Permutation Calculator
Compute permutations in seconds. Choose between without repetition (nPr = n! / (n − r)!) and with repetition (n^r), or even generate permutations of a short word like “ABC”. Perfect for counting problems, probability, and discrete math.
n must be ≥ 0
r must be ≤ n for no repetition
No repetition: order matters, elements cannot repeat. With repetition: order matters, elements can repeat.
Permutation formulas
Permutation without repetition:
\(P(n, r) = \frac{n!}{(n - r)!}\)
Total permutations of n distinct objects: \(n! = n \times (n-1) \times \dots \times 1\)
Permutation with repetition:
\(P(n, r) = n^r\)
This calculator uses exactly these formulas.
How to use this permutation calculator
- In “nPr Calculator”, enter total number of elements (n) and number taken at a time (r).
- Choose whether repetition is allowed.
- Click Calculate to get the number of permutations and the formula used.
- In “Permute a string/list”, type a short word or a short list and we will show the first permutations.
FAQs
What’s the difference between permutation and combination?
Permutation = order matters. Combination = order doesn’t matter. If you need combinations, use a combination calculator (nCr).
Why am I getting “n must be ≥ r”?
For permutations without repetition, you can’t arrange more items than you have. Either turn on “with repetition” or reduce r.
Can I use this for passwords or license plates?
Yes — those are typically permutations with repetition (like 26 letters in 6 positions → 26^6).
Formula (LaTeX) + variables + units
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Permutation without repetition: \(P(n, r) = \frac{n!}{(n - r)!}\) Total permutations of n distinct objects: \(n! = n \times (n-1) \times \dots \times 1\) Permutation with repetition: \(P(n, r) = n^r\) This calculator uses exactly these formulas.
- No variables provided in audit spec.
- NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures - FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.