Math

Permutation Calculator

Calculate permutations nPr: the number of ordered arrangements of r items chosen from n.

How to use this permutation calculator

Enter the values requested above and select Calculate. Change any input to compare another scenario. The calculation runs locally in your browser and does not require an account.

Formula and method

nPr = n! ÷ (n−r)!.

Example

Awarding gold, silver and bronze among 10 finalists gives 10P3 = 720 ordered outcomes.

Tips for a useful result

Permutations count different orders as different outcomes.

What this calculator is useful for

Calculate permutations nPr: the number of ordered arrangements of r items chosen from n. The result is intended for quick estimates, checking arithmetic and comparing scenarios. When a result affects a contract, tax filing, medical decision, building-code requirement or other high-stakes situation, verify the result with the appropriate professional or authoritative source.

Frequently asked questions

What does the Permutation Calculator calculate?

Calculate permutations nPr: the number of ordered arrangements of r items chosen from n.

How does the Permutation Calculator work?

nPr = n! ÷ (n−r)!.

Is the Permutation Calculator free to use?

Yes. ERICH Calculators is free to use and does not require an account.