Find all possible letter combinations: list every combination of your letters, or count how many 2, 3 or 4 letter combinations the alphabet or digits give.

1–12 ASCII letters/digits. Spaces and commas separate items; case is ignored.

Blank uses the full input length in letter mode; count mode requires r.

Optional settings

Blank lists up to500; exact total is uncapped.

Related Calculators

Letter Permutation Formula

This calculator counts combinations or ordered arrangements, with optional reuse. The permutation formulas below apply when order matters, reuse is off and identical input letters count once.

P = (n!) / (m₁!m₂!m₃! × s)
  • P = total number of unique letter arrangements
  • n = total number of letters entered
  • m1, m2, m3, … = counts of letters that repeat
  • Factorial means multiplying a whole number by every positive integer below it

If every letter is different, the repeated-letter adjustment is not needed and the count simplifies to:

P = n!

What This Calculator Actually Generates

Choose whether order matters, whether symbols may be reused and how many items each result uses. A blank result length uses the full input pool. Full-length permutations are one supported setting; the default counts combinations. Listed strings are not checked against a dictionary.

Why Repeated Letters Reduce the Count

When a letter appears more than once, swapping those identical letters does not create a new visible arrangement. The formula accounts for this by dividing by the factorial of each repeated-letter count, preventing duplicates from being overcounted.

Letters Pattern Unique Arrangements
EAST All letters are different
P = 4! = 24
LETTER Two E’s and two T’s repeat
P = (6!) / (2!2!) = 180
BANANA Three A’s and two N’s repeat
P = (6!) / (3!2!) = 60

How to Calculate Letter Permutations

  1. Count the total number of letters.
  2. Identify any letters that appear more than once.
  3. Compute the factorial of the total letter count.
  4. Compute the factorial of each repeated-letter count.
  5. Divide the total factorial by the product of the repeated-letter factorials.

For full-length permutations without reuse and with identical letters counted once, this gives the number of distinct outputs. The distinct-position option intentionally counts identical-looking strings separately.

Example with Distinct Letters

If all entered letters are different, every rearrangement is unique.

P = 5! = 120

So a 5-letter input with no repeats has 120 possible orderings.

Example with Repeated Letters

Suppose a set of 6 letters contains one letter repeated twice and another letter repeated twice. The total starts with the full factorial count, then duplicate orderings are removed by division.

P = (6!) / (2!2!) = 180

This is why repeated letters can dramatically shrink the final result count even when the total number of letters stays the same.

Result Growth by Letter Count

The number of possible outputs increases very quickly. For distinct letters, the growth follows factorial behavior, which is why even small increases in input size create many more arrangements.

Number of Letters Distinct-Letter Count
1
1! = 1
2
2! = 2
3
3! = 6
4
4! = 24
5
5! = 120
6
6! = 720

The exact total is computed independently of the list cap. Letter mode supports up to12symbols and lists at most5000results; no dictionary checking is included.

Tips for Using the Calculator

  • Use only letters when you want true anagram-style outputs.
  • If all letters are unique, expect the largest possible result set for that length.
  • If letters repeat, the number of unique outputs will be lower than the full factorial count.
  • Use the list cap to bound generated output; the exact total remains available.
  • If you are searching for words, remember that not every valid permutation will be a real dictionary entry.

Permutation vs. Partial Arrangement

Enter r to use only part of the available letters, or leave it blank in letter mode to use the full pool. Select whether order matters.

A = (n!) / ((n - k)!)

Here, A counts ordered selections of k distinct items without reuse. Unordered selections use C(n,k); with reuse, ordered strings use n^k and unordered selections use C(n+k−1,k). Repeated input letters without reuse use exact bounded-multiset counting.

Common Uses

  • Solving anagrams and word puzzles
  • Checking how many distinct arrangements are possible from a set of letters
  • Teaching factorials and counting principles in math courses
  • Comparing cases with repeated letters against cases with all unique letters
  • Estimating the size of a search space before trying all possible letter orders

Frequently Asked Questions

Does order matter?

Choose the order setting. In permutation mode AB and BA count separately; in combination mode they count once.

Are repeated letters handled correctly?

Yes. Choose whether repeated input letters are identical symbols or distinct positions. With reuse enabled, the available alphabet is the set of distinct symbols.

Will every result be a real word?

No. A permutation is any distinct rearrangement of the letters. Some outputs may be valid words, while many will simply be non-word letter orders.

Why do larger inputs take longer?

Counts grow quickly, but exact integer counting is separate from capped generation. This tool does not validate dictionary words; list output is bounded by your selected cap.