Calculator
What the Permutation Calculator does
Permutation Calculator: calculates P(n,r) from n and r. Example: n 10 and r 3 gives p(n,r) 720.
Give the Permutation Calculator your n and r and it works out P(n,r). Change any input and the output follows immediately.
The method matters as much as the answer when you are still learning the topic. That is usually what brings someone sanity-checking a spreadsheet here.
The work is done by JavaScript already loaded in your browser, so your input never crosses the network.
The field table, the method and a worked example are documented after the tool for anyone who wants to check the working.
What do the Permutation Calculator fields mean?
The Permutation Calculator uses 2 inputs. None of the boxes start empty. The page loads with a worked set of values you can edit or replace.
| Field | What to enter | Default |
|---|---|---|
| n | required | 10 |
| r | required | 3 |
How does the Permutation Calculator work?
Each output is derived from the inputs above in a single pass; there is no hidden state carried between runs, so the same inputs always give the same calculation.
If something is off you are told which field, not given a generic failure.
Worked example
These are the values the Permutation Calculator loads by default, and the result it produces from them. Open the tool above and you will find precisely these figures already in place.
| n | 10 |
|---|---|
| r | 3 |
| P(n,r) | 720 |
|---|---|
| What this means | P(10,3) = 720 |
Beyond the formula: permutations
Permutations count arrangements where order matters (first, second, third place), which is why P(n,r) is always greater than or equal to C(n,r) for the same n and r: reordering an already-chosen group counts as a different permutation but not a different combination.
Common mistakes and sanity checks
- P(n,r) grows extremely fast: P(10,10), the number of ways to arrange 10 distinct items in a row, is 10!, already over 3.6 million, which is why brute-force approaches to arrangement problems become impossible very quickly as n grows.
- r cannot exceed n, since you can’t select and order more items than exist. This calculator returns an invalid result if r > n, a common input mistake when the two numbers get swapped.
- The classic real-world permutation problem is a race’s finishing order or a code where character order matters. If you’re instead picking a group where order of selection doesn’t matter (a committee, a set of toppings) you actually want a combination.
How to use it
- Set n.
- Put r.
- Results update continuously rather than on submit.
- Check P(n,r) and What this means on the right.
- Use Copy Link if you want the same setup again later, or Print for a paper copy.
What this tool does not do
- Very large or very small numbers hit JavaScript floating-point limits (about 15 significant digits).
- Displayed values are rounded; the underlying calculation keeps full precision.
- Values outside the documented ranges are rejected rather than approximated.
Frequently asked questions
n and r, nothing else. Each field is pre-filled with a sensible default, so nothing is mandatory before you see a result.
With the values loaded when the page opens, p(n,r) comes out as 720. Nudge one field at a time to see which one the answer is most sensitive to.
No. There is no upload step, no database, and nothing to delete afterwards.
Free for any use, personal or commercial.
The formula is shown above precisely so you do not have to take the accuracy on trust.