Statistics & Probability

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Permutation Calculator.

Calculate ordered selections without repetition.

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Set your values

Results update as you type.

permutations: 720

permutations

720.000000

Results update automatically as you type.

Use Cases

Arranging a subset of items

Determine how many ways you can arrange a specific number of items from a larger set, where order matters. Useful for contests, seating arrangements, or scheduling.

Example: How many ways can 3 out of 5 books be arranged on a shelf? n=5, r=3 gives 60.

Creating passwords or codes

Calculate the number of possible ordered sequences (like passwords) when selecting a certain number of characters from a set without repetition.

Example: If you have 10 unique digits and need a 4-digit code without repetition, n=10, r=4 gives 5040.

Frequently Asked Questions

What is a permutation?
A permutation is an arrangement of items in a specific order. This calculator computes the number of ways to select and arrange r items from a set of n distinct items, where order matters and no item is repeated.
How do I use this permutation calculator?
Enter the total number of items (n) in the 'Items (n)' field and the number of positions (r) in the 'Positions (r)' field. The calculator will compute nPr = n! / (n-r)!, giving the total number of ordered selections without repetition.
What if r is greater than n?
If the number of positions (r) exceeds the number of items (n), the permutation is mathematically zero because you cannot arrange more items than you have. The calculator will return 0 in such cases.

Tips & Common Mistakes

Tips

  • Ensure n and r are non-negative integers. The calculator expects whole numbers for both fields.
  • Remember that order matters in permutations. If order doesn't matter, use a combination calculator instead.
  • If r equals n, the result is n! (n factorial), representing all possible arrangements of the entire set.
  • For large n (e.g., above 170), the factorial may exceed the calculator's capacity, so results may be approximate or error.

Common Mistakes to Avoid

  • Entering r greater than n, which yields zero permutations. Double-check your inputs.
  • Confusing permutations with combinations: permutations consider order, combinations do not.
  • Using decimal numbers or negative values for n or r, which are not valid for this calculator.

Last updated: August 13, 2026