How to calculate nPr with the Permutation Calculator
Enter the set size in Number of items (n) and the number of positions in Number arranged (r). Choose No repetition or Allow repetition, then select Calculate. The result area shows the selected formula, the arithmetic used, and the exact integer count.
- Enter a non-negative whole number in Number of items (n).
- Enter a non-negative whole number in Number arranged (r).
- Choose No repetition when an item can appear once at most. Choose Allow repetition when an item can fill several positions.
- Select Calculate.
What No repetition changes in a permutation calculation
No repetition uses P(n, r) = n! / (n - r)!. Number arranged (r) cannot exceed Number of items (n), because each item can be used once in the arrangement. For example:
n = 5
r = 2
No repetition
P(5, 2) = 20How permutations with repetition work
Allow repetition uses P(n, r) = n^r. Each position can use any of the n items, so r can be larger than n. With n = 2 and r = 3, the result is 2^3 = 8. With n = 0 and a positive r, the result is 0.
The calculator treats n and r as counts, so the answer has no measurement unit. It accepts whole numbers from 0 through 10,000. Empty inputs, negative values, decimals, and values above 10,000 produce an error.
What the permutation result includes
After Calculate, Formula & steps shows the selected formula, the factor or power expression, and the exact integer result. The calculation runs in your browser using the values you enter.
- Select Copy result to copy the displayed text. If clipboard access fails, the result remains available for manual selection and copying.
- Select Download result (.txt) to save the result as
permutation-calculator-result.txt. - Select Reset to clear both inputs, restore No repetition, hide the result, and clear the error.
When to use a combination or factorial calculator
Use the Combination Calculator when changing the order does not create a different choice, so A-B and B-A count as one outcome. Use the Factorial Calculator when you need n! or a subfactorial / derangement number by itself. Browse Math Calculators for equations, fractions, sequences, geometry, matrices, vectors, and number theory.
Where ordered arrangements come up
No repetition fits assignments where each item fills one position once. The order of those positions changes the result.
Allow repetition fits fixed-length codes when each position accepts one of a set of symbols and a symbol may appear more than once.
Frequently asked questions
How do I calculate nPr?
Enter the set size in Number of items (n) and the positions in Number arranged (r). Choose No repetition and select Calculate. The calculator applies n! / (n - r)! and shows the steps.
What is the permutation formula with repetition?
The permutation formula with repetition is n^r. Choose Allow repetition when an item can be used in more than one position.
Can r be larger than n in a permutation?
r can be larger than n when Allow repetition is selected. No repetition rejects that input because an item cannot be used twice.
What happens when r is 0?
When r = 0, the calculator returns 1. It displays a zero-position explanation in Formula & steps instead of the usual factor or power expression.