Permutation & Combination Calculator (nPr, nCr)
Compute permutations nPr and combinations nCr from n and r, with the factorial formulas shown. Exact whole-number results, even for large n.
π Runs entirely in your browser. Your input and output are never sent to a server or stored β fully private.
Order matters for permutations, not for combinations. Results are exact, even for large n. Click a result to copy.
About this tool
This permutations and combinations calculator counts how many ways you can choose r items from a set of n, both when the order matters and when it does not. Enter n and r and it returns the number of permutations, written nPr, and the number of combinations, written nCr, using the factorial formulas. It is handy for probability homework, lottery odds and working out arrangements. Every count is computed in your browser.
Frequently asked questions
When should I use a permutation or a combination?
Use a permutation when the order of the chosen items matters, and a combination when it does not. Picking a president, secretary and treasurer from a club is a permutation, because the roles are different; dealing three cards as a hand is a combination, because the order they arrive does not change the hand. That single question β does order count β decides which number you need.
What are the formulas behind nPr and nCr?
Permutations use nPr = n! Γ· (n - r)!, and combinations use nCr = n! Γ· (r! Γ (n - r)!), where the exclamation mark means factorial. So choosing 2 from 4 gives 4P2 = 12 ordered arrangements but only 4C2 = 6 unordered selections. Combinations are always fewer, because each unordered group corresponds to r! different orderings that are counted just once.
Are the values I enter sent to a server?
No. All of the counting is done locally in your browser, so the values of n and r you enter are never sent to or stored on a server. For very large inputs the totals can grow enormously, but the calculation still runs instantly on your own device, with nothing to install.