Combination Calculator

Count selections where the order of chosen items does not matter. Enter your own values below to see combinations and check the method behind it.

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Your inputs

Change the example values to match your situation.

Your result

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

How this calculator works

Combinations count unordered selections: n! ÷ (r! (n−r)!).

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What is Combination Calculator?

Combination Calculator helps you count selections where the order of chosen items does not matter.

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

How to use Combination 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 combinations. 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.

Combination Calculator: a worked example

With the inputs below, the result is 120 (combinations). 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
Combinations120

Understanding the Combination result

The main output is combinations. 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.

Combination 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.

Combination Calculator FAQs

What does Combination Calculator calculate?

Combination Calculator helps you count selections where the order of chosen items does not matter. Its main output is combinations.

What inputs do I need for Combination 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 Combination Calculator use?

Combinations count unordered selections: n! ÷ (r! (n−r)!).

What is a worked example for Combination Calculator?

Example inputs: Number of items (n): 10; Items selected (r): 3. The result is 120 (combinations).

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 combinations?

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

Why might my Combination 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 Combination Calculator?

Yes. Note your first combinations, 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 Combination 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.