Calculator
Example data table
| Input | Processed text | n | r | Raw nPr | Full unique count | Unique r-length count |
|---|---|---|---|---|---|---|
| MATH | MATH | 4 | 3 | 24 | 24 | 24 |
| BOOK | BOOK | 4 | 3 | 24 | 12 | 12 |
| AAB | AAB | 3 | 2 | 6 | 3 | 3 |
Formula used
1) Raw positional permutations: When every character position is treated as distinct, the number of length-r arrangements is P(n, r) = n! / (n - r)!.
2) Full unique permutations with repeated letters: When repeated characters should not create duplicate answers, the full-length count becomes n! / (f₁! × f₂! × ... × fₘ!), where each f represents a repeated-character frequency.
3) Unique r-length permutations with repeats handled: The calculator counts all distinct sequences of length r that can be formed from the available character frequencies. This avoids overcounting arrangements that look identical because of repeated letters.
How to use this calculator
- Enter a word or phrase in the input field.
- Choose whether spaces should be ignored and whether only letters should remain.
- Decide whether uppercase and lowercase characters should count separately.
- Enter r for partial arrangements, or leave it blank to use the whole processed text.
- Press the calculate button to show results above the form.
- Review the summary cards, frequency table, chart, and length analysis table.
- Use the CSV and PDF buttons to export the result summary.
FAQs
1) What is the difference between raw and unique permutation counts?
Raw counts treat every character position as different, even when letters repeat. Unique counts remove duplicate-looking arrangements caused by repeated characters, so they better match textbook word permutation questions.
2) Why does the calculator ask for arrangement length r?
r lets you study shorter arrangements instead of always using the full word. For example, a five-letter word can be analyzed for two-letter, three-letter, or full-length arrangements using the same page.
3) How are repeated letters handled?
The calculator builds a frequency table first. It then uses those frequencies to avoid counting repeated-letter duplicates more than once, which is essential for words like BOOK, LEVEL, or BALLOON.
4) Why is there a chart with log10 values?
Permutation totals grow extremely fast. A log10 chart keeps very small and very large counts visible in one graph, making length-by-length comparison easier.
5) Why are sample arrangements sometimes missing?
Listing every arrangement becomes impractical when counts are large. The page only shows samples for smaller result sets so the interface stays fast and readable.
6) Should I enable case sensitivity?
Enable it when uppercase and lowercase should behave like different symbols. Leave it off when you want A and a treated as the same letter.
7) Can I use phrases instead of single words?
Yes. You can enter phrases, then choose whether spaces stay or disappear. You can also keep letters only when punctuation or numbers should be removed before counting.
8) What do the CSV and PDF exports include?
The exports include the key summary metrics and the length analysis table. The PDF also attempts to include the chart snapshot when available in the browser.