Enter the number of times each letter appears and the total number of letters into the calculator to determine the Index of Coincidence.

## Index of Coincidence Formula

The following formula is used to calculate the Index of Coincidence (IC).

IC = Σ(ni * (ni - 1)) / (N * (N - 1))

Variables:

- IC is the Index of Coincidence
- ni is the number of times each letter appears in the text
- N is the total number of letters in the text

To calculate the Index of Coincidence, for each letter in the text, multiply the number of times it appears by the number of times it appears minus one. Sum these values for all letters. Then, multiply the total number of letters in the text by the total number of letters minus one. Divide the first result by the second result to get the Index of Coincidence.

## What is an Index of Coincidence?

The Index of Coincidence (IC) is a statistical tool used in cryptanalysis to measure the likelihood of similar letters appearing in the same position when two texts are aligned. It is used to break classical ciphers by comparing the IC of the encrypted text to the IC of the language it is believed to be in. A higher IC indicates a higher likelihood of the texts being in the same language, while a lower IC suggests the texts are in different languages or that one is encrypted.

## How to Calculate Index Of Coincidence?

The following steps outline how to calculate the Index of Coincidence (IC).

- First, count the number of times each letter appears in the text and record it as ni.
- Next, calculate the value of (ni * (ni – 1)) for each letter.
- Sum up all the values obtained in the previous step and record it as Σ(ni * (ni – 1)).
- Next, determine the total number of letters in the text and record it as N.
- Calculate the value of (N * (N – 1)).
- Finally, divide Σ(ni * (ni – 1)) by (N * (N – 1)) to obtain the Index of Coincidence (IC).

**Example Problem:**

Use the following variables as an example problem to test your knowledge.

ni (number of times each letter appears in the text) = [3, 5, 2, 4, 6]

N (total number of letters in the text) = 20