Anagram Count Calculator
Distinct anagrams of letters with repeated-letter correction.
What it does
Anagram counts correct for repeats: seven letters make 5,040 orders, but BALLOON doubles two pairs, so only 1,260 read differently. Dividing repeat factorials fixes the overcount.
The tool above takes any letters A to Z. It returns distinct arrangements with the factorial form and unique mix.
The default BALLOON gives 1,260 from 7! over 2! x 2!. LETTER gives 180; AABB gives 6.
Math follows Whitman combinatorics with Applied Combinatorics multinomials behind them. Both state n! over repeat factorials used here.
How to use
- Type the word, letters only.
- Read the count first.
- Read the factorial form beside it.
- Check unique letter mix.
- Try LETTER (180) to verify.
- Cap entries at 18 letters.
Formula
- n
- Total letters in the word.
- r1, r2
- Count of each repeated letter.
- divisor
- Factorial product of repeats.
Letters A to Z only, case folded. Factorials run exact integer loops within double precision to 18!. Repeats of one never divide; all-same words return 1.
Worked example
Example: BALLOON
Defaults: BALLOON.
- Word: BALLOON, 7 letters.
- Counts: B1 A1 L2 O2 N1.
- Numerator: 7! = 5,040.
- Divisor: 2! x 2! = 4.
- Result: 5,040 / 4 = 1,260.
- Unique letters: 5 of 7.
- Tool shows 1,260 arrangements, 7! / (2! x 2!).
Reference table
| Word | Math | Count |
|---|---|---|
| BALLOON | 7!/(2!x2!) | 1,260 |
| LETTER | 6!/(2!x2!) | 180 |
| AABB | 4!/(2!x2!) | 6 |
| ABC | 3!/1 | 6 |
Limits
- Full-length only; draws differ.
- Letters only, no spaces.
- Case folds to upper.
- 18-letter integer cap.
Common mistakes
- Forgetting repeat division.
- Counting case variants.
- Including spaces as letters.
- Running draws through full formula.
- Trusting float factorials past 18.
Try it yourself
Quick checks. Answers sit tucked under each question.
LETTER?
6 letters, E2 T2: 720 / 4 = 180.
AABB?
4 letters, 2 + 2: 24 / 4 = 6.
BALLOON with all unique?
7 distinct: 5,040 / 1 = 5,040.
Questions
How are anagrams counted?
n! divided by repeat factorials: 7!/(2!x2!) = 1,260 for BALLOON.
Why divide by repeats?
No: swapping identical letters makes nothing new, so divide the repeats out.
What if all letters differ?
Just n!: ABC gives 6 with divisor 1.
Does case matter?
Yes: case counts once, spaces and punctuation sit outside the math.
Do 5 letters from BALLOON fit?
No: partial draws need pattern casework, not the full-length formula.
How long can words run?
18 letters max keeps integer math exact in this tool.