Math & Scientific
Permutation Calculator
Permutation: it counts arrangements where order matters using P(n, r) = n! / (n−r)!. Worked through below with real figures, and the calculator repeats the working on your own inputs — free, on-device, instant.
From your n and r, Permutation Calculator computes the result via the standard method. No accounts, no uploads — just an instant way to work through a calculation.
About this calculator
Permutation is easiest to get wrong in the setup, not the arithmetic. It counts arrangements where order matters using P(n, r) = n! / (n−r)!. It matters when you need the exact relationship checked quickly rather than worked through by hand. The worked example on this page (Arrange 2 of 5: P(5,2) = 5! ÷ 3! = 120 ÷ 6 = 20 ordered arrangements.) shows the full substitution; the calculator above runs the same working on your own numbers, in your browser, with nothing uploaded.
How to use
- Enter n, the size of the full set.
- Enter r, how many you arrange.
- Press Calculate to compute P(n, r).
- Read the number of ordered arrangements, with combinations shown for comparison.
Why use Permutation Calculator
Fast
Calculations run in your browser. No round trip to a server.
Private
Your inputs never leave your device. Nothing is uploaded.
Free
No signup, no paywall, no ads-in-results, no watermarks.
Accurate
Uses standard, well-established formulas; check critical results independently.
Mobile-ready
Optimised for phones, tablets, and desktops alike.
Transparent
Honest disclaimers wherever browser limits or regional rules apply.
Common uses
Use it when revising for exams
Use it for verifying answers from a textbook
Permutation in research and report calculations
Use it for quick mental-math cross-checks
Use it for understanding a formula's behaviour
Use it for science-fair and project numbers
Technical notes
Permutation Calculator counts arrangements where order matters using P(n, r) = n! / (n−r)!.
Inputs are taken exactly as entered, so check for typos before trusting an answer.
Because it runs locally, results appear instantly with no server round-trip.
FAQ
When should I use a permutation instead of a combination?
Use a permutation when the order matters, such as ranking finishers in a race; use a combination when order does not matter, such as choosing a team.
Are large permutation results exact?
Yes. Permutations are computed with exact integer arithmetic, so large values are returned precisely.
Do n and r need to be whole numbers?
Yes. Because you are arranging whole items, both n and r must be non-negative whole numbers with r no greater than n.
Does the Permutation Calculator send my data to a server?
No. The Permutation Calculator runs entirely in your browser, so nothing you enter is uploaded, stored, or shared.
Worked example
Arrange 2 of 5: P(5,2) = 5! ÷ 3! = 120 ÷ 6 = 20 ordered arrangements.