Math · Free online calculator
Permutation and Combination Calculator
Calculate the number of ordered arrangements and unordered selections from a set of items.
CALCULATOR GUIDE
How the Permutation and Combination Calculator works
Calculate the number of ordered arrangements and unordered selections from a set of items. This guide explains the inputs, calculation method, example and key limitations so you can check whether the result fits your question.
Calculate the number of ordered arrangements and unordered selections from a set of items.
Permutations = n! ÷ (n−r)!; combinations = n! ÷ (r!(n−r)!).
Inputs to prepare
Before you calculate, gather the values the question asks for and check their units. Choose options carefully and use consistent dates, periods and starting values. The notes below describe the fields shown in the calculator above.
- Total items (n)Use a numeric value and keep the displayed unit consistent. Allowed range: 0 to 170
- Items selected (r)Use a numeric value and keep the displayed unit consistent. Allowed range: 0 to 170
How to use the Permutation and Combination Calculator
- Enter the details. Fill in each required field and use the units or formats shown next to it.
- Check your assumptions. Confirm dates, comparison values, time periods and selected options before submitting.
- Calculate and review. Read the result together with its unit, time period and any additional breakdown.
- Compare scenarios. Change one input at a time if you want to understand how different values affect the outcome.
Formula and worked example
Permutations = n! ÷ (n−r)!; combinations = n! ÷ (r!(n−r)!).
Example calculation
Selecting 3 of 10 gives 720 permutations and 120 combinations.
Try the same values in the calculator above. If your result differs, recheck the units, input order, assumptions and rounding displayed by the tool.
What your result means
Calculate the number of ordered arrangements and unordered selections from a set of items. Read the result label and unit carefully. A useful estimate describes only the inputs and assumptions supplied; it should not be treated as proof of a future outcome or a guarantee.
- Check the displayed unit and period before comparing results.
- Use values from a reliable source and keep them up to date.
- Repeat the calculation with an independent check when the outcome matters.
Assumptions and limitations
Inputs must be whole numbers with 0 ≤ r ≤ n; very large results are not displayed beyond finite numeric precision.
The calculator is a general-purpose tool. Actual outcomes may depend on local rules, provider terms, measurement standards or personal circumstances not represented in the fields. For consequential financial, health, legal, tax or construction decisions, confirm the result with an appropriate authoritative or qualified source.
Frequently asked questions
How does the permutation and combination calculator work?
Permutations = n! ÷ (n−r)!; combinations = n! ÷ (r!(n−r)!).
Which inputs does the permutation and combination calculator use?
The fields shown above describe the inputs and units required for this method. Use consistent units and verify all values before calculating.
What should I check before using the permutation and combination calculator result?
Inputs must be whole numbers with 0 ≤ r ≤ n; very large results are not displayed beyond finite numeric precision.
For transparency, use the formula and worked example to check the output. Add authoritative references and have the calculation reviewed before relying on it for a consequential decision.