This free online permutation and combination calculator finds both nPr (the number of ways to arrange r items from a set of n in order) and nCr (the number of ways to choose r items from n when order doesn't matter). It's widely used in probability, statistics, and combinatorics problems.
How to Use the Permutation and Combination Calculator
Enter the total number of items in the "Total number of items (n)" field.
Enter how many items you're choosing in the "Number of items chosen (r)" field.
Click "Calculate" to see both the nPr (permutations) and nCr (combinations) results.
Frequently Asked Questions
A permutation (nPr) counts arrangements where order matters, while a combination (nCr) counts selections where order doesn't matter. For example, choosing 2 letters from the set A, B, C gives nPr = 6 ordered pairs but only nCr = 3 unordered pairs.
It computes nPr = n × (n − 1) × ... × (n − r + 1), then derives nCr = nPr / r! by dividing the permutation count by r factorial. Both are computed iteratively rather than with full factorials, so larger values of n won't overflow as quickly.
Both n and r must be non-negative whole numbers, and r cannot be greater than n. The calculator shows "n and r must be whole numbers.", "n and r must be non-negative integers.", or "r cannot be greater than n." depending on the invalid input.
Yes, it's completely free with no sign-up required.