Permutations Calculator

Use this permutations calculator to count ordered arrangements quickly and correctly. It suits students, teachers and professionals. It explains permutations in clear terms with a real example. You see the result and the steps for each run.

How Does It Work?

A permutation counts arrangements where order matters and you pick without repeats. The formula uses factorials. nPr equals n factorial divided by the factorial of n minus r. Set n as the total number of items. Set r as the number you will arrange.

Here is a simple example that matches classroom work.

• Choose three books from five in order.
• n equals 5 and r equals 3.
• Compute 5 factorial divided by 2 factorial.
• 5 factorial equals 120. 2 factorial equals 2.
• The result equals 60 ordered arrangements.

The calculator displays each step of this process for every input.

Why Use Our Permutations Calculator?

This tool saves time and reduces errors on nPr problems. It suits homework and quick checks at work. You get clear steps and readable numbers with commas. Helpful notes guide your inputs and results.

• Arrange people on a stage or in a queue.
• Plan race podium orders from a set of finalists.
• Create seating orders for guests without repeats.
• Rank draft picks or award orders.
• Order letters or digits for a code without repeats.

The tool responds fast. Press the button or use the Enter key to run a check.

How to Use This Tool

Follow these steps to compute a permutation with this permutations calculator.

Step 1: Input Your Numbers

Enter the total number of items as n. Enter how many you will arrange as r. Use whole numbers that are zero or greater. Keep r less than or equal to n. The method assumes no repeats. Use this for tasks where order matters.

Step 2: Hit 'Calculate'

Click Calculate to run the math. You can press Enter in a field to run it. The result shows the count of ordered arrangements without repeats. You see the steps with factorial values. Big results show with commas for easier reading. If inputs break the rules the tool shows a clear message.

Notes for best results. Use whole numbers only. Stick to r less than or equal to n. Large inputs create very large outputs. Numbers can exceed common device limits for exact values. For study, compare the steps with your class notes. Use the example of five books and three picks to practice.