Permutation (nPr) Calculator
This calculator works out nPr, the number of ways you can arrange r items chosen from a set of n items when the order of selection matters. Permutations turn up whenever sequence changes the outcome: ranking runners in a race, assigning committee roles such as chairperson and treasurer, or working out possible PIN codes without repeated digits. You enter two whole numbers: n, the total items in the set, and r, how many of them you are selecting or arranging. The calculator instantly returns the nPr result (the count of ordered arrangements), the equivalent nCr figure (the same items grouped without regard to order), and r! (the order factor that links the two, since nPr = nCr multiplied by r!). Below the results sits a full step-by-step working panel that substitutes your numbers into the formula nPr = n! / (n - r)!, cancels the common factorial terms, and shows the final answer, alongside a values table listing n, r, n - r, n! and (n - r)!. To use it, simply type your n and r values and the results update as you type; r cannot be greater than n, since you cannot arrange more items than exist. All calculations use exact big-integer arithmetic for n up to 170, so nothing is rounded, though very long results are shown in scientific notation once they exceed 20 digits for readability.
1. Enter Values
2. Notation Guide
A permutation is written as nPr, P(n,r) or nPr. The subscript n is the pool size; r is the selection size.
Order matters in a permutation. Selecting {A, B, C} in a different sequence gives a different permutation.
Compare with combinations (nCr) where order does not matter. nPr = nCr x r!.