Permutations with Repetition Calculator
Calculate the number of possible permutations when repetition is allowed, useful for passwords and combination locks, free in your browser.
Enter Values
Minimum 1
Minimum 0
How to use this calculator
- Enter n (items to choose from) and r (positions to fill).
- Read the count.
How it works
When order matters and repeats are allowed, the count is n raised to the power r (n^r).
Worked example
n=10, r=3 (a 3-digit PIN). = 1000 possibilities.
Common mistakes
- Using this when items can't repeat — that's standard permutations (nPr).
- Swapping n and r.
Frequently asked questions
What is a permutation with repetition?
Arrangements where items can repeat, so the count is n^r — n choices for each of r positions, like a 4-digit PIN giving 10^4.
How is it different from a normal permutation?
Standard permutations use each item once (nPr); with repetition, every position can reuse any of the n options.
When do I use n^r?
When each of the r positions can be any of the n items independently — like PINs, number plates or binary strings.
Related tools
- Combinations with Repetition Calculator
- Permutations Calculator
- Combinations Calculator
- Factorial Calculator
- Exponent (Power) Calculator
- Scientific Calculator
Explore more in Maths, Education & Science.
Cite this tool
Zerdly. (2026). Permutations with Repetition Calculator. Retrieved from https://www.zerdly.com/tools/permutations-with-repetition-calculator/
Tip: Enter any known values to calculate the remaining results.
All calculations run in your browser. Your inputs are never saved or transmitted.