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

  1. In “nPr Calculator”, enter total number of elements (n) and number taken at a time (r).
  2. Choose whether repetition is allowed.
  3. Click Calculate to get the number of permutations and the formula used.
  4. 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).