How to Use the Permutation Calculator

Select the type of permutation calculation, enter your values, and click Calculate. The calculator supports four types of permutations with detailed results including the formula used.

Types of Permutations

Standard Permutation (nPr)

The number of ways to arrange r items from n distinct items where order matters. Formula: P(n,r) = n! / (n-r)!. For example, P(5,3) = 60 represents the 60 ways to arrange 3 items from a set of 5.

All Permutations (n!)

When r = n, you are arranging all items. This is simply n factorial. For example, there are 5! = 120 ways to arrange 5 different books on a shelf.

Circular Permutation

Arrangements in a circle where rotations are considered the same. Formula: (n-1)!. For example, seating 6 people at a round table has (6-1)! = 120 distinct arrangements.

Permutation with Repetition

When items can be repeated, the formula is n^r. For example, a 4-digit PIN using digits 0-9 has 10^4 = 10,000 possible combinations.

Common Applications

Calculating the number of possible passwords or PINs
Determining race finish orders
Seating arrangements at tables
Scheduling and ordering problems
Lottery probability calculations

Permutations vs Combinations

In permutations, order matters: ABC is different from CBA. In combinations, order does not matter: ABC and CBA represent the same selection. Permutations are always greater than or equal to combinations for the same n and r values.