# Frequency Analysis

Another helpful tip when it comes to cracking coded messages is to look at how often certain letters appear in the English language. This is called frequency analysis.

In the English language, we use some letters or combinations of letters more than others. For example, we use the letter E the most, followed by the letter A. Below is a table showing how often we use each letter of the alphabet in terms of percentages (the percent of the time, on average, certain letters are used). https://crypto.interactive-maths.com/uploads/1/1/3/4/11345755/1192197_orig.jpg

If we look at the chart, the letter E is used, on average, 12.7 percent of the time. A percentage is the same thing as saying something will occur x number of times out of 100– in this case, 12.7 times out of 100, or 12.7/100. This means that out of every 100 letters, about 12.7 will be the letter E.

However, let’s say the message has 500 letters. Using the knowledge in the chart, we can figure out roughly how many of the letters should be E using proportions.

We know that 12.7 out of 100 letters will be E, but we don’t know how many will be E out of 500 letters. Let’s call this value x. However, we do know that the same ratio will exist between 12.7 : 100 and x : 500. Therefore, we can write this:

If we cross multiply, we get that 100 times x equals 6350. 6350 divided by 100 equals 63.5. This means that out of 500 letters, we are most likely to use the letter E approximately 63.5 times.

However, while this is helpful, you can’t only rely on frequency analysis. You should also take into account the frequency of certain combinations of letters in the code. For example, words like “the” are very common, and can be substituted into sections of the code where it seems likely it would fit.

Also, if you can tell by the shape of the code that it is a letter or other distinguishable form of writing, there are certain words that are likely to appear, like “Dear.” Using this knowledge, you know four letters right off the bat that can help you crack the code.