Permutations Calculator P(n, r)
P(n, r) = n! / (n−r)!. Number of ways to arrange r items from n where order matters.
Result
General calculation reads
Amazon affiliateAs an Amazon Associate we may earn from qualifying purchases. This does not add cost for you.
How to use this calculator
- Enter n and r.
- Read permutations.
About this calculator
Permutations count ordered arrangements. P(n,r) = n! / (n-r)! = n × (n-1) × … × (n-r+1). For r = n: P(n,n) = n! (all orderings of n items). Used when sequence matters: race orderings, password permutations, seating arrangements. Always P(n,r) ≥ C(n,r) by factor of r!.
Frequently asked
When does order matter?+
When doesn't it?+
P(n,n) = n!?+
Birthday paradox?+
How to compute big P?+
Related calculators
More tools you might like
Hand-picked tools that pair well with this one — same audience, same intent.
C(n, r) = n! / (r!(n−r)!). Number of ways to choose r items from n where order doesn't matter.
Convert a z-score to one-tail or two-tail p-value via the standard normal CDF.
Compute probability density and cumulative probability at x for given μ, σ.
P(X = k) = C(n,k) p^k (1−p)^(n−k). Probability of exactly k successes in n trials.
r = Σ(xᵢ−x̄)(yᵢ−ȳ) / √(Σ(xᵢ−x̄)² Σ(yᵢ−ȳ)²). Linear correlation [−1, 1].
Generate a printable inventory count sheet PDF — items down the left, count / par / order columns, signature line.