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Frequency analysis

Paste ciphertext to see which letters turn up most and how that compares to normal English.

Letter frequency

Your text English

Letters

    Bigrams

      Trigrams

        Why letter counts break ciphers

        English isn't evenly spread across the alphabet. E is about 12% of everything written. T, A, O, I and N follow. J, Q, X and Z barely appear. A cipher that swaps each letter for another, consistently, keeps that uneven shape. Only the labels change. Count the cipher letters, match the commonest to E, and you've started cracking it. Al-Kindi described the method in the ninth century, and it has broken substitution ciphers ever since.

        Reading the chart

        The dark bars are your text. The orange tick in each column is how often that letter appears in ordinary English. Switch to “By count” to see the shape on its own.

        • Bars match the ticks: the text is English, or a transposition with the right letters in the wrong order.
        • Same lumpy shape, different letters: a single-alphabet substitution. If the shape looks slid sideways, it's a Caesar shift. Otherwise use the substitution solver.
        • Flat: several alphabets are in use, usually Vigenère.

        The index of coincidence

        Pick two letters from the text at random. The index of coincidence is the chance they're the same letter. English scores about 0.066. Perfectly random letters score 1/26, about 0.038. Because a substitution doesn't change the score, it tells you the cipher's family before you know anything else. William Friedman introduced it in 1922, and it's what our Vigenère solver uses to find the key length.

        Bigrams and trigrams

        Pairs and triples show which letters sit together. The commonest English bigrams are TH, HE, IN, ER and AN. The commonest trigrams are THE, AND, ING and ION. If one three-letter group dominates your ciphertext, it's very likely THE, and that gives you three letters at once.

        Questions

        What is frequency analysis?

        Counting how often each symbol appears in a ciphertext. In English, E, T, A, O and I are the most common letters. A simple substitution cipher changes the letters but not how often they appear, so the most common cipher letter is usually E.

        What are the most common letters in English?

        In order: E, T, A, O, I, N, S, H, R, D, L, U. E alone is about 12% of all letters. The chart on this page uses the same English figures our solvers score against.

        What do bigrams and trigrams tell me?

        Common pairs and triples point to common words and endings. TH, HE and IN are the top English bigrams, and THE and AND the top trigrams, so the most common cipher trigram is often THE.

        What does a flat frequency chart mean?

        If no letter stands out, the cipher probably uses more than one alphabet, as Vigenère does. Frequency analysis on its own won't break that, but the Vigenère tool can.

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