Online Tool Store
Permutation Calculator
Calculate nPr permutations and nCr combinations from n and r with exact, arbitrary-precision results. Runs entirely in your browser.
🔒 This tool runs entirely in your browser. Your files are never uploaded to a server.
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Example shown — enter your own n and r (order matters for permutations).
- nPr (permutations)
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- nCr (combinations)
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How it works
- Enter n, the total number of items.
- Enter r, how many of them you're arranging or choosing.
- See both nPr (order matters) and nCr (order doesn't) at once.
The formula
nPr = n! ÷ (n − r)!
nCr = nPr ÷ r!
Example: arranging 3 of 8 runners into 1st/2nd/3rd place is 8P3 = 8! ÷ 5! = 336 ways.
FAQ
What's the difference between a permutation and a combination?
A permutation counts arrangements where order matters (1st, 2nd, 3rd place in a race); a combination counts selections where order doesn't (which 3 people are on a committee, regardless of who was picked first). nPr is always greater than or equal to nCr for the same n and r.
Why is there a limit of n = 170?
Factorials grow extremely fast — 171! already exceeds what a 64-bit number can represent even with BigInt-scale precision in a browser's reasonable compute time, so 170 is a practical ceiling for an instant, exact result.
Are the results exact, or rounded?
Exact — the calculation uses arbitrary-precision integer arithmetic (BigInt), not floating-point math, so there's no rounding error even for large results.
What if r is 0?
Both nPr and nCr equal 1 when r = 0 — there's exactly one way to arrange or choose zero items (do nothing).
How we compare
| Feature | Online Tool Store | Calculator.net | Scientific calculator app |
|---|---|---|---|
| Permutations and combinations together | ✓ | Separate pages | One at a time, via nPr/nCr keys |
| Exact results, no floating-point rounding | ✓ | ✓ | Limited by calculator precision |
| No ads | ✓ | Ad-supported | ✓ |
Getting nPr and nCr side by side saves the mental step of remembering how the two relate.