Calculators
Permutation and Combination Calculator
Calculate permutations (nPr) and combinations (nCr) for given n and r locally in your browser.
Enter the total number of items (n) and the number to choose (r). Permutations (nPr) count ordered arrangements; combinations (nCr) count unordered selections. Calculations run locally in your browser; your values are not uploaded or stored.
Find the number of ordered arrangements and unordered selections.
Enter the total number of items (n) and the number to choose (r). Permutations count ordered arrangements: nPr = n! ÷ (n−r)!. Combinations count unordered selections: nCr = n! ÷ (r! × (n−r)!). Both values are calculated exactly using integer arithmetic. Everything runs locally in your browser, so your values are not uploaded or stored.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
What is the difference between permutations and combinations?
Permutations (nPr) count ordered arrangements where sequence matters. Combinations (nCr) count unordered selections where sequence does not matter. For example, choosing 3 items from 5 gives 5P3 = 60 permutations but only 5C3 = 10 combinations.
What formulas does this calculator use?
Permutations: nPr = n! ÷ (n−r)!. Combinations: nCr = n! ÷ (r! × (n−r)!). Both are calculated using exact integer arithmetic so the results are precise.
Which inputs are accepted?
Enter whole numbers for n (total items) and r (items to choose) from 0 to 1000. The calculator requires r ≤ n. Values outside the range or non-integer inputs show a clear error.
Do my numbers stay private?
Yes. The calculation and copy action run locally in your browser. CodeASystem does not upload or store the values you enter.