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Permutation Calculator

P(n, r) = n! / (n − r)! for ordered arrangements.

Best for: Use it for rankings, race finishes, passwords, seat orderings - anywhere order matters.

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Input

How it's calculated & sources
The Permutation Calculator uses the standard, deterministic formula, so the same inputs always produce the same result. It runs entirely in your browser, so your inputs are never uploaded. Last reviewed June 2026.

Free & no sign-up · runs entirely in your browser. Results are estimates for general information, not professional advice — verify important decisions with a qualified expert. Last reviewed June 2026.

How it works

P(n, r) = n! / (n − r)! — number of ordered arrangements of r items from n.

Example

P(5, 2) = 5! / 3! = 20

Frequently asked questions

Permutation vs combination?+

Permutation cares about order (ABC ≠ CAB). Combination ignores order (ABC = CAB).

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Quick answers

Short, sourced answers to the questions people (and AI assistants) ask most.

What is Permutation?
A permutation calculator counts how many ordered arrangements of r items can be drawn from n items.
Why does Permutation matter?
The number of distinct ordered selections. Permutations count more than combinations because different orders are counted separately.
How is Permutation calculated?
It divides n factorial by (n - r) factorial, because order matters. Formula: nPr = n! / (n - r)!.
What are common permutation mistakes?
Using permutations when order does not matter (use combinations).
When should you use the Permutation Calculator?
Use it for rankings, race finishes, passwords, seat orderings - anywhere order matters.

What is the Permutation Calculator?

A permutation calculator counts how many ordered arrangements of r items can be drawn from n items.

How the Permutation Calculator works

It divides n factorial by (n - r) factorial, because order matters.

nPr = n! / (n - r)!

Permutations P(n, r) — ordered arrangements of r from n

52060120120
630120360720
7422108402,520
8563361,6806,720
9725043,02415,120
10907205,04030,240

Common mistakes to avoid

  • Using permutations when order does not matter (use combinations).
  • Requiring r greater than n, which is impossible.
  • Confusing nPr with nCr.

Keywords: permutation, npr.

Reviewed by the Free Tools Galaxy editorial team · Updated June 2026 · Calculated privately in your browser.

Frequently asked questions

Is the Permutation Calculator free to use?+

Yes. Every tool on Free Tools Galaxy is 100% free, runs in your browser and requires no signup.

How accurate is the Permutation Calculator?+

Permutation Calculator uses the standard permutation formula in double-precision arithmetic, so the same inputs always produce the same result and you can verify any figure by hand. It is an educational estimate — real-world outcomes depend on your actual rates, rules and assumptions.

Do you store my inputs?+

No. The Permutation Calculator runs entirely in your browser. Nothing is uploaded or saved to a server.

Can I use the Permutation Calculator on mobile?+

Yes — the interface is fully responsive and works on phones, tablets and desktops.

What are common mistakes to avoid?+

The most frequent mistake is mixing units. Double-check your inputs use a single, consistent unit before clicking Calculate.

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Title: I built/used this free permutation calculator — instant, no signup

Body: P(n, r) = n! / (n − r)! for ordered arrangements. Try it: https://freetoolsgalaxy.com/tools/permutation-calculator
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Permutation Calculator on Free Tools Galaxy — P(n, r) = n! / (n − r)! for ordered arrangements. https://freetoolsgalaxy.com/tools/permutation-calculator
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# Permutation Calculator — the free tool I keep coming back to

P(n, r) = n! / (n − r)! for ordered arrangements.

Try it: https://freetoolsgalaxy.com/tools/permutation-calculator
Quora answer
The fastest way is to use a free in-browser permutation calculator: https://freetoolsgalaxy.com/tools/permutation-calculator. P(n, r) = n! / (n − r)! for ordered arrangements.

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<iframe src="https://freetoolsgalaxy.com/tools/permutation-calculator?embed=1" title="Permutation Calculator" loading="lazy"
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I built a free mortgage calculator that works instantly in the browser — no signup, no ads in your face
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Hey r/[subreddit],

I kept needing a quick mortgage calculator and most options online were slow or behind paywalls, so I built one that:

• Runs 100% in your browser (your data never leaves your device)
• No signup, no email wall, no popups
• Loads in under a second on mobile

It covers the standard mortgage use cases (mortgage, home, loan, payment) and links out to the formula + worked examples if you want to learn the math.

Link: https://freetoolsgalaxy.com/tools/mortgage-calculator

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