Permutation Calculator

Count ordered arrangements when selecting items from a group. Enter your own values below to see permutations and check the method behind it.

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Your inputs

Change the example values to match your situation.

Your result

Let’s work it out.

Fill in your inputs and select Calculate.
Your result and breakdown will appear here.

How this calculator works

Permutations count ordered selections: n! ÷ (n−r)!.

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What is Permutation Calculator?

Permutation Calculator helps you count ordered arrangements when selecting items from a group.

The main result is permutations. The formula, example and assumptions below explain how to interpret it.

How to use Permutation Calculator

Use the example to get familiar with the form, then enter your own figures. Any rates in the example are illustrative. Check the field labels and units before calculating.

  1. Gather number of items (n) and items selected (r). Use values from the same situation or reporting period.
  2. Replace the example number of items (n) with your own value, then complete the other fields. Check the displayed units.
  3. Select Calculate and read permutations. Change one input and calculate again to compare a second scenario. Reset restores the original example.
  • Enter number of items (n), at least 0 and at most 1000. Use a whole number.
  • Enter items selected (r), at least 0 and at most 1000. Use a whole number.

Permutation Calculator: a worked example

With the inputs below, the result is 720 (permutations). Follow the example, then replace these illustrative values with your own.

Example inputs and output
Input or outputExample value
Number of items (n)10
Items selected (r)3
Permutations720

Understanding the Permutation result

The main output is permutations. It applies to the inputs and operation you selected.

Displayed results use a readable number of decimal places. When checking a result by hand, keep extra precision until the last step. To compare scenarios, change one input at a time and keep the others fixed.

Permutation Calculator: assumptions and common mistakes

A useful estimate starts with the right inputs. Check the following assumptions and limits before applying the result to your situation.

  • Check the base value, sample definition and chosen operation. Display rounding should come after the calculation.

For wider guidance, visit NIST statistical handbook. The formula and scope of this specific tool are stated on this page.

Permutation Calculator FAQs

What does Permutation Calculator calculate?

Permutation Calculator helps you count ordered arrangements when selecting items from a group. Its main output is permutations.

What inputs do I need for Permutation Calculator?

You need number of items (n) and items selected (r). Use the field labels and units to match your figures to the formula.

Which formula does Permutation Calculator use?

Permutations count ordered selections: n! ÷ (n−r)!.

What is a worked example for Permutation Calculator?

Example inputs: Number of items (n): 10; Items selected (r): 3. The result is 720 (permutations).

How should I enter number of items (n)?

Enter number of items (n), at least 0 and at most 1000. Use a whole number.

How do I choose items selected (r)?

Enter items selected (r), at least 0 and at most 1000. Use a whole number. The example uses 3; replace it if your circumstances differ.

How should I read permutations?

The main output is permutations. It applies to the inputs and operation you selected.

Why might my Permutation Calculator result differ from my records?

Check the base value, sample definition and chosen operation. Display rounding should come after the calculation. Differences in entered values, units or rounding can also change the comparison.

Can I compare two scenarios in Permutation Calculator?

Yes. Note your first permutations, change number of items (n) or another input, and select Calculate again. Editing a field clears the old result so it is not mistaken for a new calculation.

Is Permutation Calculator free, and where are my inputs calculated?

This calculator is free to use without signing in. Its formula runs in your browser; calculator inputs are not sent to a calculation API. The inputs reset to the example values when you reset the form or start a fresh page.