Calculator Input
Formula Used
P(n, r) = n! / (n - r)!
nr
n!
n! / (a! × b! × c! ...)
Here, n is the number of available characters, r is the selected arrangement length, and repeated character counts are divided out when duplicates exist.
How to Use This Calculator
- Enter the source string you want to analyze, such as product codes, mixed IDs, or custom alphanumeric tokens.
- Choose the arrangement length r to define how many character positions each permutation should contain.
- Pick a filter to keep letters, digits, alphanumeric characters, or all symbols from the input.
- Set case sensitivity and decide whether repeated characters may appear in each arrangement.
- Press calculate to show the result section below the header and above the input form.
- Review the table, graph, and sample arrangements, then export the results to CSV or PDF.
Example Data Table
| Input | Filter | Distinct Characters | r | P(n,r) | n^r |
|---|---|---|---|---|---|
| A1B2 | Alphanumeric | 4 | 2 | 12 | 16 |
| AA11B | Alphanumeric | 3 | 3 | 6 | 27 |
| Code99 | Letters only | 4 | 3 | 24 | 64 |
| 9988 | Digits only | 2 | 2 | 2 | 4 |
Frequently Asked Questions
1. What does this calculator count?
It counts ordered arrangements built from letters, digits, or mixed characters. You can compare length-r permutations, repeated arrangements, and duplicate-adjusted full-string permutations in one place.
2. What is the difference between combinations and permutations?
Permutations care about order, while combinations do not. In this tool, AB and BA are different results, so the calculator focuses on permutation counts instead of combination totals.
3. Why do duplicate characters reduce distinct full permutations?
Repeated characters create arrangements that look identical after swapping equal symbols. Dividing by each repeated count factorial removes those duplicate orderings and leaves only distinct outcomes.
4. When should I allow repetition?
Allow repetition when characters may be reused in different positions, such as generating possible codes or trial sequences. Disable it when each distinct character can appear only once per arrangement.
5. What does case sensitivity change?
Case-sensitive mode treats A and a as different symbols. Case-insensitive mode merges them into one character, which usually reduces the distinct character count and changes the permutation totals.
6. Why does the graph use logarithms?
Permutation counts grow extremely fast. A logarithmic scale keeps very large values readable, so you can compare categories without one bar visually overwhelming all others.
7. Can I use this for passwords or code spaces?
Yes, it can estimate ordered search spaces for short code-like strings. Still, real password strength also depends on entropy, predictability, hashing, and attacker knowledge.
8. What happens if the requested length is too large?
If repetition is disabled, the requested length cannot exceed the number of distinct available characters. The calculator shows a validation message instead of returning an invalid count.