CALCULATE WITH CONFIDENCE

Counting, Permutations & Combinations

Anagram & Repeated-Letter Permutation Calculator

Count distinct arrangements of a word, phrase, or multiset containing repeated symbols.

Counting & Combinatorics

Count distinct arrangements of repeated symbols

Multiset permutations
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example

Distinct arrangements

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Enter valid values to see the result.

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Understand the subject

Why do repeated letters reduce anagram counts?

Repeated symbols create duplicate orderings. Swapping two identical letters changes no visible arrangement, so those duplicate orders must be removed.

Use it for words, phrases, multiset arrangements, and repeated-symbol permutations.

The relationship

The counting rule

See the structure

Identical swaps do not create a new word

Worked example

Check the rule with a small case

LEVEL has 5! ÷ (2! × 2!) = 30 distinct arrangements.

Interpret with care

Choose the right counting model

Case and spaces only matter when you choose to treat them as distinct symbols.

Use the Permutation & Combination Generator when a small case needs to be inspected rather than only counted.

Quick guide

How to use this calculator

  1. Enter the symbols to arrange.
  2. Choose whether spaces and letter case distinguish symbols.
  3. Read the number of unique arrangements after duplicate orders are removed.

Calculation method

Divide out repeated-symbol orders

If n symbols contain repeated frequencies r₁, r₂, and so on, the number of distinct arrangements is n! divided by r₁!r₂!⋯.

Worked example

Arrange LEVEL

LEVEL has five letters, with L repeated twice and E repeated twice.

5!/(2!2!) = 30

Supported inputs

Precision and limits

Discrete domain

Inputs are whole counts. Negative, fractional, grouped, and scientific-notation inputs are rejected.

Exact integers

Results use arbitrary-precision integers and are never rounded. Inputs and output size are bounded to keep the page responsive.

Text

Up to 1,000 Unicode grapheme clusters are supported. Canonically equivalent text is normalized before counting. The result is a count; the anagrams themselves are not generated.