Frequency Analysis Tool (Letters, Bigrams, IoC)

Frequency analysis is the oldest code-breaking method: count how often each letter appears and compare the counts with normal English, where E, T, A, O, I and N dominate. It breaks Caesar and substitution ciphers, tells transposition from substitution, and shows whether a text is English at all. This tool counts letters (or every character), compares them with English, and adds χ², the index of coincidence, top bigrams, trigrams and doubled letters.

How to use this tool

1. Paste the text or ciphertext.
2. Choose letters only, or every character for encodings and symbols.
3. Sort the table alphabetically or by frequency, and set how many bigrams and trigrams to list.
4. Compare the chart and the "letters by frequency" line with English.

Formula

share = count ÷ N × 100% IoC = Σ nᵢ(nᵢ − 1) / (N(N − 1)) χ² = Σ (nᵢ − N·pᵢ)² / (N·pᵢ)

N is the number of letters, nᵢ the count of letter i and pᵢ its English share. The index of coincidence is the chance that two letters picked at random are equal: about 0.066 for English, 0.038 for random letters. χ² measures the distance from English; it grows with text length, so compare it with the letter count.

Example

For AAB, A appears twice out of three letters: 66.67%. For AABB the index of coincidence is (2·1 + 2·1) / (4·3) = 0.3333. A pangram such as "The quick brown fox jumps over the lazy dog" has 35 letters, and O is the most common with 4 (11.43%).