so the permutation count reflects n distinct slots rather than the smaller count you'd get from a multiset permutation formula.