What is the Permutations Calculator?
Calculate permutations (nPr) and factorials (n!) online for free. Enter n and r to count ordered arrangements where order matters, or compute n! for full permutations of n distinct items. Each result includes the formula, multiplication steps, and support for large values. Runs entirely in your browser with no signup.
How to use the Permutations Calculator
- Choose Permutations (nPr) or Factorial (n!).
- Enter n and r (for nPr) or just n (for factorial).
- Click Calculate.
- Review the count, formula, and product steps.
- Copy the result or the full summary.
Common use cases
- Finding P(8,3) = 336 ways to arrange 3 items from 8
- Computing 10! = 3,628,800 for arranging 10 distinct objects
- Counting P(52,5) ordered 5-card sequences from a deck
Frequently asked questions
- What is a permutation?
- A permutation is an ordered arrangement. P(n,r) counts how many ways to arrange r items chosen from n distinct items when order matters.
- What is the permutations formula?
- P(n,r) = n! ÷ (n−r)! = n × (n−1) × … × (n−r+1). When r = n, P(n,n) = n!.
- How is this different from combinations?
- Permutations count ordered arrangements; combinations count unordered selections. P(n,r) is always at least as large as C(n,r), and equals C(n,r) × r!.
- What are the limits?
- nPr supports n up to 10,000. Factorial mode supports n up to 1,000.
