Permutations and Combinations Calculator
Fill in the values and the answer updates as you type.
How the Permutations and Combinations Calculator works
nPr = n! ÷ (n − r)! and nCr = n! ÷ (r! × (n − r)!). Choosing 3 people from 10 for a ranked podium gives 720 permutations, but choosing 3 for a committee gives 120 combinations because order is ignored.
Inputs and results
The Permutations and Combinations Calculator takes 2 inputs and gives 3 results.
What you enter
- Total items (n) — starts at 10.
- Items chosen (r) — starts at 3.
What you get
- Permutations nPr (order matters)
- Combinations nCr (order does not matter)
- Arrangements with repetition (n^r)
Example: Permutations and Combinations Calculator with the starting values
With total items (n) 10 and items chosen (r) 3, the calculator returns:
| Permutations nPr (order matters) | 720 |
|---|---|
| Combinations nCr (order does not matter) | 120 |
| Arrangements with repetition (n^r) | 1,000 |
Change any value above and the results update straight away.
Permutations and Combinations Calculator FAQ
How do I use the Permutations and Combinations Calculator?
Enter total items (n) and items chosen (r) in the fields, then read permutations npr (order matters), combinations ncr (order does not matter) and arrangements with repetition (n^r) in the result panel. The answer updates as you type, and you can press Calculate or Enter to refresh it. Use “Copy link” to share your exact numbers with someone else.
What does the Permutations and Combinations Calculator calculate?
Count arrangements and selections of r items from n. It returns permutations npr (order matters), combinations ncr (order does not matter) and arrangements with repetition (n^r) from the 2 values you provide.
What values does the Permutations and Combinations Calculator start with?
It opens with total items (n) 10 and items chosen (r) 3 so you can see a working result straight away. Replace them with your own numbers, or press Reset to return to these starting values.
Is the Permutations and Combinations Calculator free and private?
Yes. It is free, needs no account, and runs in your browser, so nothing you type is sent to or stored on our servers. See the Privacy Policy for details.
Can I rely on the Permutations and Combinations Calculator for important decisions?
Treat the result as a well-rounded estimate. Real situations often have details a general calculator cannot know, so confirm important decisions with a qualified professional. See the Disclaimer for more.