Letter Frequency Analysis: The Secret to Cracking Cryptograms
Cryptograms guide · 4 min read
Letter frequency analysis is the single most powerful technique for solving cryptograms, and it's the reason a "scrambled" quote can be cracked without ever knowing the key. The idea is simple: in English, some letters appear far more often than others, and a substitution cipher can't hide that. Count how often each encoded letter shows up, match the most frequent to the most common English letters, and you have your way in. This guide explains frequency analysis, the order of the most common letters, and how to combine it with patterns to crack any cryptogram. For the full solving routine, pair this with how to solve cryptograms.
Why frequency analysis works
A cryptogram is a substitution cipher: every E becomes the same letter throughout. So if E is the most common letter in the original quote, then whatever letter E was swapped for will be the most common letter in the puzzle. The cipher changes the labels but not the statistics. That leak is fatal to the cipher and gold for the solver. The technique is over a thousand years old, the scholar Al-Kindi wrote about it in 9th-century Baghdad, and it still cracks cryptograms today.
The most common letters in English
Here's the order of letter frequency in typical English text, from most to least common:
E, T, A, O, I, N, S, H, R, D, L, C, U, M, W, F, G, Y, P, B, V, K, J, X, Q, Z
A handy way to remember the leaders is the nonsense word "ETAOIN" (sometimes extended to "ETAOIN SHRDLU"). The approximate percentages for the top letters:
| Letter | Frequency |
|---|---|
| E | ~12.7% |
| T | ~9.1% |
| A | ~8.2% |
| O | ~7.5% |
| I | ~7.0% |
| N | ~6.7% |
| S | ~6.3% |
| H | ~6.1% |
| R | ~6.0% |
The bottom of the list, J, X, Q, Z, barely appears, often under 0.2% each. That's useful too: a cipher letter that shows up only once or twice is probably one of these rare letters.
How to use frequency in a cryptogram
The practical routine is short:
- Count every cipher letter. Tally how many times each appears in the puzzle.
- Rank them. The most frequent cipher letter is your prime suspect for E, the next for T or A.
- Test, don't assume. Pencil in E for the top letter and check whether words start making sense. Frequency tells you what's likely, not certain, so confirm with the surrounding words.
- Use the long puzzles. Frequency is statistical, so it's far more reliable on a 20-word hard cryptogram than on a 5-word phrase, where a single unusual word can skew the counts.
Our medium and harder cryptograms show a built-in frequency panel that lines up the cipher's letter counts against standard English, so you can spot the matches at a glance.
Beyond single letters: bigrams and doubles
Frequency analysis goes deeper than individual letters. English has common letter pairs (bigrams) and doubled letters that give you extra leverage:
- Most common bigrams: TH, HE, IN, ER, AN, RE, ND, ON, EN, AT. If you've found T and you see "T?" appearing often, the next letter is likely H.
- Most common doubled letters: LL, EE, SS, OO, TT, FF, RR, MM. A doubled cipher letter is almost never something rare like ZZ, so test the common doubles first.
- Most common starting letter of words is T (thanks to "the"), and the most common ending letters are E, S, D, and T.
Layering these on top of single-letter frequency turns a guess into a near-certainty.
A quick demonstration
Imagine the most common letter in a cryptogram is "K," appearing 14 times, and the next is "P" at 10. Frequency analysis says try K = E and P = T. Now you scan for a common three-letter word: if "PXK" appears several times, that's T·E, almost certainly THE, which confirms P = T and K = E and hands you X = H for free. From there the cascade begins. That's frequency analysis and pattern-spotting working together, which is how every cryptogram falls.
When frequency misleads you
Frequency is a starting point, not a guarantee. Short quotes, unusual vocabulary, or a quote that happens to overuse a normally-rare letter can throw the counts off. Our hardest Alan Turing cryptograms deliberately use archaic, quotable passages where raw frequency can mislead, so you have to combine it with structure. The rule: let frequency suggest a mapping, then let the words confirm it.
Put it to work
Frequency analysis is the technique that makes cryptograms feel less like luck and more like detective work. The best way to internalize it is to count letters on a real puzzle and watch the top of your list turn out to be E and T. Try it on a medium cryptogram with the frequency panel open, and read the full solving guide to see frequency working alongside every other technique.