utility calculator

Anagram & Scramble Word Solver

Detect if two words are anagrams of each other, generate all letter permutations, and analyze character frequency with a sorted histogram.

Formula Verified by Dr. Arthur Pendelton, PhD

Quick actions: Save inputs, view saved runs, print, share, or export results

Saved Runs

Inputs

Configuration

Calculation mode

Word or Phrase A

Word or Phrase B

Results

Anagram Verification

Yes, they are anagrams!

Distinct letters6

Bookmark this anagram solver

Save this page for word game preparation, puzzle solving, and linguistics analysis.

Formula

Anagram Detection and Permutations

Anagram = Sorted(A) === Sorted(B)
Permutations (N Distinct) = N!
Permutations (Repeated) = N! / ∏(K!)

Two phrases are anagrams if their alphabetically sorted letters match. The count of distinct permutations is determined by the total letters factorial divided by the product of duplicate letter factorials.

Step by step

How the calculation works

1Choose the mode: Anagram Checker or Permutation Generator.
2For Anagram Checker, enter Word A and Word B to compare.
3For Permutation Generator, enter a single word (maximum 7 characters) to generate all combinations.
4Analyze the letter frequency chart below to view letter occurrence distributions.

Example

Example Anagram Pairs

"Silent" and "Listen" contain the exact same characters: e, i, l, n, s, t. The word "cat" has 3! = 6 permutations (cat, cta, act, atc, tca, tac).

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How to understand and use this calculator

What is an Anagram?

An anagram is a word or phrase formed by rearranging all the letters of another word or phrase, using each letter exactly once. For example, "listen" is an anagram of "silent," "astronomer" is an anagram of "moon starer," and "the classroom" is an anagram of "school master."

Anagrams have been used throughout history for cryptography, literary games, and wordplay. Famous examples include "William Shakespeare" → "I am a weakish speller" and "Clint Eastwood" → "Old West action." In the modern era, anagrams appear in word games like Scrabble, crossword puzzles, and literary puzzles.

Detecting anagrams algorithmically is simple: sort both strings alphabetically (ignoring spaces and case) and check if they are identical. If yes, they are anagrams. This O(n log n) approach works for any length strings.

Permutations and Combinatorics

A permutation is an arrangement of elements in a specific order. The number of permutations of n distinct characters is n! (n factorial). For example, "ABC" has 3! = 6 permutations: ABC, ACB, BAC, BCA, CAB, CBA.

When characters repeat, the number of distinct permutations is reduced: n! / (k₁! × k₂! × ... × kₘ!), where k₁, k₂, ..., kₘ are the frequencies of each repeated character. For "AAB", it is 3! / 2! = 3 permutations: AAB, ABA, BAA.

For long strings, the number of permutations grows explosively. A 10-letter word with all distinct characters has 10! = 3,628,800 permutations. This calculator generates all permutations for short inputs (up to 7-8 characters) and estimates the count for longer ones.

Character Frequency Analysis

Character frequency analysis counts how often each letter appears in a text. It is one of the oldest cryptanalysis techniques, used since the 9th century by Arab polymath Al-Kindi in his "Manuscript on Deciphering Cryptographic Messages."

In English, the most frequent letters are E, T, A, O, I, N, S, H, R (remembered by the word "ETAOIN SHRDLU"). This frequency distribution allows cryptanalysts to break simple substitution ciphers by matching the most frequent ciphertext characters to the most common plaintext letters.

Letter frequency histograms are also used in typesetting (to calculate average word spacing), data compression (Huffman coding assigns shorter codes to more frequent characters), and natural language processing (to identify the language of a text).

How to Use This Anagram Solver

Switch to Anagram Checker mode to compare two words or phrases — enter Word A and Word B and the tool sorts and compares their letters (ignoring spaces, punctuation, and case) to confirm whether they are true anagrams.

Switch to Permutation Generator mode to enter a single word of up to 7 characters. The tool generates every unique letter arrangement and displays a character frequency histogram for whichever input is active.

Worked Example: Checking "Listen" vs. "Silent" and Permuting "Word"

Checker mode: "listen" and "silent" both reduce to the sorted letters e-i-l-n-s-t, so the tool confirms they are anagrams, with a frequency table showing each of the 6 letters appearing exactly once.

Generator mode: the 4-letter input "word" has all distinct characters, so it produces 4! = 24 unique permutations. A shorter 3-letter example, "cat", produces 3! = 6 permutations: cat, cta, act, atc, tca, tac.

Related Calculators

This solver is part of a Text & Encoding Tools cluster. Count letters, words, and reading time with the Word Counter Calculator, convert text casing with the Text Case Converter, or explore other letter-substitution tools like the Morse Code Calculator and the Roman Numerals Calculator.

Related concepts

Permutation

An arrangement of all elements of a set in a specific order; n distinct elements have n! permutations.

Frequency analysis

The study of how often letters or patterns appear in a text, used in cryptanalysis and linguistics.

Transposition cipher

A cryptographic technique that rearranges the letters of a plaintext message without changing them.

Frequently Asked Questions

What is an anagram?+

An anagram is a word or phrase created by rearranging all the letters of another word or phrase, using each letter exactly once. "Earth" and "Heart" are anagrams of each other.

How do you check if two words are anagrams?+

Sort both words alphabetically and compare. If the sorted strings are identical, the words are anagrams. Alternatively, count the frequency of each letter in both words and verify that all counts match.

How many permutations does a 4-letter word have?+

If all 4 letters are distinct, there are 4! = 24 permutations. If letters repeat, the count is lower: 4! divided by the factorial of each repeated letter count.

What is the most common letter in English?+

E is the most frequently used letter in English text, appearing approximately 12.7% of the time. The top 5 most common letters are E, T, A, O, and I.

What is a pangram?+

A pangram is a sentence that uses every letter of the alphabet at least once. The most famous is "The quick brown fox jumps over the lazy dog," which contains all 26 letters.

What is a heterogram?+

A heterogram is a word or phrase in which no letter appears more than once. "Subjectivity" is not a heterogram because it repeats letters, but "background" is (all 10 letters are unique).

Are anagrams used in cryptography?+

Historically, yes. Simple letter transposition ciphers are essentially anagrams. Modern encryption uses far more sophisticated mathematical transformations, but anagram analysis (permutation counting) underpins transposition cipher cryptanalysis.

What is a word square?+

A word square is a grid of words arranged so that each row and column spells a word, forming a square matrix of letters. Constructing word squares requires extensive anagram and permutation analysis.

What is frequency analysis in cryptography?+

Frequency analysis is the technique of studying the occurrence rates of letters or groups of letters in ciphertext to deduce the plaintext. It exploits the fact that every natural language has a characteristic letter frequency distribution.

What are the most common two-letter words in English?+

The most common two-letter words are: of, to, in, is, it, be, as, at, so, we, he, by, or, on, do, if, me, my, up, an. These are useful anchors in anagram solving for short phrases.

What is the Scrabble value of having many permutations?+

In Scrabble and similar word games, knowing anagrams of your letter tiles lets you spot high-scoring plays you might otherwise miss. Letters with many valid anagrams (like AELRST → anagram of ALERTS, ALTERS, ARTELS, LASTER, RASTLE, SLATER, STALER, TARSEL) are particularly valuable.

What is Huffman coding?+

Huffman coding is a lossless data compression algorithm that assigns variable-length binary codes to characters based on their frequency — shorter codes for more frequent characters. It relies on character frequency analysis to minimize the average code length.

Anagram Detection and Permutations

Anagram = Sorted(A) === Sorted(B) Permutations (N Distinct) = N! Permutations (Repeated) = N! / ∏(K!)

How to understand and use this calculator

What is an Anagram?

Permutations and Combinatorics

Character Frequency Analysis

How to Use This Anagram Solver

Worked Example: Checking "Listen" vs. "Silent" and Permuting "Word"

Checker mode: "listen" and "silent" both reduce to the sorted letters e-i-l-n-s-t, so the tool confirms they are anagrams, with a frequency table showing each of the 6 letters appearing exactly once.

Related Calculators

Related concepts

Permutation

An arrangement of all elements of a set in a specific order; n distinct elements have n! permutations.

Frequency analysis

The study of how often letters or patterns appear in a text, used in cryptanalysis and linguistics.

Transposition cipher

A cryptographic technique that rearranges the letters of a plaintext message without changing them.

Frequently Asked Questions

What is an anagram?+

An anagram is a word or phrase created by rearranging all the letters of another word or phrase, using each letter exactly once. "Earth" and "Heart" are anagrams of each other.

How do you check if two words are anagrams?+

How many permutations does a 4-letter word have?+

If all 4 letters are distinct, there are 4! = 24 permutations. If letters repeat, the count is lower: 4! divided by the factorial of each repeated letter count.

What is the most common letter in English?+

E is the most frequently used letter in English text, appearing approximately 12.7% of the time. The top 5 most common letters are E, T, A, O, and I.

What is a pangram?+

A pangram is a sentence that uses every letter of the alphabet at least once. The most famous is "The quick brown fox jumps over the lazy dog," which contains all 26 letters.

What is a heterogram?+

A heterogram is a word or phrase in which no letter appears more than once. "Subjectivity" is not a heterogram because it repeats letters, but "background" is (all 10 letters are unique).

Are anagrams used in cryptography?+

What is a word square?+

A word square is a grid of words arranged so that each row and column spells a word, forming a square matrix of letters. Constructing word squares requires extensive anagram and permutation analysis.

What is frequency analysis in cryptography?+

What are the most common two-letter words in English?+

The most common two-letter words are: of, to, in, is, it, be, as, at, so, we, he, by, or, on, do, if, me, my, up, an. These are useful anchors in anagram solving for short phrases.

What is the Scrabble value of having many permutations?+

What is Huffman coding?+

Anagram & Scramble Word Solver

Inputs

Configuration

Results

Bookmark this anagram solver

Anagram Detection and Permutations

How the calculation works

Example Anagram Pairs

Learn more about this calculation

Understanding Calculator Formulas: How DTC Turns Inputs into Results

How to Use Do The Calculation Calculators: A Practical Step-by-Step Guide

Anagram & Scramble Word Solver

Inputs

Configuration

Results

Bookmark this anagram solver

Key output metrics

Character Frequency Distribution

How to understand and use this calculator

What is an Anagram?

Permutations and Combinatorics

Character Frequency Analysis

How to Use This Anagram Solver

Worked Example: Checking "Listen" vs. "Silent" and Permuting "Word"

Related Calculators

Related concepts

Frequently Asked Questions

Anagram Detection and Permutations

How the calculation works

Example Anagram Pairs

Learn more about this calculation

Understanding Calculator Formulas: How DTC Turns Inputs into Results

How to Use Do The Calculation Calculators: A Practical Step-by-Step Guide

Key output metrics

Character Frequency Distribution

How to understand and use this calculator

What is an Anagram?

Permutations and Combinatorics

Character Frequency Analysis

How to Use This Anagram Solver

Worked Example: Checking "Listen" vs. "Silent" and Permuting "Word"

Related Calculators

Related concepts

Frequently Asked Questions