Permutation Calculator

What is the Permutation Calculator?

Count ordered arrangements (permutations) of r items chosen from n. Permutations count arrangements where order matters, such as race finishes, seating plans and PIN codes.

How to use the Permutation Calculator

1. Enter your total items, your chosen.
2. Results update automatically as you type; you can also press Calculate.
3. Read the output: permutations npr, with repetition (nʳ).
4. Use the 📊 chart to see the result visually, then copy or share it.

Formula and method

Worked example

With total items = 10, chosen = 3, the Permutation Calculator returns permutations npr: 720; with repetition (nʳ): 1,000.

Where the Permutation Calculator helps in real life

Eight runners are in a race and you want to know how many ways the gold, silver and bronze could be awarded. The calculator gives 336 different podiums.

A club chooses a president, secretary and treasurer from 15 members. Because each role is different, the order matters and there are 2,730 possibilities.

Common mistakes to avoid

• Using permutations when order does not matter.
• Swapping n (the total) and r (the number chosen).
• Allowing repeats when each item can be used only once.
• Forgetting that nPr grows much faster than nCr.

💡 Practical tip: If order matters, use permutations; if it does not, use combinations — they give very different answers.

Tips for better results

• Ask whether ABC and CBA are different outcomes; if yes, use permutations.
• Use the combination calculator when order is irrelevant.
• Check with small numbers you can list by hand.

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