BYTETOOLS

Permutation & Combination Calculator

Calculate permutations (nPr) and combinations (nCr) instantly from n and r, with the factorial formulas shown. Free online nPr and nCr calculator.

720
Permutations (10P3)
120
Combinations (10C3)

Permutations — order matters

nPr = n! / (n − r)! = 10! / (10 − 3)! = 720

Combinations — order does not matter

nCr = n! / (r! · (n − r)!) = 10! / (3! · (10 − 3)!) = 120

  • Computes nPr and nCr together from n and r
  • Exact BigInt arithmetic — no overflow on large results
  • Shows the factorial formula for each answer
  • Validates that r is not greater than n
  • One-click copy of either result
  • 100% private, client-side calculation

How to use the Permutation & Combination Calculator

  1. 1

    Enter the total number of items, n.

  2. 2

    Enter how many you are choosing or arranging, r.

  3. 3

    Read the permutations (nPr) and combinations (nCr) results instantly.

  4. 4

    Expand the formula boxes to see the factorial expressions used.

  5. 5

    Copy either exact result to your clipboard.

About the Permutation & Combination Calculator

The ByteTools Permutation & Combination Calculator works out nPr and nCr from any two whole numbers, n (the total items) and r (the items chosen). It is built for students, statisticians and anyone solving counting, probability or lottery problems who needs both the answer and the formula behind it.

Permutations count arrangements where order matters, while combinations count selections where order does not. The calculator shows both values side by side along with the factorial expressions, so you can check your working rather than just copy a number.

Everything runs locally in your browser using JavaScript and BigInt maths, so even large results are computed exactly and privately. Nothing you type is uploaded, logged or stored, making it safe for homework, exams and research alike.

Frequently asked questions

What is the difference between a permutation and a combination?

A permutation counts ordered arrangements, so ABC and CAB are different. A combination counts unordered selections, so ABC and CAB are the same group. That is why nPr is always greater than or equal to nCr for the same n and r.

How is nPr calculated?

nPr equals n! divided by (n − r)!. In practice the calculator multiplies n by (n−1) down to (n−r+1), which is faster and avoids computing huge factorials. For example, 5P2 is 5 × 4 = 20.

How is nCr calculated?

nCr equals n! divided by (r! × (n − r)!). It counts how many groups of r you can choose from n items when order does not matter. For example, 5C2 is 10, the number of unique pairs from five items.

Why must r be less than or equal to n?

You cannot choose or arrange more items than you actually have, so r must not exceed n. If r is larger, no valid permutation or combination exists and the calculator shows a friendly error instead of a result.

Can it handle large numbers?

Yes. The tool uses JavaScript BigInt, so results with hundreds of digits stay exact. It is capped only to keep your browser responsive, and it warns you if a value is too large.

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