Converter Web ToolsConverter WebTools

Permutations Calculator (nPr)

Permutations Calculator (nPr) — get the answer instantly in your browser, free and private.

Enter n (total items) and r (items to arrange) to compute nPr — the number of ordered arrangements of r items from n, where order matters. The formula is nPr = n! / (n − r)!. For example, the number of ways to award gold, silver and bronze among 10 runners is 720. Calculated in your browser.

About permutations (nPr)

This calculator works out nPr — the number of ways to arrange r items from a set of n when order matters. Enter n and r and it returns the count using nPr = n! / (n − r)!. It runs in your browser.

How Permutations works

How to use it

  1. Enter n (total items) and r (how many to arrange).
  2. Read the number of permutations.

How it works

A permutation counts ordered arrangements — first, second and third place are different outcomes. The tool multiplies n × (n−1) × … for r terms, which equals n! / (n − r)!.

Common uses

  • Count ordered arrangements
  • Work out race finishing orders
  • Count passwords or codes
  • Solve probability problems
  • Help with statistics homework
  • Count seating orders
  • Plan ordered selections
  • Learn combinatorics

Frequently asked questions

What is nPr?
The number of ordered arrangements of r items from n.
What is the formula?
nPr = n! / (n − r)!.
How is it different from combinations?
Permutations count order; combinations do not.
What if r is greater than n?
That is invalid — r cannot exceed n.
Is my input uploaded?
No — it calculates in your browser.
Can it handle big numbers?
Yes — large results are shown clearly.
Is it free?
Yes — completely free with no sign-up.