When to use this calculator
Use permutations when the sequence matters, such as first, second and third places in a competition.
Explore the algebra & number calculators for other questions in this topic. For a related calculation, use the Permutation With Repetition Calculator: Count ordered codes or sequences when choices can repeat.
PUTTING IT INTO PRACTICE
Permutation: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Available items (integer) | 10 |
| Positions (integer) | 3 |
| Result | 720 ways |
- Check the input labels and enter the example values above.
- Apply the relationship: Permutations = n! ÷ (n − k)!.
- The result is 720 ways, rounded for display.
How to interpret your result
Items are distinct and cannot repeat. The number of positions cannot exceed available items.
Identify whether the question asks for one term, a total or a count of possible selections. Sequences use a fixed difference or ratio. In counting problems, order and replacement determine the correct model.
Frequently asked questions
Do combinations and permutations count the same thing?
No. Combinations ignore the order of selection; permutations count different orders separately.
When is the permutation calculator useful?
Use permutations when the sequence matters, such as first, second and third places in a competition.
How do I use the permutation calculator?
Enter available items (integer), positions (integer). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Permutations = n! ÷ (n − k)!.
What should I check before using the result?
Items are distinct and cannot repeat. The number of positions cannot exceed available items.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
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