Permutation Calculator
Ordered arrangements nPr.
Enter your values
Enter the total items n you are working with.
Enter the choose r you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- Permutations nPr
- 720
- With repetition (n^r)
- 1,000
- Combinations nCr
- 120
- Ratio P/C
- 6
Quick answer
A permutation counts arrangements where order matters: nPr = n!/(n−r)!.
nPr = n! / (n − r)!
At a glance
| What it does | Ordered arrangements nPr. |
|---|---|
| Category | Math |
| Inputs needed | Total items n, Choose r |
| Main output | Permutations nPr |
| Formula | nPr = n! / (n − r)! |
| Cost | Free — no sign-up, no download |
How to use the Permutation Calculator
- 1Enter the total number of items.
- 2Enter how many you are arranging.
- 3Compare with combinations if order does not matter.
Inputs explained
- Total items n
- Enter the total items n you are working with.
- Choose r
- Enter the choose r you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- Total items n10
- Choose r3
Results
- Permutations nPr720
- With repetition (n^r)1,000
- Combinations nCr120
- Ratio P/C6
Frequently asked questions
Permutation or combination?
Permutation when order matters (podium places), combination when it does not (lottery).
What is nP0?
1 — there is one way to arrange nothing.
What do I need to enter into the Permutation Calculator?
Just 2 values: total items n, choose r. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Permutation Calculator work out the answer?
A permutation counts arrangements where order matters: nPr = n!/(n−r)!. It applies the formula nPr = n! / (n − r)! and shows the working so you can check each step by hand.
Is the Permutation Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.