Anagram Solver Odds Calculator
Why Some Words Have Far More Anagrams Than Others
The number of ways to rearrange a word's letters isn't obvious from its length alone — it depends heavily on how many letters repeat. A six-letter word with no repeated letters has vastly more possible arrangements than a six-letter word with a doubled letter, because repeats collapse arrangements that would otherwise be counted as distinct. This calculator applies the permutations-with-repetition formula to any word you enter.
The Formula
Here n is the total letter count, and each r is the number of times a particular letter repeats. A word with all distinct letters simplifies to plain n!, since every repeat factor is 1.
Worked Examples
| Word | Letters | Repeats | Distinct arrangements |
|---|---|---|---|
| LISTEN | 6 (all distinct) | none | 720 |
| PUZZLE | 6 | Z×2 | 360 |
| MISSISSIPPI | 11 | I×4, S×4, P×2 | 34,650 |
The odds of randomly landing on one specific arrangement out of all distinct arrangements is 1 in that arrangement count — for MISSISSIPPI, that's 1 in 34,650.
Where This Calculation Matters
- Word game strategy — understanding why longer words with repeated letters (like double letters in Scrabble racks) can still have relatively few unique arrangements to search through.
- Anagram puzzle design — puzzle setters use this figure to judge how "findable" a solution is by brute-force rearranging versus needing insight.
- Teaching permutations — a concrete, checkable example of the permutations-with-repetition formula from combinatorics.
How to Use This Calculator
- Enter a Word or Letters (for example, LISTEN). Only alphabetic characters are counted.
- Select Calculate to see the total number of distinct letter arrangements and the corresponding 1-in-N odds.
Related Calculations
For the reverse question — how many of those arrangements are actual valid words — see the Word Puzzle Odds Calculator.